From 075132a122f909e1093fcf5ab5ee3a7172cac084 Mon Sep 17 00:00:00 2001 From: Seasawher Date: Wed, 1 Nov 2023 12:02:28 +0000 Subject: [PATCH] deploy: b9f7c0608b835897f0d3b94102842cd6cedd2a75 --- 404.html | 2 +- aesop.html | 45 +- apply.html | 6 +- apply_assumption.html | 25 +- apply_question.html => apply_search.html | 57 +- assumption.html | 6 +- by.html | 2 +- by_cases.html | 2 +- by_contra.html | 2 +- calc.html | 2 +- cases.html | 2 +- choose.html | 2 +- congr.html | 2 +- constructor.html | 2 +- contradiction.html | 2 +- conv.html | 2 +- convert.html | 2 +- done.html | 2 +- exact.html | 6 +- exact_question.html => exact_search.html | 18 +- exists.html | 6 +- ext.html | 2 +- funext.html | 2 +- guard_hyp.html | 2 +- have.html | 2 +- highlight.js | 2394 +++++++++++----------- index.html | 2 +- induction.html | 2 +- intro.html | 2 +- left_right.html | 2 +- linarith.html | 2 +- nlinarith.html | 2 +- print.html | 154 +- push_neg.html | 2 +- refine.html | 2 +- rel.html | 2 +- replace.html | 4 +- rfl.html | 2 +- ring.html | 2 +- rw.html | 11 +- says.html | 4 +- searchindex.js | 2 +- searchindex.json | 2 +- show.html | 2 +- simp.html | 2 +- sorry.html | 2 +- split.html | 2 +- suffices.html | 2 +- tauto.html | 2 +- trivial.html | 2 +- wlog.html | 2 +- 51 files changed, 1446 insertions(+), 1366 deletions(-) rename apply_question.html => apply_search.html (66%) rename exact_question.html => exact_search.html (70%) diff --git a/404.html b/404.html index ffbb103b..9d59737c 100644 --- a/404.html +++ b/404.html @@ -89,7 +89,7 @@ diff --git a/aesop.html b/aesop.html index 2d11e650..ad5a080d 100644 --- a/aesop.html +++ b/aesop.html @@ -88,7 +88,7 @@ @@ -175,21 +175,42 @@

Lean4 タクティク逆引きリスト

aesop

-

needs: import Aesop

-

aesop は，intro や simp を使用してルーチンな証明を自動で行おうとします．

-
-- 合成 `g ∘ f` が単射なら，`f` も単射
+
aesop は，intro や simp を使用してルーチンな証明を自動で行う，強力なタクティクです． aesop? を使うことにより，中身を見ることも可能です．

+
import Aesop -- `aesop` を使用するため
+import Mathlib.Init.Function -- `Injective` を使用するため
+import Mathlib.Tactic.Says -- `says` を使用するため
+
+-- CI 環境で `says` のチェックをしない
+set_option says.no_verify_in_CI true
+
+-- 以下 `X` `Y` `Z`を集合とする
+variable {X Y Z : Type}
+
+open Function
+
+/-! ## aesop -/
+
+-- 合成 `g ∘ f` が単射なら，`f` も単射
 example {f : X → Y} {g : Y → Z} (hgfinj : Injective (g ∘ f)) : Injective f := by
   rw [Injective]
+  show ∀ ⦃a₁ a₂ : X⦄, f a₁ = f a₂ → a₁ = a₂
+
+  -- 示すべきことがまだまだあるように見えるが，一発で証明が終わる
   aesop
-

-
aesop?

-
aesop が成功したとき，aesop? に置き換えると，ゴールを達成するのにどんなタクティクを使用したか教えてくれます．

-
example {f : X → Y} {g : Y → Z} (hgfinj : Injective (g ∘ f)) : Injective f := by
+
+/-!
+  ## aesop?
+  aesop が成功するとき，aesop? に置き換えると，
+  ゴールを達成するのにどんなタクティクを使用したか教えてくれる．
+-/
+
+example {f : X → Y} {g : Y → Z} (hgfinj : Injective (g ∘ f)) : Injective f := by
   rw [Injective]
-  -- `aesop?` は以下を返す
-  intro a₁ a₂ a
-  apply hgfinj
-  simp_all only [comp_apply]
+  -- `aesop?` は `says` 以下に続く一連のタクティクを示す
+  aesop? says
+    intro a₁ a₂ a
+    apply hgfinj
+    simp_all only [comp_apply]
diff --git a/apply.html b/apply.html index e834f685..523e8415 100644 --- a/apply.html +++ b/apply.html @@ -88,7 +88,7 @@ @@ -220,7 +220,7 @@

- @@ -234,7 +234,7 @@

- diff --git a/apply_assumption.html b/apply_assumption.html index 652f734e..8e110ccf 100644 --- a/apply_assumption.html +++ b/apply_assumption.html @@ -88,7 +88,7 @@ @@ -177,7 +177,13 @@

Lean4 タクティク逆引きリスト

apply_assumption

needs: import Mathlib.Tactic.SolveByElim

apply_assumption は，ゴールが ⊢ head であるときに，... → ∀ _, ... → head という形の命題をローカルコンテキストから探し，それを用いてゴールを書き換えます．

-
example (hPQ : P → Q) : ¬ Q → ¬ P := by
+
import Mathlib.Tactic.SolveByElim
+
+variable (P Q R : Prop)
+
+/-! ## apply_assumption -/
+
+example (hPQ : P → Q) : ¬ Q → ¬ P := by
   intro hQn hP
 
   -- 矛盾を示したい
@@ -193,10 +199,19 @@ 
apply_assum
 
   -- 自動で `hP` を適用
   apply_assumption
+
+  -- 証明終わり
   done
-

-
タクティクを繰り返すことを指示するタクティク repeat と組み合わせると，「ローカルコンテキストにある仮定を適切に選んで apply, exact することを繰り返し，ゴールを閉じる」ことができます．

-
example (hPQ : P → Q) (hQR : Q → R) (hQ : P) : R := by
+
+/-!
+  ## repeat apply_assumption
+
+  タクティクを繰り返すことを指示するタクティク `repeat` と組み合わせると，
+  「ローカルコンテキストにある仮定を適切に選んで apply, exact することを繰り返し，
+  ゴールを閉じる」ことができます．
+-/
+
+example (hPQ : P → Q) (hQR : Q → R) (hQ : P) : R := by
   repeat apply_assumption
 

 
diff --git a/apply_question.html b/apply_search.html
similarity index 66%
rename from apply_question.html
rename to apply_search.html
index c5710711..6fa249b1 100644
--- a/apply_question.html
+++ b/apply_search.html
@@ -3,7 +3,7 @@
     
         
         
-        apply?: ライブラリ検索で後方推論 - Lean4 タクティク逆引きリスト
+        apply?: apply できるか検索 - Lean4 タクティク逆引きリスト
 
 
         
@@ -88,7 +88,7 @@
 
         
@@ -175,36 +175,37 @@ 
Lean4 タクティク逆引きリスト

                 

                     

                         
apply?

-
needs: import Mathlib.Tactic.LibrarySearch

-
apply? は，ゴールを閉じるのに必要な命題をライブラリから検索してきて，提案してくれるタクティクです．

-
-- 群準同型は積を保つ
+
apply? は，カレントゴールを apply や refine で変形することができないか，ライブラリから検索して提案してくれるタクティクです．

+
複数の候補が提案されたときは，どれを選ぶとゴールが何に変わるのか表示されるので，その中から好ましいものを選ぶと良いでしょう．

+
import Mathlib.Algebra.Group.Defs
+import Mathlib.Algebra.Hom.Group.Defs
+import Mathlib.Tactic.LibrarySearch -- apply? を使うのに必要
+
+/-- 群準同型は積を保つ -/
 example [Group G] [Group H] (f : G →* H) (a b : G) :
     f (a * b) = f a * f b := by
-    -- `exact MonoidHom.map_mul f a b` を提案してくれる
-    apply?
-

-
複数の候補が提案されたときは，どれを選ぶとゴールが何に変わるのか表示されるので，その中から好ましいものを選ぶと良いでしょう．

-
補足

-
apply? はあくまで証明を書くときに補助として使うものです．sorry と同じように，清書した証明に残してはいけません．

-
sorry と同じと言いましたが，実際 apply? は sorryAx 1 を裏で使用します．これは，#explode で証明の中身を出力させれば分かります．sorry を使っているという旨の警告も出ます．

-
theorem T (x y : Nat) (_: x ≤ y) : 2 ^ x ≤ 2 ^ y := by
-    apply?
-
-    -- `apply?` しただけで `done` が通り，示せているように見える
-    done
-
-/-
-T : ∀ (x y : ℕ), x ≤ y → 2 ^ x ≤ 2 ^ y
-
-0│       │ x       ├ ℕ
-1│       │ y       ├ ℕ
-2│       │ h       ├ x ≤ y
-3│       │ sorryAx │ 2 ^ x ≤ 2 ^ y
-4│0,1,2,3│ ∀I      │ ∀ (x y : ℕ), x ≤ y → 2 ^ x ≤ 2 ^ y
+  -- `exact MonoidHom.map_mul f a b` を提案してくれる
+  apply?
+
+/-!
+  ## 補足
+
+  `apply?` はあくまで証明を書くときに補助として使うものです．
+  `sorry` と同じように，清書した証明に残してはいけません．
+  `sorry` と同じと言いましたが，実際 `apply?` は `sorryAx` を裏で使用します．
 -/
-#explode T
+
+theorem T (x y : Nat) (_: x ≤ y) : 2 ^ x ≤ 2 ^ y := by
+  apply?
+
+  -- `apply?` しただけで `done` が通り，示せているように見える
+  done
+
+-- 以下に示すように，裏で `sorryAx` が使われている
+
+/-- info: 'T' depends on axioms: [sorryAx] -/
+#guard_msgs in #print axioms T
 

-
1 sorry が裏で使用している公理のこと

 
                     

 
diff --git a/assumption.html b/assumption.html
index c4530bf7..458fee0b 100644
--- a/assumption.html
+++ b/assumption.html
@@ -88,7 +88,7 @@
 
         
@@ -186,7 +186,7 @@ 
exact 
 
                     

 
             
diff --git a/exact_question.html b/exact_search.html
similarity index 70%
rename from exact_question.html
rename to exact_search.html
index da453c3f..85b3145f 100644
--- a/exact_question.html
+++ b/exact_search.html
@@ -3,7 +3,7 @@
     
         
         
-        exact?: ゴールをライブラリ検索 - Lean4 タクティク逆引きリスト
+        exact?: exact できるか検索 - Lean4 タクティク逆引きリスト
 
 
         
@@ -88,7 +88,7 @@
 
         
@@ -175,15 +175,17 @@ 
Lean4 タクティク逆引きリスト

                 

                     

                         
exact?

-
needs: import Mathlib.Tactic.LibrarySearch

-
exact? は，ライブラリとローカルコンテキストにある命題を使って，ゴールを閉じることができないか探索します．

-
-- `exact?` はライブラリ検索を行う
+
exact? は，カレントゴールを exact で閉じることができないか，ライブラリから検索して提案してくれるタクティクです．閉じることができなければ，エラーになります．

+
import Mathlib.Tactic.LibrarySearch -- `exact?` を使うのに必要
+
+variable (P Q : Prop)
+
+-- `exact?` はライブラリ検索を行う
 example : x < x + 1 := by
   -- `Try this: exact Nat.lt.base x` と出力される
   exact?
-

-
apply? と似ていますが，apply? とは異なりゴールを変形するのではなくて exact で直接閉じようとします．

-
-- ローカルコンテキストにある仮定を自動で使ってゴールを導いてくれる
+
+-- ローカルコンテキストにある仮定を自動で使ってゴールを導いてくれる
 example (hPQ : P → Q) (hQR : Q → R) (hQ : P) : R := by
   -- `Try this: exact hQR (hPQ hQ)` と出力される
   exact?
diff --git a/exists.html b/exists.html
index 99f683fd..378b7bce 100644
--- a/exists.html
+++ b/exists.html
@@ -88,7 +88,7 @@
 
         
@@ -185,7 +185,7 @@ 
exists

 
                     

 
             
diff --git a/induction.html b/induction.html
index ce0bced2..1331c666 100644
--- a/induction.html
+++ b/induction.html
@@ -88,7 +88,7 @@
 
         
diff --git a/intro.html b/intro.html
index 7d8a84b3..9e9ce4bc 100644
--- a/intro.html
+++ b/intro.html
@@ -88,7 +88,7 @@
 
         
diff --git a/left_right.html b/left_right.html
index b3876af8..4958651b 100644
--- a/left_right.html
+++ b/left_right.html
@@ -88,7 +88,7 @@
 
         
diff --git a/linarith.html b/linarith.html
index 73807c99..3ed83170 100644
--- a/linarith.html
+++ b/linarith.html
@@ -88,7 +88,7 @@
 
         
diff --git a/nlinarith.html b/nlinarith.html
index 7ca29c12..1f4bb945 100644
--- a/nlinarith.html
+++ b/nlinarith.html
@@ -88,7 +88,7 @@
 
         
diff --git a/print.html b/print.html
index 159a2bc6..3a82446a 100644
--- a/print.html
+++ b/print.html
@@ -89,7 +89,7 @@
 
         
@@ -197,26 +197,53 @@ 
リンク集
 
 
aesop

-
needs: import Aesop

-
aesop は，intro や simp を使用してルーチンな証明を自動で行おうとします．

-
-- 合成 `g ∘ f` が単射なら，`f` も単射
+
aesop は，intro や simp を使用してルーチンな証明を自動で行う，強力なタクティクです． aesop? を使うことにより，中身を見ることも可能です．

+
import Aesop -- `aesop` を使用するため
+import Mathlib.Init.Function -- `Injective` を使用するため
+import Mathlib.Tactic.Says -- `says` を使用するため
+
+-- CI 環境で `says` のチェックをしない
+set_option says.no_verify_in_CI true
+
+-- 以下 `X` `Y` `Z`を集合とする
+variable {X Y Z : Type}
+
+open Function
+
+/-! ## aesop -/
+
+-- 合成 `g ∘ f` が単射なら，`f` も単射
 example {f : X → Y} {g : Y → Z} (hgfinj : Injective (g ∘ f)) : Injective f := by
   rw [Injective]
+  show ∀ ⦃a₁ a₂ : X⦄, f a₁ = f a₂ → a₁ = a₂
+
+  -- 示すべきことがまだまだあるように見えるが，一発で証明が終わる
   aesop
-

-
aesop?

-
aesop が成功したとき，aesop? に置き換えると，ゴールを達成するのにどんなタクティクを使用したか教えてくれます．

-
example {f : X → Y} {g : Y → Z} (hgfinj : Injective (g ∘ f)) : Injective f := by
+
+/-!
+  ## aesop?
+  aesop が成功するとき，aesop? に置き換えると，
+  ゴールを達成するのにどんなタクティクを使用したか教えてくれる．
+-/
+
+example {f : X → Y} {g : Y → Z} (hgfinj : Injective (g ∘ f)) : Injective f := by
   rw [Injective]
-  -- `aesop?` は以下を返す
-  intro a₁ a₂ a
-  apply hgfinj
-  simp_all only [comp_apply]
+  -- `aesop?` は `says` 以下に続く一連のタクティクを示す
+  aesop? says
+    intro a₁ a₂ a
+    apply hgfinj
+    simp_all only [comp_apply]
 

 
apply_assumption

 
needs: import Mathlib.Tactic.SolveByElim

 
apply_assumption は，ゴールが ⊢ head であるときに，... → ∀ _, ... → head という形の命題をローカルコンテキストから探し，それを用いてゴールを書き換えます．

-
example (hPQ : P → Q) : ¬ Q → ¬ P := by
+
import Mathlib.Tactic.SolveByElim
+
+variable (P Q R : Prop)
+
+/-! ## apply_assumption -/
+
+example (hPQ : P → Q) : ¬ Q → ¬ P := by
   intro hQn hP
 
   -- 矛盾を示したい
@@ -232,10 +259,19 @@ 
aesop?

 
   -- 自動で `hP` を適用
   apply_assumption
+
+  -- 証明終わり
   done
-

-
タクティクを繰り返すことを指示するタクティク repeat と組み合わせると，「ローカルコンテキストにある仮定を適切に選んで apply, exact することを繰り返し，ゴールを閉じる」ことができます．

-
example (hPQ : P → Q) (hQR : Q → R) (hQ : P) : R := by
+
+/-!
+  ## repeat apply_assumption
+
+  タクティクを繰り返すことを指示するタクティク `repeat` と組み合わせると，
+  「ローカルコンテキストにある仮定を適切に選んで apply, exact することを繰り返し，
+  ゴールを閉じる」ことができます．
+-/
+
+example (hPQ : P → Q) (hQR : Q → R) (hQ : P) : R := by
   repeat apply_assumption
 

 
apply

@@ -276,36 +312,37 @@ 
exact 
 
apply_assumption との関連

 
apply は常にどの命題を使うか明示する必要がありますが，「ゴールに apply が適用できるような命題をローカルコンテキストから自動で探す」 apply_assumption というタクティクもあります．

 
apply?

-
needs: import Mathlib.Tactic.LibrarySearch

-
apply? は，ゴールを閉じるのに必要な命題をライブラリから検索してきて，提案してくれるタクティクです．

-
-- 群準同型は積を保つ
+
apply? は，カレントゴールを apply や refine で変形することができないか，ライブラリから検索して提案してくれるタクティクです．

+
複数の候補が提案されたときは，どれを選ぶとゴールが何に変わるのか表示されるので，その中から好ましいものを選ぶと良いでしょう．

+
import Mathlib.Algebra.Group.Defs
+import Mathlib.Algebra.Hom.Group.Defs
+import Mathlib.Tactic.LibrarySearch -- apply? を使うのに必要
+
+/-- 群準同型は積を保つ -/
 example [Group G] [Group H] (f : G →* H) (a b : G) :
     f (a * b) = f a * f b := by
-    -- `exact MonoidHom.map_mul f a b` を提案してくれる
-    apply?
-

-
複数の候補が提案されたときは，どれを選ぶとゴールが何に変わるのか表示されるので，その中から好ましいものを選ぶと良いでしょう．

-
補足

-
apply? はあくまで証明を書くときに補助として使うものです．sorry と同じように，清書した証明に残してはいけません．

-
sorry と同じと言いましたが，実際 apply? は sorryAx 1 を裏で使用します．これは，#explode で証明の中身を出力させれば分かります．sorry を使っているという旨の警告も出ます．

-
theorem T (x y : Nat) (_: x ≤ y) : 2 ^ x ≤ 2 ^ y := by
-    apply?
-
-    -- `apply?` しただけで `done` が通り，示せているように見える
-    done
-
-/-
-T : ∀ (x y : ℕ), x ≤ y → 2 ^ x ≤ 2 ^ y
-
-0│       │ x       ├ ℕ
-1│       │ y       ├ ℕ
-2│       │ h       ├ x ≤ y
-3│       │ sorryAx │ 2 ^ x ≤ 2 ^ y
-4│0,1,2,3│ ∀I      │ ∀ (x y : ℕ), x ≤ y → 2 ^ x ≤ 2 ^ y
+  -- `exact MonoidHom.map_mul f a b` を提案してくれる
+  apply?
+
+/-!
+  ## 補足
+
+  `apply?` はあくまで証明を書くときに補助として使うものです．
+  `sorry` と同じように，清書した証明に残してはいけません．
+  `sorry` と同じと言いましたが，実際 `apply?` は `sorryAx` を裏で使用します．
 -/
-#explode T
+
+theorem T (x y : Nat) (_: x ≤ y) : 2 ^ x ≤ 2 ^ y := by
+  apply?
+
+  -- `apply?` しただけで `done` が通り，示せているように見える
+  done
+
+-- 以下に示すように，裏で `sorryAx` が使われている
+
+/-- info: 'T' depends on axioms: [sorryAx] -/
+#guard_msgs in #print axioms T
 

-
1 sorry が裏で使用している公理のこと

 
assumption

 
assumption は，現在のゴール ⊢ P がローカルコンテキストにあるとき，ゴールを閉じます．

 
example (hP: P) (_: Q) : P := by
@@ -453,7 +490,7 @@ 
rcases

 
   exact ⟨g, hg⟩
 

-
補足

+
補足

 
choose が自動で示してくれることは選択原理 Classical.choice を使って手動で示すことができます．たとえば次のようになります．

 
variable (P : X → Y → Prop)
 
@@ -565,15 +602,17 @@ 
同値を示
 
assumption との関連

 
exact は常にどの命題を使うか明示する必要がありますが，「ゴールを exact で閉じることができるような命題をローカルコンテキストから自動で探す」 assumption というタクティクもあります．

 
exact?

-
needs: import Mathlib.Tactic.LibrarySearch

-
exact? は，ライブラリとローカルコンテキストにある命題を使って，ゴールを閉じることができないか探索します．

-
-- `exact?` はライブラリ検索を行う
+
exact? は，カレントゴールを exact で閉じることができないか，ライブラリから検索して提案してくれるタクティクです．閉じることができなければ，エラーになります．

+
import Mathlib.Tactic.LibrarySearch -- `exact?` を使うのに必要
+
+variable (P Q : Prop)
+
+-- `exact?` はライブラリ検索を行う
 example : x < x + 1 := by
   -- `Try this: exact Nat.lt.base x` と出力される
   exact?
-

-
apply? と似ていますが，apply? とは異なりゴールを変形するのではなくて exact で直接閉じようとします．

-
-- ローカルコンテキストにある仮定を自動で使ってゴールを導いてくれる
+
+-- ローカルコンテキストにある仮定を自動で使ってゴールを導いてくれる
 example (hPQ : P → Q) (hQR : Q → R) (hQ : P) : R := by
   -- `Try this: exact hQR (hPQ hQ)` と出力される
   exact?
@@ -845,7 +884,7 @@ 

-
補足

+
補足

 
もう少し詳細に書くと，linarith は「ロールコンテキストにある線形な(不)等式系に矛盾があるか調べる」タクティクなので，次のような使い方もできます．

 
example (h1: x = 2 * y) (h2 : - x + 2 * y = 1) : False := by
   linarith
@@ -983,7 +1022,7 @@

rfl

@@ -1001,7 +1040,7 @@

-- `import Mathlib.Data.Nat.Basic` が必要 example (n : Nat) : n ≤ n := by rfl -

補足

+

補足

実は Mathlib.Tactic.Relation.Rfl を import するかどうかにより，内部で呼び出されるタクティクが変わります．

  • Mathlib.Tactic.Relation.Rfl ありなら Lean.MVarId.rfl が，
    • @@ -1038,7 +1077,8 @@

    補足

    順番は重要で，b を a に置き換えたいときなどは rw [← hab] のように ← をつけます．

    h1, h2, ... について続けて置き換えを行いたいときは，rw [h1, h2, ...] のようにします．

    ゴールではなく，ローカルコンテキストにある h: P を書き換えたいときには at をつけて rw [hPQ] at h とします．すべての箇所で置き換えたいときは rw [hPQ] at * とします．

    -
    example (a b c d e f : Nat) (h : a * b = c * d) (h' : e = f) : a * (b * e) = c * (d * f) := by
+
    example (a b c d e f : Nat) (h : a * b = c * d) (h' : e = f) :
+    a * (b * e) = c * (d * f) := by
   rw [h']
 
   -- 結合法則を使う
@@ -1048,23 +1088,23 @@ 
    補足
    
   -- 結合法則を使う
   rw [Nat.mul_assoc]
 
    
-
    nth_rewrite
    
+
    nth_rw
    
 
    needs: import Mathlib.Tactic.NthRewrite
    
-
    rw はマッチした項をすべて置き換えてしまいます．特定の項だけを書き換えたいとき，nth_rewrite が使用できます．対象の式中に現れる順番を1始まりで指定することで，項を指定します．指定された順番が式中の対象の項の数よりも多い場合はエラーになります．
    
+
    rw はマッチした項をすべて置き換えてしまいます．特定の項だけを書き換えたいとき，nth_rw が使用できます．対象の式中に現れる順番を1始まりで指定することで，項を指定します．指定された順番が式中の対象の項の数よりも多い場合はエラーになります．
    
 
    -- `G` は群
 variable [Group G]
 
 example (a b : G) : a * b⁻¹ = 1 ↔ a = b := by
   -- `one_mul: 1 * b = b` を使って `b` を `1 * b` に書き換える
   -- `b` は2回出現するが，2番目だけ置き換える
-  nth_rewrite 2 [← one_mul b]
+  nth_rw 2 [← one_mul b]
 
   -- `mul_inv_eq_iff_eq_mul: a * b⁻¹ = c ↔ a = c * b` を使う
   exact mul_inv_eq_iff_eq_mul
 
    
 
    says
    
 
    needs: import Mathlib.Tactic.Says
    
-
    exact? や apply? は証明を書いている過程で使用することを想定したタクティクです．Try this:  という提案をクリックして採用したら，exact? や apply? は提案内容で上書きされて，最終的な証明には残りません．
    
+
    exact? や apply? は証明を書いている過程で使用することを想定したタクティクです．Try this:  という提案をクリックして採用したら，exact? や apply? は提案内容で上書きされて，最終的な証明には残りません．
    
 
    では，証明のある部分が apply? などにより提案された内容であることを明示したい場合はどうしたら良いでしょうか？says タクティクはまさにその問題を解決するタクティクです．
    
 
    example (hPQ : P → Q) (hQR : Q → R) (hRS : R → S) (hP : P) : S := by
   -- `exact?` は実行されない
diff --git a/push_neg.html b/push_neg.html
index 8f24f43e..9066d2b4 100644
--- a/push_neg.html
+++ b/push_neg.html
@@ -88,7 +88,7 @@
 
         
diff --git a/refine.html b/refine.html
index 941be62e..a183ecdf 100644
--- a/refine.html
+++ b/refine.html
@@ -88,7 +88,7 @@
 
         
diff --git a/rel.html b/rel.html
index 0695f756..0249cdd0 100644
--- a/rel.html
+++ b/rel.html
@@ -88,7 +88,7 @@
 
         
diff --git a/replace.html b/replace.html
index 3aa088df..b5c94126 100644
--- a/replace.html
+++ b/replace.html
@@ -88,7 +88,7 @@
 
         
@@ -204,7 +204,7 @@ 
    replace
    
       _ = 2 * (k - 2 * n) := by ring
 
   exists k - 2 * n
-  nth_rewrite 1 [this]
+  nth_rw 1 [this]
   ring
 
    
 
diff --git a/rfl.html b/rfl.html
index 9db292c9..91611fc7 100644
--- a/rfl.html
+++ b/rfl.html
@@ -88,7 +88,7 @@
 
         
diff --git a/ring.html b/ring.html
index a9aba490..60b15c01 100644
--- a/ring.html
+++ b/ring.html
@@ -88,7 +88,7 @@
 
         
diff --git a/rw.html b/rw.html
index 4a025d34..04df8bfd 100644
--- a/rw.html
+++ b/rw.html
@@ -88,7 +88,7 @@
 
         
@@ -184,7 +184,8 @@ 
    rw
    
 
    順番は重要で，b を a に置き換えたいときなどは rw [← hab] のように ← をつけます．
    
 
    h1, h2, ... について続けて置き換えを行いたいときは，rw [h1, h2, ...] のようにします．
    
 
    ゴールではなく，ローカルコンテキストにある h: P を書き換えたいときには at をつけて rw [hPQ] at h とします．すべての箇所で置き換えたいときは rw [hPQ] at * とします．
    
-
    example (a b c d e f : Nat) (h : a * b = c * d) (h' : e = f) : a * (b * e) = c * (d * f) := by
+
    example (a b c d e f : Nat) (h : a * b = c * d) (h' : e = f) :
+    a * (b * e) = c * (d * f) := by
   rw [h']
 
   -- 結合法則を使う
@@ -194,16 +195,16 @@ 
    rw
    
   -- 結合法則を使う
   rw [Nat.mul_assoc]
 
    
-
    nth_rewrite
    
+
    nth_rw
    
 
    needs: import Mathlib.Tactic.NthRewrite
    
-
    rw はマッチした項をすべて置き換えてしまいます．特定の項だけを書き換えたいとき，nth_rewrite が使用できます．対象の式中に現れる順番を1始まりで指定することで，項を指定します．指定された順番が式中の対象の項の数よりも多い場合はエラーになります．
    
+
    rw はマッチした項をすべて置き換えてしまいます．特定の項だけを書き換えたいとき，nth_rw が使用できます．対象の式中に現れる順番を1始まりで指定することで，項を指定します．指定された順番が式中の対象の項の数よりも多い場合はエラーになります．
    
 
    -- `G` は群
 variable [Group G]
 
 example (a b : G) : a * b⁻¹ = 1 ↔ a = b := by
   -- `one_mul: 1 * b = b` を使って `b` を `1 * b` に書き換える
   -- `b` は2回出現するが，2番目だけ置き換える
-  nth_rewrite 2 [← one_mul b]
+  nth_rw 2 [← one_mul b]
 
   -- `mul_inv_eq_iff_eq_mul: a * b⁻¹ = c ↔ a = c * b` を使う
   exact mul_inv_eq_iff_eq_mul
diff --git a/says.html b/says.html
index 52302a4e..91a70bf5 100644
--- a/says.html
+++ b/says.html
@@ -88,7 +88,7 @@
 
         
@@ -176,7 +176,7 @@ 
    Lean4 タクティク逆引きリスト
    
                     
    
                         
    says
    
 
    needs: import Mathlib.Tactic.Says
    
-
    exact? や apply? は証明を書いている過程で使用することを想定したタクティクです．Try this:  という提案をクリックして採用したら，exact? や apply? は提案内容で上書きされて，最終的な証明には残りません．
    
+
    exact? や apply? は証明を書いている過程で使用することを想定したタクティクです．Try this:  という提案をクリックして採用したら，exact? や apply? は提案内容で上書きされて，最終的な証明には残りません．
    
 
    では，証明のある部分が apply? などにより提案された内容であることを明示したい場合はどうしたら良いでしょうか？says タクティクはまさにその問題を解決するタクティクです．
    
 
    example (hPQ : P → Q) (hQR : Q → R) (hRS : R → S) (hP : P) : S := by
   -- `exact?` は実行されない
diff --git a/searchindex.js b/searchindex.js
index b130c8f1..138fda2a 100644
--- a/searchindex.js
+++ b/searchindex.js
@@ -1 +1 @@
-Object.assign(window.search, {"doc_urls":["index.html#lean4-タクティク逆引きリスト","index.html#オプションについて","index.html#リンク集","aesop.html#aesop","aesop.html#aesop-1","apply_assumption.html#apply_assumption","apply.html#apply","apply.html#否定--について","apply.html#よくあるエラー","apply.html#exact-との関連","apply.html#apply_assumption-との関連","apply_question.html#apply","apply_question.html#補足","assumption.html#assumption","assumption.html#exact-との関連","by_cases.html#by_cases","by_contra.html#by_contra","by.html#by","by.html#by-1","calc.html#calc","cases.html#cases","cases.html#case-を書かない","cases.html#cases-1","cases.html#rcases","choose.html#choose","choose.html#補足","congr.html#congr","constructor.html#constructor","constructor.html#同値を示す","contradiction.html#contradiction","conv.html#conv","convert.html#convert","done.html#done","exact.html#exact","exact.html#assumption-との関連","exact_question.html#exact","exists.html#exists","ext.html#ext","funext.html#funext","guard_hyp.html#guard_hyp","have.html#have","have.html#パターンマッチ","have.html#論理積-","have.html#存在-","induction.html#induction","induction.html#induction-1","induction.html#一般のについての帰納法","induction.html#強い帰納法","intro.html#intro","intro.html#否定--について","left_right.html#left-right","linarith.html#linarith","linarith.html#補足","nlinarith.html#nlinarith","push_neg.html#push_neg","refine.html#refine","refine.html#apply-との関連","refine.html#constructor-との関連","rel.html#rel","replace.html#replace","rfl.html#rfl","rfl.html#補足","ring.html#ring","rw.html#rw","rw.html#nth_rewrite","says.html#says","says.html#オプション","show.html#show","simp.html#simp","simp.html#simp-1","simp.html#simp_all","simp.html#dsimp","sorry.html#sorry","split.html#split","suffices.html#suffices","tauto.html#tauto","trivial.html#trivial","wlog.html#wlog"],"index":{"documentStore":{"docInfo":{"0":{"body":1,"breadcrumbs":2,"title":1},"1":{"body":6,"breadcrumbs":1,"title":0},"10":{"body":3,"breadcrumbs":2,"title":1},"11":{"body":24,"breadcrumbs":2,"title":1},"12":{"body":60,"breadcrumbs":1,"title":0},"13":{"body":9,"breadcrumbs":2,"title":1},"14":{"body":2,"breadcrumbs":2,"title":1},"15":{"body":30,"breadcrumbs":2,"title":1},"16":{"body":31,"breadcrumbs":2,"title":1},"17":{"body":37,"breadcrumbs":0,"title":0},"18":{"body":24,"breadcrumbs":0,"title":0},"19":{"body":4,"breadcrumbs":2,"title":1},"2":{"body":10,"breadcrumbs":1,"title":0},"20":{"body":49,"breadcrumbs":2,"title":1},"21":{"body":33,"breadcrumbs":2,"title":1},"22":{"body":26,"breadcrumbs":2,"title":1},"23":{"body":61,"breadcrumbs":2,"title":1},"24":{"body":64,"breadcrumbs":2,"title":1},"25":{"body":67,"breadcrumbs":1,"title":0},"26":{"body":75,"breadcrumbs":2,"title":1},"27":{"body":36,"breadcrumbs":2,"title":1},"28":{"body":27,"breadcrumbs":1,"title":0},"29":{"body":31,"breadcrumbs":2,"title":1},"3":{"body":25,"breadcrumbs":2,"title":1},"30":{"body":4,"breadcrumbs":2,"title":1},"31":{"body":37,"breadcrumbs":2,"title":1},"32":{"body":1,"breadcrumbs":2,"title":1},"33":{"body":25,"breadcrumbs":2,"title":1},"34":{"body":3,"breadcrumbs":2,"title":1},"35":{"body":35,"breadcrumbs":2,"title":1},"36":{"body":23,"breadcrumbs":2,"title":1},"37":{"body":48,"breadcrumbs":2,"title":1},"38":{"body":40,"breadcrumbs":2,"title":1},"39":{"body":13,"breadcrumbs":2,"title":1},"4":{"body":23,"breadcrumbs":2,"title":1},"40":{"body":39,"breadcrumbs":0,"title":0},"41":{"body":0,"breadcrumbs":0,"title":0},"42":{"body":17,"breadcrumbs":0,"title":0},"43":{"body":38,"breadcrumbs":0,"title":0},"44":{"body":67,"breadcrumbs":2,"title":1},"45":{"body":22,"breadcrumbs":2,"title":1},"46":{"body":51,"breadcrumbs":1,"title":0},"47":{"body":40,"breadcrumbs":1,"title":0},"48":{"body":101,"breadcrumbs":2,"title":1},"49":{"body":42,"breadcrumbs":1,"title":0},"5":{"body":44,"breadcrumbs":2,"title":1},"50":{"body":29,"breadcrumbs":4,"title":2},"51":{"body":43,"breadcrumbs":2,"title":1},"52":{"body":13,"breadcrumbs":1,"title":0},"53":{"body":21,"breadcrumbs":2,"title":1},"54":{"body":62,"breadcrumbs":2,"title":1},"55":{"body":17,"breadcrumbs":2,"title":1},"56":{"body":26,"breadcrumbs":2,"title":1},"57":{"body":62,"breadcrumbs":2,"title":1},"58":{"body":36,"breadcrumbs":2,"title":1},"59":{"body":81,"breadcrumbs":2,"title":1},"6":{"body":49,"breadcrumbs":2,"title":1},"60":{"body":34,"breadcrumbs":2,"title":1},"61":{"body":27,"breadcrumbs":1,"title":0},"62":{"body":33,"breadcrumbs":2,"title":1},"63":{"body":55,"breadcrumbs":2,"title":1},"64":{"body":34,"breadcrumbs":2,"title":1},"65":{"body":70,"breadcrumbs":0,"title":0},"66":{"body":13,"breadcrumbs":0,"title":0},"67":{"body":19,"breadcrumbs":2,"title":1},"68":{"body":142,"breadcrumbs":2,"title":1},"69":{"body":2,"breadcrumbs":2,"title":1},"7":{"body":21,"breadcrumbs":1,"title":0},"70":{"body":2,"breadcrumbs":2,"title":1},"71":{"body":2,"breadcrumbs":2,"title":1},"72":{"body":26,"breadcrumbs":2,"title":1},"73":{"body":115,"breadcrumbs":2,"title":1},"74":{"body":38,"breadcrumbs":2,"title":1},"75":{"body":39,"breadcrumbs":2,"title":1},"76":{"body":16,"breadcrumbs":2,"title":1},"77":{"body":42,"breadcrumbs":2,"title":1},"8":{"body":1,"breadcrumbs":1,"title":0},"9":{"body":17,"breadcrumbs":2,"title":1}},"docs":{"0":{"body":"「普段の数学を Lean でどうやって実現するんだろう」という疑問に答えるために，よく使うタクティクをユースケースから逆引きできるようにまとめたリストです． なお，タクティクの説明に付記している名前の由来についての説明は公式に説明があったものではなく，あくまで憶測であることをお断りしておきます．","breadcrumbs":"Lean4 タクティク逆引きリスト » Lean4 タクティク逆引きリスト","id":"0","title":"Lean4 タクティク逆引きリスト"},"1":{"body":"タクティクによっては，オプションを設定することで挙動を変更することができます．オプションの設定には，set_option を使用します．たとえば，set_option warningAsError true と書くと，warning(警告) がエラーとして扱われるようになります． 使用できるオプションの一覧は #help option または こちらのリスト で確認することができます．","breadcrumbs":"Lean4 タクティク逆引きリスト » オプションについて","id":"1","title":"オプションについて"},"10":{"body":"apply は常にどの命題を使うか明示する必要がありますが，「ゴールに apply が適用できるような命題をローカルコンテキストから自動で探す」 apply_assumption というタクティクもあります．","breadcrumbs":"apply: 含意→を使う » apply_assumption との関連","id":"10","title":"apply_assumption との関連"},"11":{"body":"needs: import Mathlib.Tactic.LibrarySearch apply? は，ゴールを閉じるのに必要な命題をライブラリから検索してきて，提案してくれるタクティクです． -- 群準同型は積を保つ\nexample [Group G] [Group H] (f : G →* H) (a b : G) : f (a * b) = f a * f b := by -- `exact MonoidHom.map_mul f a b` を提案してくれる apply? 複数の候補が提案されたときは，どれを選ぶとゴールが何に変わるのか表示されるので，その中から好ましいものを選ぶと良いでしょう．","breadcrumbs":"apply?: ライブラリ検索で後方推論 » apply?","id":"11","title":"apply?"},"12":{"body":"apply? はあくまで証明を書くときに補助として使うものです．sorry と同じように，清書した証明に残してはいけません． sorry と同じと言いましたが，実際 apply? は sorryAx [1] を裏で使用します．これは，#explode で証明の中身を出力させれば分かります．sorry を使っているという旨の警告も出ます． theorem T (x y : Nat) (_: x ≤ y) : 2 ^ x ≤ 2 ^ y := by apply? -- `apply?` しただけで `done` が通り，示せているように見える done /-\nT : ∀ (x y : ℕ), x ≤ y → 2 ^ x ≤ 2 ^ y 0│ │ x ├ ℕ\n1│ │ y ├ ℕ\n2│ │ h ├ x ≤ y\n3│ │ sorryAx │ 2 ^ x ≤ 2 ^ y\n4│0,1,2,3│ ∀I │ ∀ (x y : ℕ), x ≤ y → 2 ^ x ≤ 2 ^ y\n-/\n#explode T [1] sorry が裏で使用している公理のこと","breadcrumbs":"apply?: ライブラリ検索で後方推論 » 補足","id":"12","title":"補足"},"13":{"body":"assumption は，現在のゴール ⊢ P がローカルコンテキストにあるとき，ゴールを閉じます． example (hP: P) (_: Q) : P := by assumption","breadcrumbs":"assumption: 仮定からゴールを閉じる » assumption","id":"13","title":"assumption"},"14":{"body":"assumption による証明は，どの仮定を使うか明示すれば exact で書き直すことができます．","breadcrumbs":"assumption: 仮定からゴールを閉じる » exact との関連","id":"14","title":"exact との関連"},"15":{"body":"by_cases は排中律を使って場合分けをするタクティクです． by_cases h: P とすると，P が成り立つときと成り立たないときのゴールがそれぞれ生成されます． example (P: Prop) : ¬¬P → P := by intro hnnP -- `P` が成り立つかどうかで場合分けする by_cases hP: P case inl => -- `P` が成り立つとき guard_hyp hP : P assumption case inr => -- `¬ P` が成り立つとき guard_hyp hP : ¬P contradiction","breadcrumbs":"by_cases: 排中律 » by_cases","id":"15","title":"by_cases"},"16":{"body":"needs: import Mathlib.Tactic.ByContra by_contra は，背理法を使いたいときに役立つタクティクです． ゴールが ⊢ P であるときに by_contra h を実行すると，h : ¬ P がローカルコンテキストに追加されて，同時にゴールが ⊢ False になります． example (h: ¬Q → ¬P) : P → Q := by -- `P` であると仮定する intro hP -- `¬Q` であると仮定して矛盾を導きたい by_contra hnQ show False -- `¬ Q → ¬ P` と `¬Q` から `¬P` が導かれる have := h hnQ -- これは仮定に矛盾 contradiction","breadcrumbs":"by_contra: 背理法 » by_contra","id":"16","title":"by_contra"},"17":{"body":"Lean においては，命題は型で，証明はその項です．命題 P の証明を構成するとは項 h : P を構成するということです．by は，証明の構成をタクティクで行いたいときに使います． -- `P → R` というのは `P` の証明を与えられたときに `R` の証明を返す関数の型\n-- したがって，その証明は関数となる\nexample (hPQ : P → Q) (hQR : Q → R) : P → R := fun hP ↦ hQR (hPQ hP) -- 同じ命題をタクティクで示した例\nexample (hPQ : P → Q) (hQR : Q → R) : P → R := by intro hP exact hQR (hPQ hP)","breadcrumbs":"by: タクティクモードに入る » by","id":"17","title":"by"},"18":{"body":"needs: import Std.Tactic.ShowTerm by? を使うとタクティクモードで構成した証明を直接構成した証明に変換してくれます． example (hPQ : P → Q) (hQR : Q → R) : P → R := by? -- `Try this: fun hP => hQR (hPQ hP)` と提案してくれる intro hP exact hQR (hPQ hP)","breadcrumbs":"by: タクティクモードに入る » by?","id":"18","title":"by?"},"19":{"body":"calc は計算モードに入るためのタクティクです．詳細については Theorem Proving in Lean4 をご参照ください．","breadcrumbs":"calc: 計算モードに入る » calc","id":"19","title":"calc"},"2":{"body":"Mathematics in type Theory 日本語訳 このリストでは「命題は型，証明はその項」という型理論を基礎として数学を実装する際の事実は既知としています．こういった話に全く馴染みがない方は，まずこちらの記事を読まれると良いと思います． mathlib4-all-tactics 全タクティクの網羅的なリスト． 数学系のためのLean勉強会 Lean で数学をどのように実装するのか，実際に実装する過程を追うことで学べる教材です．いくつかコード例を拝借させていただきました． Lean phrasebook 英語ですが，数学でのよくある推論ステップが，Lean にどのように翻訳されるかがよくまとめられたリストです．","breadcrumbs":"Lean4 タクティク逆引きリスト » リンク集","id":"2","title":"リンク集"},"20":{"body":"cases は場合分けを行います．ローカルコンテキストに h: P ∨ Q があるときに cases h とすると，仮定に P を付け加えたゴール inl と，仮定に Q を付け加えたゴール inr を生成します．それぞれ，insert left と insert right の略ではないかと思います． example : P ∨ Q → (P → R) → (Q → R) → R := by -- `h: P ∨ Q` intro h hPR hQR -- `case inl` と `case inr` の２つのゴールを生成する cases h -- `P` が成り立つ場合 case inl hP => exact hPR hP -- `Q` が成り立つ場合 case inr hQ => exact hQR hQ","breadcrumbs":"cases: 論理和∨を使う » cases","id":"20","title":"cases"},"21":{"body":"上記の例では case を場合分けの枝ごとに書いていますが，下の例のように case を書かずに済ませることもできます． example : P ∨ Q → (P → R) → (Q → R) → R := by -- `h: P ∨ Q` intro h hPR hQR -- `case inl` と `case inr` の２つのゴールを生成する cases h with | inl hP => exact hPR hP | inr hQ => exact hQR hQ","breadcrumbs":"cases: 論理和∨を使う » case を書かない","id":"21","title":"case を書かない"},"22":{"body":"needs: import Mathlib.Tactic.Cases cases' を使用すると分解した仮定に簡潔に名前をつけることができます． example : P ∨ Q → (P → R) → (Q → R) → R := by intro h hPR hQR -- 場合分けをする cases' h with hP hQ · apply hPR hP · apply hQR hQ","breadcrumbs":"cases: 論理和∨を使う » cases'","id":"22","title":"cases'"},"23":{"body":"needs: import Std.Tactic.RCases named after: 再帰的(recursive) cases rcases は cases をパターンに従って再帰的に適用します．論理和∨以外にも使うことができます． variable (P Q R : Prop) example : P ∨ Q → (P → R) → (Q → R) → R := by intro h hPR hQR -- 場合分けをする rcases h with hP | hQ · apply hPR hP · apply hQR hQ example : P ∧ Q → Q ∧ P := by -- `h: P ∧ Q` と仮定する intro h -- `h: P ∧ Q` を `hP: P` と `hQ: Q` に分解する rcases h with ⟨hP, hQ⟩ -- `Q ∧ P` を証明する exact ⟨hQ, hP⟩","breadcrumbs":"cases: 論理和∨を使う » rcases","id":"23","title":"rcases"},"24":{"body":"needs: import Mathlib.Tactic.Choose h : ∀ x, ∃ y, P(x, y) が成り立っているときに，choose f hf using h は写像 f: X → Y と f が満たす性質 hf : ∀ x, P(x, f x) のペアを作ります． example (f : X → Y) (hf : ∀ y, ∃ x, f x = y) : ∃ g : Y → X, ∀ y, f (g y) = y := by -- 写像 `g : Y → X` を構成する choose g hg using hf -- `g` が満たす条件がローカルコンテキストに追加される guard_hyp g: Y → X guard_hyp hg: ∀ (y : Y), f (g y) = y exact ⟨g, hg⟩","breadcrumbs":"choose: 選択関数を得る » choose","id":"24","title":"choose"},"25":{"body":"choose が自動で示してくれることは選択原理 Classical.choice を使って手動で示すことができます．たとえば次のようになります． variable (P : X → Y → Prop) noncomputable example (h : ∀ x, ∃ y, P x y) : ∃ f : X → Y, ∀ x, P x (f x) := by -- `f` を作る let f' : (x : X) → {y // P x y} := fun x ↦ have hne_st : Nonempty {y // P x y} := let ⟨y, py⟩ := h x; ⟨⟨y, py⟩⟩ Classical.choice hne_st let f : X → Y := fun x ↦ (f' x).val -- 上記で作った関数が条件を満たすことを示す have h₁ : ∀ x, P x (f x) := by intro x exact (f' x).property exists f","breadcrumbs":"choose: 選択関数を得る » 補足","id":"25","title":"補足"},"26":{"body":"named after: 合同(congruence) congr は，⊢ f as = f bs という形のゴールがあったときに，ゴールを ⊢ as = bs に変えます．再帰的に適用されるので，⊢ g (f as) = g (f bs) という形のゴールでも同じ結果になります． example (f : Int → X) (h : x = 0) : f (2 + x) = f 2 := by congr show 2 + x = 2 simp only [h, add_zero] congr が適用される再帰の深さを引数として渡すことができます．これは，主に単に congr とするだけだと「行き過ぎ」になるときに調整する目的で使用されます． example (f : Int → Int) (g : Int → X) (h : x = 0) (hf : ∀ x, f x = f (- x)) : g (f (2 + x)) = g (f (- 2)) := by -- 仮に `congr` とすると -- ゴールが `⊢ 2 + x = -2` になってしまう congr 1 show f (2 + x) = f (-2) simp only [h, add_zero] exact hf _","breadcrumbs":"congr: ゴールの差異に注目する » congr","id":"26","title":"congr"},"27":{"body":"ゴールが ⊢ P ∧ Q であるとき，constructor を実行すると，ゴールが２つのゴール ⊢ P と ⊢ Q に分割されます． example (hP: P) (hQ: Q) : P ∧ Q := by -- goal が `left` と `right` に分割される constructor · -- `P` を示す exact hP · -- `Q` を示す exact hQ なお h: P ∧ Q から P や Q の証明を得るのは，それぞれ h.left と h.right で可能です． example (h: P ∧ Q) : P := by exact h.left","breadcrumbs":"constructor: 論理積∧を示す » constructor","id":"27","title":"constructor"},"28":{"body":"constructor はゴールが ⊢ P ↔ Q であるときにも使用できます． example (x : Nat) : x = 0 ↔ x + 1 = 1 := by constructor · -- `x = 0 → x + 1 = 1` を示す intro hx rw [hx] · -- `x + 1 = 1 → x = 0` を示す simp_all","breadcrumbs":"constructor: 論理積∧を示す » 同値を示す","id":"28","title":"同値を示す"},"29":{"body":"矛盾からはどんな命題でも証明することができます．これを爆発律(principle of explosion)と呼びますが，contradiction は，この爆発律を使ってゴールを閉じるタクティクです． ローカルコンテキストに P と ¬ P が同時にあるなど，矛盾した状況にあるときにゴールを閉じます． -- `False`\nexample (h : False) : P := by contradiction -- 明らかに偽な等式\nexample (h : 2 + 2 = 3) : P := by contradiction -- 明らかに偽な等式\nexample (x : Nat) (h : x ≠ x) : P := by contradiction -- 矛盾する仮定\nexample (hP : P) (hnP : ¬ P) : Q := by contradiction","breadcrumbs":"contradiction: 爆発律 » contradiction","id":"29","title":"contradiction"},"3":{"body":"needs: import Aesop aesop は，intro や simp を使用してルーチンな証明を自動で行おうとします． -- 合成 `g ∘ f` が単射なら，`f` も単射\nexample {f : X → Y} {g : Y → Z} (hgfinj : Injective (g ∘ f)) : Injective f := by rw [Injective] aesop","breadcrumbs":"aesop: ルーチン自動化 » aesop","id":"3","title":"aesop"},"30":{"body":"conv は変換モードに入るためのタクティクです．詳細については Theorem Proving in Lean4 をご参照ください．","breadcrumbs":"conv: 変換モードに入る » conv","id":"30","title":"conv"},"31":{"body":"needs: import Mathlib.Tactic.Convert ローカルコンテキストに現在のゴールに近いけれども等しくはない h があるとき，exact h としても失敗します．しかし convert h は成功する可能性があり，成功した場合は h とゴールの差分を新たなゴールとします． example (f : Nat → Nat) (h : f (a + b) = 0) (hc: a + b = c) : f (c) = 0 := by -- `h` はゴールと等しくないので失敗する try exact [h] -- `h` とゴールの差分を新たなゴールにする convert h -- ゴールが `⊢ c = a + b` に変わっている show c = a + b rw [hc]","breadcrumbs":"convert: 惜しい補題を使う » convert","id":"31","title":"convert"},"32":{"body":"done は，証明終了の合図です．証明すべきゴールが残っていない時に成功し，それ以外の時にはエラーになります．QED のようなものです．","breadcrumbs":"done: 証明終了を宣言 » done","id":"32","title":"done"},"33":{"body":"ゴールが P で，ローカルコンテキストに hP: P があるときに，exact hP はゴールを閉じます． example (hP: P) : P := by exact hP hP がゴールの証明になっていないときには，失敗してエラーになります． exact ⟨ hP, hQ ⟩ のようにすると，論理積∧の形をした命題を証明することができます． example (hP: P) (hQ: Q) : P ∧ Q := by exact ⟨ hP, hQ ⟩","breadcrumbs":"exact: 証明を直接構成 » exact","id":"33","title":"exact"},"34":{"body":"exact は常にどの命題を使うか明示する必要がありますが，「ゴールを exact で閉じることができるような命題をローカルコンテキストから自動で探す」 assumption というタクティクもあります．","breadcrumbs":"exact: 証明を直接構成 » assumption との関連","id":"34","title":"assumption との関連"},"35":{"body":"needs: import Mathlib.Tactic.LibrarySearch exact? は，ライブラリとローカルコンテキストにある命題を使って，ゴールを閉じることができないか探索します． -- `exact?` はライブラリ検索を行う\nexample : x < x + 1 := by -- `Try this: exact Nat.lt.base x` と出力される exact? apply? と似ていますが，apply? とは異なりゴールを変形するのではなくて exact で直接閉じようとします． -- ローカルコンテキストにある仮定を自動で使ってゴールを導いてくれる\nexample (hPQ : P → Q) (hQR : Q → R) (hQ : P) : R := by -- `Try this: exact hQR (hPQ hQ)` と出力される exact? -- 証明は `exact?` だけで終わっている done","breadcrumbs":"exact?: ゴールをライブラリ検索 » exact?","id":"35","title":"exact?"},"36":{"body":"exists は，「～という x が存在する」という命題を示すために，「この x を使え」と指示するコマンドです． ゴールが ⊢ ∃ x, P x のとき，x: X がローカルコンテキストにあれば，exists x によりゴールが P x に変わります．同時に，P x が自明な場合は証明が終了します． example : ∃ x : Nat, 3 * x + 1 = 7 := by exists 2","breadcrumbs":"exists: 存在∃を示す » exists","id":"36","title":"exists"},"37":{"body":"needs: import Std.Tactic.Ext named after: 外延性(extensionality) ext は，外延性を使うタクティクです．外延性とは，「同じものから作られているものは同じである」という主張のことです．たとえば 集合 A, B ⊂ α について A = B は x ∈ A ↔ x ∈ B と同じ 2つの写像 f g : A → B があるとき f = g は ∀ a ∈ A, f a = g a と同じ といったことを指します． @[ext] で登録されたルールを使用するため，集合の等式 A = B を示すときは Mathlib.Data.SetLike.Basic も必要です． variable {α : Type} -- `s` と `t` は `α` の部分集合\nvariable (s t : Set α) example : s ∩ t = t ∩ s := by -- `x ∈ α` を取る．` x ∈ s ∩ t ↔ x ∈ t ∩ s` を証明すればよい ext x aesop なお A ⊂ B を示すために元を取るのは intro x で可能です．","breadcrumbs":"ext: 外延性を使う » ext","id":"37","title":"ext"},"38":{"body":"関数 f と g が等しいことを示す際に，引数 x をとって f x = g x を示そうとすることがありますが，funext はそれを行うタクティクです. def f := fun (x : Nat) ↦ x + x def g := fun (x : Nat) ↦ 2 * x example : f = g := by -- 引数 `x` を取る funext x -- `f x` と `g x` を展開する dsimp [f, g] -- `x + x` と `2 * x` が等しいことを証明する ring","breadcrumbs":"funext: 関数等式を示す » funext","id":"38","title":"funext"},"39":{"body":"needs: import Std.Tactic.GuardExpr guard_hyp は，ローカルコンテキストにある命題を確認するタクティクです．指定した仮定が存在すれば成功し，そうでなければ失敗します． example (hP : P) : P := by -- 現在ローカルコンテキストにある命題を確認できる guard_hyp hP : P exact hP 通常の証明で使うことはあまりないかもしれません．このタクティクリストでは，ローカルコンテキストの変化を説明するために使用することがあります．","breadcrumbs":"guard_hyp: 仮定や補題を確認 » guard_hyp","id":"39","title":"guard_hyp"},"4":{"body":"aesop が成功したとき，aesop? に置き換えると，ゴールを達成するのにどんなタクティクを使用したか教えてくれます． example {f : X → Y} {g : Y → Z} (hgfinj : Injective (g ∘ f)) : Injective f := by rw [Injective] -- `aesop?` は以下を返す intro a₁ a₂ a apply hgfinj simp_all only [comp_apply]","breadcrumbs":"aesop: ルーチン自動化 » aesop?","id":"4","title":"aesop?"},"40":{"body":"have は，証明の途中でわかることをローカルコンテキストに追加するコマンドです． have h: P := ... で P という命題の証明を構成し，その証明に h という名前を付けることができます． example (hPQ: P → Q) (hQR: Q → R) : P → R := by -- 示したいことが `P → R` なので，`P` だと仮定する intro hP -- 仮定 `hPQ : P → Q` と `hP : P` から `Q` が導かれる have hQ : Q := by exact hPQ hP -- 仮定 `hQR : Q → R` と `hQ : Q` から `R` が導かれる exact hQR hQ 名前を省略して have : P := ... とすると，自動的に this という名前になります．","breadcrumbs":"have: 補題を用意する » have","id":"40","title":"have"},"41":{"body":"補題を示すだけでなく，ある特定の形をした主張を分解するのにも have は使うことができます．","breadcrumbs":"have: 補題を用意する » パターンマッチ","id":"41","title":"パターンマッチ"},"42":{"body":"次のように，P ∧ Q という命題から P と Q を取り出すことができます． example (hPQ: P ∧ Q) : P := by -- `P ∧ Q` という仮定を分解する -- `hQ: Q` は不要なのでアンダースコアに置き換える have ⟨ hP, _ ⟩ := hPQ assumption","breadcrumbs":"have: 補題を用意する » 論理積 ∧","id":"42","title":"論理積 ∧"},"43":{"body":"次のように，∃ x: X, P x という命題から，条件を満たす x を取り出すことができます．x: X と hx: P x がローカルコンテキストに追加されます． -- `x`が偶数のとき`3 * x`も偶数\nexample (x : ℕ) (hx : ∃ y, x = 2 * y) : ∃ z, 3 * x = 2 * z := by -- `hx` で存在が主張されている `y` と， -- `x = 2 * y` という命題を得る have ⟨y, hy⟩ := hx exists 3 * y rw [hy] ring","breadcrumbs":"have: 補題を用意する » 存在 ∃","id":"43","title":"存在 ∃"},"44":{"body":"induction は，帰納法のためのタクティクです． 自然数を例に説明します．Lean では自然数は次のように帰納的に定義されています. inductive Nat | zero : Nat | succ (n : Nat) : Nat succ は後者関数と呼ばれる関数で，n + 1 := succ n です． n : Nat についてゴール P n ⊢ Q n があったとします．このとき induction n を行うと，コンストラクタ zero と succ のそれぞれに対して，対応するゴールを生成します．つまり P 0 ⊢ Q 0 (P (succ a)) (P a → Q a) ⊢ Q (succ a) の２つのゴールです． -- 階乗関数\ndef fac : Nat → Nat | 0 => 1 | n + 1 => (n + 1) * fac n example (n : Nat) : 0 < fac n := by -- `n` についての帰納法で示す induction n with | zero => -- `fac` の定義から従う simp [fac] | succ n ih => -- `fac` の定義から従う simp [fac] positivity","breadcrumbs":"induction: 帰納法 » induction","id":"44","title":"induction"},"45":{"body":"needs: import Mathlib.Tactic.Cases induction' というタクティクもあります．こちらは箇条書きによる，より簡潔な書き方が可能です． example (n : Nat) : 0 < fac n := by -- `ih` は帰納法の仮定 -- `k` は `ih` に登場する変数 induction' n with k ih · simp [fac] · simp [fac] positivity","breadcrumbs":"induction: 帰納法 » induction'","id":"45","title":"induction'"},"46":{"body":"また，induction' では「リストの長さに対する帰納法」のようなより複雑な帰納法を行うことができます． example (l : List α) (P : List α → Prop) : P l := by -- リストの長さに対する帰納法 induction' h : l.length generalizing l case zero => -- リストの長さが 0 のとき guard_hyp h: List.length l = 0 show P l sorry case succ n IH => -- リストの長さが `n + 1` のとき guard_hyp h: List.length l = n + 1 -- 帰納法の仮定が使える guard_hyp IH: ∀ (l : List α), List.length l = n → P l show P l sorry","breadcrumbs":"induction: 帰納法 » 一般の～についての帰納法","id":"46","title":"一般の～についての帰納法"},"47":{"body":"時には，より強い帰納法が必要なこともあります．強い帰納法とは，たとえば P(0) を示す (∀ k < n, P (k)) → P (n) を示す したがって ∀ n, P (n) である という形式で表されるような帰納法のことです．これは超限帰納法の特別な場合です．これを使用するには，Nat.strong_induction_on を使って次のようにします． variable (P : Nat → Prop) example (n : Nat) : P n := by -- `n` についての強い帰納法で示す induction' n using Nat.strong_induction_on with n ih -- 仮定が追加される guard_hyp ih : ∀ (m : ℕ), m < n → P m match n with | 0 => sorry | k + 1 => sorry","breadcrumbs":"induction: 帰納法 » 強い帰納法","id":"47","title":"強い帰納法"},"48":{"body":"named after: 導入(introduce) intro は数学で慣習的に行われる P → Q を示すときに最初に P を仮定する ∀ x ∈ A, P(x) を示すときに最初に x ∈ A が与えられたと仮定する といった導入を実行します． 具体的には，intro は ゴールが ⊢ P → Q という形であるときに P をローカルコンテキストに追加して，ゴールを ⊢ Q に変える ゴールが ⊢ ∀ x, P x という形であるときに x をローカルコンテキストに追加してゴールを ⊢ P x に変える といった挙動をします． example (hPQ: P → Q) (hQR: Q → R) : P → R := by -- 示したいことが `P → R` なので，`P` だと仮定する intro hP -- `R` を示したい show R -- 仮定 `hPQ : P → Q` と `hP : P` から `Q` が導かれる have hQ : Q := hPQ hP -- 仮定 `hQR : Q → R` と `hQ : Q` から `R` が導かれる exact hQR hQ もう一つ使用例を挙げておきます： example (P Q : Nat → Prop) (h : ∀ n, P n ↔ Q n) : ∀ y, P (y + 1) → Q (y + 1) := by -- 任意の `y` について示すので，`intro` で `y` を導入する -- そして `P (y + 1) → Q(y + 1)` を示したいので，`P (y + 1)` を仮定する intro y hyP -- `Q (y + 1)` を示せば良い show Q (y + 1) -- 同値を使ってゴールを書き換える rw [← h] -- 仮定 `P (y + 1)` より従う assumption","breadcrumbs":"intro: 含意→や全称∀を示す » intro","id":"48","title":"intro"},"49":{"body":"Lean では否定 ¬ P は P → False として定義されているので，ゴールが ¬ P のときに intro すると P が仮定に追加されて，ゴールが False に変わります． False は矛盾を導けば証明できます． example (h: P → Q) : ¬Q → ¬P := by -- 示したいことが `¬Q → ¬P` なので，`¬Q` だと仮定する -- そうするとゴールが `¬P` になるので， -- さらに `intro` を行って仮定 `hP : P` を導入する intro hnQ hP -- 矛盾を示したい show False -- `hP : P` と `h : P → Q` から `Q` が導かれる have hQ : Q := h hP -- `hQ : Q` と `hnQ : ¬Q` から矛盾が導かれる contradiction","breadcrumbs":"intro: 含意→や全称∀を示す » 否定 ¬ について","id":"49","title":"否定 ¬ について"},"5":{"body":"needs: import Mathlib.Tactic.SolveByElim apply_assumption は，ゴールが ⊢ head であるときに，... → ∀ _, ... → head という形の命題をローカルコンテキストから探し，それを用いてゴールを書き換えます． example (hPQ : P → Q) : ¬ Q → ¬ P := by intro hQn hP -- 矛盾を示したい show False -- 自動で `hQn` を適用 apply_assumption show Q -- 自動で `hPQ` を適用 apply_assumption show P -- 自動で `hP` を適用 apply_assumption done タクティクを繰り返すことを指示するタクティク repeat と組み合わせると，「ローカルコンテキストにある仮定を適切に選んで apply, exact することを繰り返し，ゴールを閉じる」ことができます． example (hPQ : P → Q) (hQR : Q → R) (hQ : P) : R := by repeat apply_assumption","breadcrumbs":"apply_assumption: 仮定から後方推論 » apply_assumption","id":"5","title":"apply_assumption"},"50":{"body":"needs: import Mathlib.Tactic.LeftRight ゴールが ⊢ P ∨ Q であるとき，left はゴールを ⊢ P に，right はゴールを ⊢ Q に変えます． example (hP: P) : P ∨ Q := by left assumption left, right を使わずに Mathlib4 なしで同じことをするには，Or.inl または Or.inr を使用します． example (hP: P) : P ∨ Q := by apply Or.inl assumption","breadcrumbs":"left, right: 論理和∨を示す » left, right","id":"50","title":"left, right"},"51":{"body":"needs: import Mathlib.Tactic.Linarith named after: 線形算術(linear arithmetic) linarith は線形な(不)等式を導くことができます． example (h1 : 2 * x < 3 * y) (h2 : -4 * x + 2 * z < 0): 12 * y - 4 * z ≥ 0 := by linarith linarith はローカルコンテキストを読み取ってくれるので，linarith が通らないとき補題を追加してあげると通るようになることがあります． example : id x ≤ x := by -- `linarith` で示すことはできない try linarith have : id x = x := rfl -- `id x = x` だと教えてあげると `linarith` で示せる linarith","breadcrumbs":"linarith: 線形(不)等式を示す » linarith","id":"51","title":"linarith"},"52":{"body":"もう少し詳細に書くと，linarith は「ロールコンテキストにある線形な(不)等式系に矛盾があるか調べる」タクティクなので，次のような使い方もできます． example (h1: x = 2 * y) (h2 : - x + 2 * y = 1) : False := by linarith","breadcrumbs":"linarith: 線形(不)等式を示す » 補足","id":"52","title":"補足"},"53":{"body":"needs: import Mathlib.Tactic.Linarith named after: non-linear(非線形) arithmetic(算術) nlinarith は非線形な式も扱えるように linarith にいくつか前処理を追加したものです． example (a b: Nat) (h : a ≤ b) : a ^ 2 ≤ b ^ 2 := by -- `linarith` では示すことができない try linarith nlinarith","breadcrumbs":"nlinarith: 非線形な(不)等式を示す » nlinarith","id":"53","title":"nlinarith"},"54":{"body":"needs: import Mathlib.Tactic.PushNeg named after: 押し込む(push) 否定(negation) push_neg はドモルガン則を使って，否定を式の中に押し込みます．たとえば ¬ (P ∧ Q) は P → ¬ Q に， ¬ ∀ x, P x は ∃ x, ¬ P x に という調子で変形します． [1] example (h: P → Q) : ¬ (P ∧ ¬ Q) := by -- ドモルガン則を適用して，`¬` を内側に押し込む push_neg -- `¬` を内側に押し込んだ結果，`¬ P ∨ Q` が得られる -- これは `P → Q` と同値 show P → Q exact h example : ¬ ∃ x : Int , ∀ y : Int, (x + y = 0) := by -- ドモルガン則を適用して，`¬` を内側に押し込む push_neg -- `¬` を内側に押し込んだ結果，ゴールが変わる show ∀ x, ∃ y, ¬ (x + y = 0) intro x exists (- x + 1) linarith [1] モードによって ¬ (P ∧ Q) を P → ¬ Q としたり，¬ P ∨ ¬ Q としたりします．","breadcrumbs":"push_neg: ドモルガン » push_neg","id":"54","title":"push_neg"},"55":{"body":"refine は exact と同様に機能しますが，プレースホルダを受け入れて新しいゴールを生成するという違いがあります． example (hP: P) (hQ: Q) : P ∧ Q := by -- 穴埋め形式で証明を作ることができる refine ⟨?_, hQ⟩ -- ゴールが `⊢ P` になる show P exact hP","breadcrumbs":"refine: 一般の後方推論 » refine","id":"55","title":"refine"},"56":{"body":"h : P → Q という命題があって，ゴールが ⊢ Q であるとき refine h ?_ は apply h と同様に機能するので，refine で apply を代用することができます． example (hPQ : P → Q) (hP : P) : Q := by refine hPQ ?_ -- ゴールが `⊢ P` になる show P refine hP","breadcrumbs":"refine: 一般の後方推論 » apply との関連","id":"56","title":"apply との関連"},"57":{"body":"refine は constructor の代わりに使うこともできます．実際 refine は constructor よりも柔軟で，⊢ P ∧ Q ∧ R のような形のゴールは constructor よりも簡潔に分割できます． example (hP: P) (hQ: Q) (hR : R) : P ∧ Q ∧ R := by -- ゴールを３つに分割する refine ⟨?_, ?_, ?_⟩ · show P exact hP · show Q exact hQ · show R exact hR -- `constructor` を使った場合\n-- 一度に２つのゴールに分割することしかできない\nexample (hP: P) (hQ: Q) (hR : R) : P ∧ Q ∧ R := by constructor · show P exact hP · show Q ∧ R constructor · show Q exact hQ · show R exact hR","breadcrumbs":"refine: 一般の後方推論 » constructor との関連","id":"57","title":"constructor との関連"},"58":{"body":"needs: import Mathlib.Tactic.GCongr named after: 関係(relation) rel は，不等式を代入して適用し，不等式を示します． example (h1 : a ≤ b) (h2 : c ≤ d) : a + c ≤ b + d := by rel [h1, h2] rel は，たとえば整数 x: Int に対して 0 ≤ x ^ 2 であることを自動的に適用するなど, 多少の推論を行います． example (x: Int) (h1 : a ≤ b) : x ^ 2 * a ≤ x ^ 2 * b := by rel [h1]","breadcrumbs":"rel: 不等式を使う » rel","id":"58","title":"rel"},"59":{"body":"needs: import Std.Tactic.Replace replace は have と同じく補題を入手するためのタクティクですが，have とは異なりローカルコンテキストにすでにある命題を置き換えることができます． have を使った場合，ローカルコンテキストにすでに h : P がある状態で，再び h という名前で別の命題を示すと，古い方の h はアクセス不能になって † が付いた状態になってしまいます． replace であれば，古い方が新しい方に置き換えられ，† の付いた命題は出現しません． example : ∀ (n : Int), Even (5 * n) → Even n := by intro n hn -- `Even (5 * n)` という仮定を分解 obtain ⟨ k, hk ⟩ := hn -- 以下がローカルコンテキストに追加される guard_hyp hk: 5 * n = k + k -- `k + k` という形が使いづらいので，`2 * k` に置き換える replace hk : 5 * n = 2 * k := by rw [hk] ring -- `hk` の内容が変化している guard_hyp hk: 5 * n = 2 * k -- 計算をする have := by calc n _ = 5 * n - 4 * n := by ring _ = 2 * k - 4 * n := by rw [hk] _ = 2 * (k - 2 * n) := by ring exists k - 2 * n nth_rewrite 1 [this] ring","breadcrumbs":"replace: 補題の入れ替え » replace","id":"59","title":"replace"},"6":{"body":"apply は含意 → をゴールに適用するタクティクです． ゴールが ⊢ Q で，ローカルコンテキストに h: P → Q があるときに，apply h を実行するとゴールが ⊢ P に書き換わります． -- `P → Q` かつ `P` ならば `Q`\nexample (h: P → Q) (hP: P) : Q := by apply h -- ゴールが `P` に変わっている show P exact hP 注意点として，h: P → Q は P の証明を受け取って Q の証明を返す関数でもあるので，上記の例は apply を使わずに exact h hP で閉じることもできます． -- `P → Q` かつ `P` ならば `Q`\nexample (h: P → Q) (hP: P) : Q := by exact h hP","breadcrumbs":"apply: 含意→を使う » apply","id":"6","title":"apply"},"60":{"body":"needs: import Mathlib.Tactic.Relation.Rfl named after: 反射律(reflexivity) rfl は，refl attribute の付けられた定理を用いて関係の反射性を示すタクティクです． inductive MyEq {α : Type u} : α → α → Prop | refl (a : α) : MyEq a a attribute [refl] MyEq.refl example (n : ℕ) : MyEq n n := by rfl @[refl] で登録された定理を用いるので，追加でライブラリを import することにより示すことができる命題が増えます． -- `import Mathlib.Data.Nat.Basic` が必要\nexample (n : Nat) : n ≤ n := by rfl","breadcrumbs":"rfl: 関係の反射性を示す » rfl","id":"60","title":"rfl"},"61":{"body":"実は Mathlib.Tactic.Relation.Rfl を import するかどうかにより，内部で呼び出されるタクティクが変わります． Mathlib.Tactic.Relation.Rfl ありなら Lean.MVarId.rfl が， なしなら Lean.MVarId.refl が それぞれ参照されます．後者は @[refl] が付けられた一般の関係の反射性にアクセスできず，等号 = の反射性しか使うことができません． 後者の場合 rfl は，単に定義から等しいものが等しいことを示すタクティクになります． variable (α : Type) example : 1 + 1 = 2 := by rfl example (x : α) : x = x := by rfl example : (2 ^ 70 + 3 ^ 70) % 13 = 0 := by rfl","breadcrumbs":"rfl: 関係の反射性を示す » 補足","id":"61","title":"補足"},"62":{"body":"needs: import Mathlib.Tactic.Ring ring は，可換環の等式を示します． example : (x + y) ^ 2 = x ^ 2 + 2 * x * y + y ^ 2 := by ring simp 等と異なり，ring? タクティクは用意されていませんが，show_term で具体的にどんなルールが適用されたのかを知ることができます．ただし，その出力結果は非常に長く読みづらいものであることがしばしばです．例えば， example : (x + y) ^ 2 = x ^ 2 + 2 * x * y + y ^ 2 := by show_term ring の出力をここに掲載すると100行を超えてしまいます．","breadcrumbs":"ring: 環の等式を示す » ring","id":"62","title":"ring"},"63":{"body":"rw は rewrite（書き換え）を行うタクティクです．等式や同値をもとに書き換えを行います． hab: a = b や hPQ : P ↔ Q がローカルコンテキストにあるとき， rw [hab] はゴールの中の a をすべて b に置き換え， rw [hPQ] はゴールの中の P をすべて Q に置き換えます． 順番は重要で，b を a に置き換えたいときなどは rw [← hab] のように ← をつけます． h1, h2, ... について続けて置き換えを行いたいときは，rw [h1, h2, ...] のようにします． ゴールではなく，ローカルコンテキストにある h: P を書き換えたいときには at をつけて rw [hPQ] at h とします．すべての箇所で置き換えたいときは rw [hPQ] at * とします． example (a b c d e f : Nat) (h : a * b = c * d) (h' : e = f) : a * (b * e) = c * (d * f) := by rw [h'] -- 結合法則を使う rw [← Nat.mul_assoc] rw [h] -- 結合法則を使う rw [Nat.mul_assoc]","breadcrumbs":"rw: 同値変形 » rw","id":"63","title":"rw"},"64":{"body":"needs: import Mathlib.Tactic.NthRewrite rw はマッチした項をすべて置き換えてしまいます．特定の項だけを書き換えたいとき，nth_rewrite が使用できます．対象の式中に現れる順番を1始まりで指定することで，項を指定します．指定された順番が式中の対象の項の数よりも多い場合はエラーになります． -- `G` は群\nvariable [Group G] example (a b : G) : a * b⁻¹ = 1 ↔ a = b := by -- `one_mul: 1 * b = b` を使って `b` を `1 * b` に書き換える -- `b` は2回出現するが，2番目だけ置き換える nth_rewrite 2 [← one_mul b] -- `mul_inv_eq_iff_eq_mul: a * b⁻¹ = c ↔ a = c * b` を使う exact mul_inv_eq_iff_eq_mul","breadcrumbs":"rw: 同値変形 » nth_rewrite","id":"64","title":"nth_rewrite"},"65":{"body":"needs: import Mathlib.Tactic.Says exact? や apply? は証明を書いている過程で使用することを想定したタクティクです．Try this: という提案をクリックして採用したら，exact? や apply? は提案内容で上書きされて，最終的な証明には残りません． では，証明のある部分が apply? などにより提案された内容であることを明示したい場合はどうしたら良いでしょうか？says タクティクはまさにその問題を解決するタクティクです． example (hPQ : P → Q) (hQR : Q → R) (hRS : R → S) (hP : P) : S := by -- `exact?` は実行されない exact? says exact hRS (hQR (hPQ hP)) また，simp? や aesop? などに対しても使用することができ，やはりドキュメントとして役に立ちます． -- 合成 `g ∘ f` が単射なら，`f` も単射\nexample {f : X → Y} {g : Y → Z} (hgfinj : Injective (g ∘ f)) : Injective f := by rw [Injective] aesop? says intro a₁ a₂ a apply hgfinj simp_all only [comp_apply] より詳細には，検索タクティク X があり，その提案内容が Try this: Y だったとき，X says とすると says は Try this: Y の代わりに Try this: X says Y という提案を infoview 上で出します．それをクリックすると，X says の内容が X says Y で置換されます．そして，X says Y が実行されるときには X は飛ばされます．","breadcrumbs":"says: タクティク提案の痕跡を残す » says","id":"65","title":"says"},"66":{"body":"says.verify : Bool : true にすると，X says Y の Y のところに，実際には提案されていないタクティクを入れたときにエラーになります． says.no_verify_in_CI : Bool : true にすると，CI 環境で X says Y の Y の部分が実際に提案されている内容と一致するかのチェックが走らなくなります．","breadcrumbs":"says: タクティク提案の痕跡を残す » オプション","id":"66","title":"オプション"},"67":{"body":"show P は, ゴールの中に ⊢ P があるときにそれをメインのゴールにします． たとえば，証明中にこれから示すべきことを明示し，コードを読みやすくする目的で使うことができます． example (hP: P) (hQ: Q) : P ∧ Q := by constructor · show P exact hP · show Q exact hQ","breadcrumbs":"show: 示すべきことを宣言 » show","id":"67","title":"show"},"68":{"body":"simp は，ターゲットを決められた規則に基づいて自動で簡約（simplify）するタクティクです．カスタマイズすることが可能で，簡約に使ってほしい命題を登録することができます． universe u v -- 圏の公理\nclass Category (C : Type u) where -- 射 Hom : C → C → Type v -- 射の合成 comp : ∀ {a b c : C}, Hom a b → Hom b c → Hom a c -- 恒等射. `id a` が `a` 上の恒等射を意味する id : ∀ (a : C), Hom a a -- 恒等射の性質 id_comp : ∀ {a b : C} (f : Hom a b), comp (id a) f = f comp_id : ∀ {a b : C} (f : Hom a b), comp f (id b) = f -- 射の結合律 assoc : ∀ {a b c d : C} (f : Hom a b) (g : Hom b c) (h : Hom c d), comp (comp f g) h = comp f (comp g h) -- `f : Hom a b`と`g : Hom b c`の合成を`f ≫ g`と書く\ninfixr:80 \" ≫ \" => Category.comp -- `Category.hoge` ではなく `hoge` で呼び出せるようにする\nopen Category -- 公理の等式が `simp` で使えるようにする\nattribute [simp] id_comp comp_id assoc -- 変数の定義\nvariable {C : Type u} [Category.{u, v} C] {a b c d e : C} example (f : Hom a b) (g : Hom b c) (h : Hom c d) (i : Hom d e) : (f ≫ (id b ≫ g)) ≫ (h ≫ i) = f ≫ (g ≫ ((id c ≫ h) ≫ i)) := by -- 上で `simp` で使えるようにした等式を使って自動で簡約する simp 既知の h: P という証明を使って簡約させたいときは，明示的に simp [h] と指定することで可能です． 何も指定しなければゴールを簡約しますが，ローカルコンテキストにある h: P を簡約させたければ simp at h と指定することで可能です．","breadcrumbs":"simp: 簡約 » simp","id":"68","title":"simp"},"69":{"body":"simp は自動的に証明を行ってくれますが，何が使われたのか知りたいときもあります．simp? は簡約に何が使われたのかを示してくれるので，rw などを用いて明示的に書き直すことができます．","breadcrumbs":"simp: 簡約 » simp?","id":"69","title":"simp?"},"7":{"body":"また，Lean では否定 ¬ P は P → False として実装されているため，ゴールが ⊢ False であるときに hn: ¬P に対して apply hn とするとゴールが ⊢ P に書き換わります． -- 矛盾\nexample (hn: ¬ P) (hP: P) : False := by -- ゴールが `P` に変わる apply hn exact hP","breadcrumbs":"apply: 含意→を使う » 否定 ¬ について","id":"7","title":"否定 ¬ について"},"70":{"body":"simp_all は simp [*] at * の強化版で，ローカルコンテキストとゴールをこれ以上簡約できなくなるまですべて簡約します．","breadcrumbs":"simp: 簡約 » simp_all","id":"70","title":"simp_all"},"71":{"body":"dsimp は，定義上(definitionally)等しいもの同士しか簡約しないという制約付きの simp です．","breadcrumbs":"simp: 簡約 » dsimp","id":"71","title":"dsimp"},"72":{"body":"証明の細部を埋める前にコンパイルが通るようにしたいとき，証明で埋めるべき箇所に sorry と書くとコンパイルが通るようになります．ただし，sorry を使用しているという旨の警告が出ます． -- Fermat の最終定理\ndef FermatLastTheorem := ∀ x y z n : Nat, n > 2 ∧ x * y * z ≠ 0 → x ^ n + y ^ n ≠ z ^ n theorem flt : FermatLastTheorem := sorry","breadcrumbs":"sorry: 証明したことにする » sorry","id":"72","title":"sorry"},"73":{"body":"ゴールにある if ... then ... else 式を扱うのに有用なタクティクです． if 式を扱う必要が生じるのは，典型的には Lean で定義したアルゴリズムや関数に関して，何か性質を証明しようとしたときです． ゴールが ⊢ Q (if P then a else b) であったときに，split を使用すると2つのサブゴールが生成されます．具体的には 1つはローカルコンテキストに † : P が追加され，ゴールが ⊢ Q (a) 1つはローカルコンテキストに † : ¬ P が追加され，ゴールが ⊢ Q (b) というサブゴールです．split によって追加される仮定は名前がついているとは限りません．名前がついていなかった場合，case などで名前を付けることができます． -- if 式を使って関数を定義する\ndef myabs (x : Int) : Int := if x ≥ 0 then x else - x example (x : Int) : myabs (2 * x) = 2 * myabs x := by -- `myabs` の定義を展開する unfold myabs -- ゴールの中に if 式があって複雑 show (if 2 * x ≥ 0 then 2 * x else -(2 * x)) = 2 * if x ≥ 0 then x else -x -- `split` タクティクでケース分割する split case inl h => -- `2 * x ≥ 0` の場合 guard_hyp h: 2 * x ≥ 0 -- 左辺にあった if 式が消えた show 2 * x = 2 * if x ≥ 0 then x else -x replace h : x ≥ 0 := by linarith [h] -- `simp` で if を消すことができる simp? [h] says simp only [ge_iff_le, h, ite_true] case inr h => -- `2 * x < 0` の場合 guard_hyp h: ¬2 * x ≥ 0 -- 左辺にあった if 式が消えた show -(2 * x) = 2 * if x ≥ 0 then x else -x -- if 式を消すための補題を準備する have hx : ¬ x ≥ 0 := by linarith [h] -- `simp` で簡約 simp? [h, hx] says simp only [ge_iff_le, hx, ite_false, mul_neg]","breadcrumbs":"split: if 式を含む命題を示す » split","id":"73","title":"split"},"74":{"body":"suffices は，数学でよくある「～を示せば十分である」という推論を行うタクティクです． ゴールが ⊢ P であるときに suffices Q from を実行すると， suffices Q from のブロック内では，仮定に this: Q が追加され， suffices Q from 以降では，ゴールが ⊢ Q に書き換えられます． apply と似ていますが，apply と違って「十分条件になっていること」の証明が明らかでないときにも使うことができます． example : 13 ∣ (2 ^ 70 + 3 ^ 70) := by -- 余りがゼロであることを示せば十分 suffices (2 ^ 70 + 3 ^ 70) % 13 = 0 from by exact Iff.mpr (Nat.dvd_iff_div_mul_eq (2 ^ 70 + 3 ^ 70) 13) rfl rfl suffices Q from ... という形式の場合は，証明を直接構成することが必要です．suffices Q from by ... とすると，タクティクによって証明を構成するモードになります．","breadcrumbs":"suffices: 十分条件に帰着 » suffices","id":"74","title":"suffices"},"75":{"body":"needs: import Mathlib.Tactic.Tauto named after: トートロジー(tautology) tauto は， トートロジー(恒真式)であることに基づいてゴールを閉じるタクティクです． ゴールを閉じることができなければエラーになります． -- 含意の導入\nexample (h : P) : Q → P := by tauto -- フレーゲの3段論法\nexample : (P → (Q → R)) → ((P → Q) → (P → R)) := by tauto -- 排中律\nexample : P ∨ ¬ P := by -- `aesop` では示すことができない try aesop tauto -- 対偶\nexample (h : P → Q) : ¬ Q → ¬ P := by -- `exact?` では示すことができない try exact? tauto","breadcrumbs":"tauto: トートロジーを示す » tauto","id":"75","title":"tauto"},"76":{"body":"trivial は明らかなことを示します． trivial は，rfl や contradiction などのタクティクを実行して，現在のゴールを閉じようとします． -- 定義から明らかな等式\nexample : 1 + 1 = 2 := by trivial -- 矛盾があるので, どんな命題でも証明できる\nexample (h: False) : P := by trivial 普段の数学でいう「自明」な命題は trivial では示せないことがほとんどだと思います． aesop を試してみてください．","breadcrumbs":"trivial: 自明 » trivial","id":"76","title":"trivial"},"77":{"body":"needs: import Mathlib.Tactic.WLOG named after: 一般性を失わずに(without loss of generarity) wlog は，数学でよく使われる「一般性を失うことなく～と仮定してよい」というフレーズの Lean での対応物です． example (a b : Nat) : a + b = b + a := by -- `a ≤ b` だと仮定しても一般性を失わない wlog h : a ≤ b with H -- `a ≤ b` なら成り立つと仮定して，そうでないときにも成り立つことを示す · show a + b = b + a guard_hyp H : ∀ (a b : Nat), a ≤ b → a + b = b + a guard_hyp h : ¬a ≤ b abel -- `a ≤ b` であるときに成り立つことを示す · show a + b = b + a guard_hyp h: a ≤ b abel","breadcrumbs":"wlog: 一般性を失わずに特殊化 » wlog","id":"77","title":"wlog"},"8":{"body":"apply には引数が必須なのですが，省略しても近くにエラーが出ません．一般に，構文的に間違った証明を書いた場合には，エラーがわかりやすい場所に出てくれる保証はありません．","breadcrumbs":"apply: 含意→を使う » よくあるエラー","id":"8","title":"よくあるエラー"},"9":{"body":"exact の代わりに apply を使うことができます． -- `P → Q` かつ `P` ならば `Q`\nexample (h: P → Q) (hP: P) : Q := by apply h apply hP","breadcrumbs":"apply: 含意→を使う » exact との関連","id":"9","title":"exact との関連"}},"length":78,"save":true},"fields":["title","body","breadcrumbs"],"index":{"body":{"root":{"0":{"df":15,"docs":{"12":{"tf":1.0},"26":{"tf":1.4142135623730951},"28":{"tf":1.7320508075688772},"31":{"tf":1.4142135623730951},"44":{"tf":2.0},"45":{"tf":1.0},"46":{"tf":1.4142135623730951},"47":{"tf":1.0},"51":{"tf":1.4142135623730951},"54":{"tf":1.4142135623730951},"58":{"tf":1.0},"61":{"tf":1.0},"72":{"tf":1.0},"73":{"tf":3.3166247903554},"74":{"tf":1.0}}},"1":{"0":{"0":{"df":1,"docs":{"62":{"tf":1.0}}},"df":0,"docs":{}},"2":{"df":1,"docs":{"51":{"tf":1.0}}},"3":{"df":2,"docs":{"61":{"tf":1.0},"74":{"tf":1.7320508075688772}}},"df":16,"docs":{"12":{"tf":1.7320508075688772},"26":{"tf":1.0},"28":{"tf":2.449489742783178},"35":{"tf":1.0},"36":{"tf":1.0},"44":{"tf":2.0},"46":{"tf":1.4142135623730951},"47":{"tf":1.0},"48":{"tf":2.8284271247461903},"52":{"tf":1.0},"54":{"tf":1.7320508075688772},"59":{"tf":1.0},"61":{"tf":1.4142135623730951},"64":{"tf":1.7320508075688772},"73":{"tf":1.4142135623730951},"76":{"tf":1.4142135623730951}}},"2":{"df":19,"docs":{"12":{"tf":3.0},"26":{"tf":3.1622776601683795},"29":{"tf":1.4142135623730951},"36":{"tf":1.0},"37":{"tf":1.0},"38":{"tf":1.4142135623730951},"43":{"tf":1.7320508075688772},"51":{"tf":1.4142135623730951},"52":{"tf":1.4142135623730951},"53":{"tf":1.4142135623730951},"58":{"tf":1.7320508075688772},"59":{"tf":2.6457513110645907},"61":{"tf":1.4142135623730951},"62":{"tf":2.8284271247461903},"64":{"tf":1.0},"72":{"tf":1.0},"73":{"tf":3.872983346207417},"74":{"tf":1.7320508075688772},"76":{"tf":1.0}},"回":{"df":0,"docs":{},"出":{"df":0,"docs":{},"現":{"df":0,"docs":{},"す":{"df":0,"docs":{},"る":{"df":0,"docs":{},"が":{"df":0,"docs":{},"，":{"2":{"df":1,"docs":{"64":{"tf":1.0}}},"df":0,"docs":{}}}}}}}}},"3":{"df":8,"docs":{"12":{"tf":1.0},"29":{"tf":1.0},"36":{"tf":1.0},"43":{"tf":1.4142135623730951},"51":{"tf":1.0},"61":{"tf":1.0},"74":{"tf":1.7320508075688772},"75":{"tf":1.0}}},"4":{"df":2,"docs":{"51":{"tf":1.4142135623730951},"59":{"tf":1.4142135623730951}},"│":{"0":{",":{"1":{",":{"2":{",":{"3":{"df":1,"docs":{"12":{"tf":1.0}}},"df":0,"docs":{}},"df":0,"docs":{}},"df":0,"docs":{}},"df":0,"docs":{}},"df":0,"docs":{}},"df":0,"docs":{}},"df":0,"docs":{}}},"5":{"df":1,"docs":{"59":{"tf":2.449489742783178}}},"7":{"0":{"df":2,"docs":{"61":{"tf":1.4142135623730951},"74":{"tf":2.449489742783178}}},"df":1,"docs":{"36":{"tf":1.0}}},"_":{"df":9,"docs":{"12":{"tf":1.0},"13":{"tf":1.0},"26":{"tf":1.0},"42":{"tf":1.0},"5":{"tf":1.0},"55":{"tf":1.0},"56":{"tf":1.4142135623730951},"57":{"tf":1.7320508075688772},"59":{"tf":1.7320508075688772}}},"a":{"b":{"df":0,"docs":{},"e":{"df":0,"docs":{},"l":{"df":1,"docs":{"77":{"tf":1.4142135623730951}}}}},"d":{"d":{"_":{"df":0,"docs":{},"z":{"df":0,"docs":{},"e":{"df":0,"docs":{},"r":{"df":0,"docs":{},"o":{"df":1,"docs":{"26":{"tf":1.4142135623730951}}}}}}},"df":0,"docs":{}},"df":0,"docs":{}},"df":0,"docs":{},"e":{"df":0,"docs":{},"s":{"df":0,"docs":{},"o":{"df":0,"docs":{},"p":{"df":6,"docs":{"3":{"tf":2.0},"37":{"tf":1.0},"4":{"tf":2.0},"65":{"tf":1.4142135623730951},"75":{"tf":1.4142135623730951},"76":{"tf":1.0}}}}}},"p":{"df":0,"docs":{},"p":{"df":0,"docs":{},"l":{"df":0,"docs":{},"i":{"df":16,"docs":{"10":{"tf":1.4142135623730951},"11":{"tf":1.7320508075688772},"12":{"tf":2.0},"22":{"tf":1.4142135623730951},"23":{"tf":1.4142135623730951},"35":{"tf":1.4142135623730951},"4":{"tf":1.0},"5":{"tf":1.0},"50":{"tf":1.0},"56":{"tf":1.7320508075688772},"6":{"tf":2.23606797749979},"65":{"tf":2.0},"7":{"tf":1.4142135623730951},"74":{"tf":1.4142135623730951},"8":{"tf":1.0},"9":{"tf":1.7320508075688772}}},"y":{"_":{"a":{"df":0,"docs":{},"s":{"df":0,"docs":{},"s":{"df":0,"docs":{},"u":{"df":0,"docs":{},"m":{"df":0,"docs":{},"p":{"df":0,"docs":{},"t":{"df":2,"docs":{"10":{"tf":1.4142135623730951},"5":{"tf":2.449489742783178}}}}}}}}},"df":0,"docs":{}},"df":0,"docs":{}}}}},"r":{"df":0,"docs":{},"i":{"df":0,"docs":{},"t":{"df":0,"docs":{},"h":{"df":0,"docs":{},"m":{"df":0,"docs":{},"e":{"df":0,"docs":{},"t":{"df":2,"docs":{"51":{"tf":1.0},"53":{"tf":1.0}}}}}}}}},"s":{"df":0,"docs":{},"s":{"df":0,"docs":{},"o":{"c":{"df":1,"docs":{"68":{"tf":1.4142135623730951}}},"df":0,"docs":{}},"u":{"df":0,"docs":{},"m":{"df":0,"docs":{},"p":{"df":0,"docs":{},"t":{"df":7,"docs":{"13":{"tf":1.7320508075688772},"14":{"tf":1.0},"15":{"tf":1.0},"34":{"tf":1.4142135623730951},"42":{"tf":1.0},"48":{"tf":1.0},"50":{"tf":1.4142135623730951}}}}}}}},"t":{"df":0,"docs":{},"t":{"df":0,"docs":{},"r":{"df":0,"docs":{},"i":{"b":{"df":0,"docs":{},"u":{"df":0,"docs":{},"t":{"df":2,"docs":{"60":{"tf":1.4142135623730951},"68":{"tf":1.0}}}}},"df":0,"docs":{}}}}}},"b":{"`":{"df":0,"docs":{},"と":{"`":{"df":0,"docs":{},"g":{"df":1,"docs":{"68":{"tf":1.0}}}},"df":0,"docs":{}}},"df":10,"docs":{"11":{"tf":2.0},"31":{"tf":2.0},"37":{"tf":2.449489742783178},"53":{"tf":1.7320508075688772},"58":{"tf":2.0},"63":{"tf":2.449489742783178},"64":{"tf":3.3166247903554},"68":{"tf":4.0},"73":{"tf":1.4142135623730951},"77":{"tf":4.123105625617661}},"o":{"df":0,"docs":{},"o":{"df":0,"docs":{},"l":{"df":1,"docs":{"66":{"tf":1.4142135623730951}}}}},"s":{"df":1,"docs":{"26":{"tf":1.7320508075688772}}},"y":{"_":{"c":{"a":{"df":0,"docs":{},"s":{"df":1,"docs":{"15":{"tf":2.0}}}},"df":0,"docs":{},"o":{"df":0,"docs":{},"n":{"df":0,"docs":{},"t":{"df":0,"docs":{},"r":{"a":{"df":1,"docs":{"16":{"tf":2.0}}},"df":0,"docs":{}}}}}},"df":0,"docs":{}},"df":0,"docs":{}}},"c":{"`":{"df":0,"docs":{},"の":{"df":0,"docs":{},"合":{"df":0,"docs":{},"成":{"df":0,"docs":{},"を":{"`":{"df":0,"docs":{},"f":{"df":1,"docs":{"68":{"tf":1.0}}}},"df":0,"docs":{}}}}}},"a":{"df":0,"docs":{},"l":{"c":{"df":2,"docs":{"19":{"tf":1.4142135623730951},"59":{"tf":1.0}}},"df":0,"docs":{}},"s":{"df":0,"docs":{},"e":{"df":7,"docs":{"15":{"tf":1.4142135623730951},"20":{"tf":2.8284271247461903},"21":{"tf":2.449489742783178},"22":{"tf":1.7320508075688772},"23":{"tf":1.4142135623730951},"46":{"tf":1.4142135623730951},"73":{"tf":1.4142135623730951}}}},"t":{"df":0,"docs":{},"e":{"df":0,"docs":{},"g":{"df":0,"docs":{},"o":{"df":0,"docs":{},"r":{"df":0,"docs":{},"i":{"df":1,"docs":{"68":{"tf":1.4142135623730951}}},"y":{".":{"c":{"df":0,"docs":{},"o":{"df":0,"docs":{},"m":{"df":0,"docs":{},"p":{"df":1,"docs":{"68":{"tf":1.0}}}}}},"df":0,"docs":{},"h":{"df":0,"docs":{},"o":{"df":0,"docs":{},"g":{"df":1,"docs":{"68":{"tf":1.0}}}}},"{":{"df":0,"docs":{},"u":{"df":1,"docs":{"68":{"tf":1.0}}}}},"df":0,"docs":{}}}}}}}},"df":5,"docs":{"31":{"tf":2.0},"58":{"tf":1.4142135623730951},"63":{"tf":1.7320508075688772},"64":{"tf":1.4142135623730951},"68":{"tf":4.58257569495584}},"h":{"df":0,"docs":{},"o":{"df":0,"docs":{},"o":{"df":0,"docs":{},"s":{"df":2,"docs":{"24":{"tf":1.7320508075688772},"25":{"tf":1.0}}}}}},"i":{"df":1,"docs":{"66":{"tf":1.0}}},"l":{"a":{"df":0,"docs":{},"s":{"df":0,"docs":{},"s":{"df":1,"docs":{"68":{"tf":1.0}},"i":{"c":{"a":{"df":0,"docs":{},"l":{".":{"c":{"df":0,"docs":{},"h":{"df":0,"docs":{},"o":{"df":0,"docs":{},"i":{"c":{"df":1,"docs":{"25":{"tf":1.4142135623730951}}},"df":0,"docs":{}}}}},"df":0,"docs":{}},"df":0,"docs":{}}},"df":0,"docs":{}},"df":0,"docs":{}}}}},"df":0,"docs":{}},"o":{"df":0,"docs":{},"m":{"df":0,"docs":{},"p":{"_":{"a":{"df":0,"docs":{},"p":{"df":0,"docs":{},"p":{"df":0,"docs":{},"l":{"df":0,"docs":{},"i":{"df":2,"docs":{"4":{"tf":1.0},"65":{"tf":1.0}}}}}}},"df":0,"docs":{},"i":{"d":{"df":1,"docs":{"68":{"tf":1.4142135623730951}}},"df":0,"docs":{}}},"df":1,"docs":{"68":{"tf":2.6457513110645907}}}},"n":{"df":0,"docs":{},"g":{"df":0,"docs":{},"r":{"df":1,"docs":{"26":{"tf":2.6457513110645907}},"u":{"df":0,"docs":{},"e":{"df":0,"docs":{},"n":{"c":{"df":1,"docs":{"26":{"tf":1.0}}},"df":0,"docs":{}}}}}},"s":{"df":0,"docs":{},"t":{"df":0,"docs":{},"r":{"df":0,"docs":{},"u":{"c":{"df":0,"docs":{},"t":{"df":0,"docs":{},"o":{"df":0,"docs":{},"r":{"df":4,"docs":{"27":{"tf":1.7320508075688772},"28":{"tf":1.4142135623730951},"57":{"tf":2.6457513110645907},"67":{"tf":1.0}}}}}},"df":0,"docs":{}}}}},"t":{"df":0,"docs":{},"r":{"a":{"d":{"df":0,"docs":{},"i":{"c":{"df":0,"docs":{},"t":{"df":5,"docs":{"15":{"tf":1.0},"16":{"tf":1.0},"29":{"tf":2.23606797749979},"49":{"tf":1.0},"76":{"tf":1.0}}}},"df":0,"docs":{}}},"df":0,"docs":{}},"df":0,"docs":{}}},"v":{"df":1,"docs":{"30":{"tf":1.4142135623730951}},"e":{"df":0,"docs":{},"r":{"df":0,"docs":{},"t":{"df":1,"docs":{"31":{"tf":1.7320508075688772}}}}}}}}},"d":{"df":3,"docs":{"58":{"tf":1.4142135623730951},"63":{"tf":1.7320508075688772},"68":{"tf":2.23606797749979}},"e":{"df":0,"docs":{},"f":{"df":4,"docs":{"38":{"tf":1.4142135623730951},"44":{"tf":1.0},"72":{"tf":1.0},"73":{"tf":1.0}}}},"o":{"df":0,"docs":{},"n":{"df":0,"docs":{},"e":{"df":4,"docs":{"12":{"tf":1.4142135623730951},"32":{"tf":1.4142135623730951},"35":{"tf":1.0},"5":{"tf":1.0}}}}},"s":{"df":0,"docs":{},"i":{"df":0,"docs":{},"m":{"df":0,"docs":{},"p":{"df":2,"docs":{"38":{"tf":1.0},"71":{"tf":1.4142135623730951}}}}}}},"df":0,"docs":{},"e":{"df":2,"docs":{"63":{"tf":1.7320508075688772},"68":{"tf":1.4142135623730951}},"v":{"df":0,"docs":{},"e":{"df":0,"docs":{},"n":{"df":1,"docs":{"59":{"tf":1.7320508075688772}}}}},"x":{"a":{"c":{"df":0,"docs":{},"t":{"df":30,"docs":{"11":{"tf":1.0},"14":{"tf":1.4142135623730951},"17":{"tf":1.0},"18":{"tf":1.0},"20":{"tf":1.4142135623730951},"21":{"tf":1.4142135623730951},"23":{"tf":1.0},"24":{"tf":1.0},"25":{"tf":1.0},"26":{"tf":1.0},"27":{"tf":1.7320508075688772},"31":{"tf":1.4142135623730951},"33":{"tf":2.23606797749979},"34":{"tf":1.4142135623730951},"35":{"tf":3.0},"39":{"tf":1.0},"40":{"tf":1.4142135623730951},"48":{"tf":1.0},"5":{"tf":1.0},"54":{"tf":1.0},"55":{"tf":1.4142135623730951},"57":{"tf":2.449489742783178},"6":{"tf":1.7320508075688772},"64":{"tf":1.0},"65":{"tf":2.23606797749979},"67":{"tf":1.4142135623730951},"7":{"tf":1.0},"74":{"tf":1.0},"75":{"tf":1.4142135623730951},"9":{"tf":1.4142135623730951}}}},"df":0,"docs":{},"m":{"df":0,"docs":{},"p":{"df":0,"docs":{},"l":{"df":61,"docs":{"11":{"tf":1.0},"13":{"tf":1.0},"15":{"tf":1.0},"16":{"tf":1.0},"17":{"tf":1.4142135623730951},"18":{"tf":1.0},"20":{"tf":1.0},"21":{"tf":1.0},"22":{"tf":1.0},"23":{"tf":1.4142135623730951},"24":{"tf":1.0},"25":{"tf":1.0},"26":{"tf":1.4142135623730951},"27":{"tf":1.4142135623730951},"28":{"tf":1.0},"29":{"tf":2.0},"3":{"tf":1.0},"31":{"tf":1.0},"33":{"tf":1.4142135623730951},"35":{"tf":1.4142135623730951},"36":{"tf":1.0},"37":{"tf":1.0},"38":{"tf":1.0},"39":{"tf":1.0},"4":{"tf":1.0},"40":{"tf":1.0},"42":{"tf":1.0},"43":{"tf":1.0},"44":{"tf":1.0},"45":{"tf":1.0},"46":{"tf":1.0},"47":{"tf":1.0},"48":{"tf":1.4142135623730951},"49":{"tf":1.0},"5":{"tf":1.4142135623730951},"50":{"tf":1.4142135623730951},"51":{"tf":1.4142135623730951},"52":{"tf":1.0},"53":{"tf":1.0},"54":{"tf":1.4142135623730951},"55":{"tf":1.0},"56":{"tf":1.0},"57":{"tf":1.4142135623730951},"58":{"tf":1.4142135623730951},"59":{"tf":1.0},"6":{"tf":1.4142135623730951},"60":{"tf":1.4142135623730951},"61":{"tf":1.7320508075688772},"62":{"tf":1.4142135623730951},"63":{"tf":1.0},"64":{"tf":1.0},"65":{"tf":1.4142135623730951},"67":{"tf":1.0},"68":{"tf":1.0},"7":{"tf":1.0},"73":{"tf":1.0},"74":{"tf":1.0},"75":{"tf":2.0},"76":{"tf":1.4142135623730951},"77":{"tf":1.0},"9":{"tf":1.0}}}}}},"df":0,"docs":{},"i":{"df":0,"docs":{},"s":{"df":0,"docs":{},"t":{"df":5,"docs":{"25":{"tf":1.0},"36":{"tf":2.0},"43":{"tf":1.0},"54":{"tf":1.0},"59":{"tf":1.0}}}}},"p":{"df":0,"docs":{},"l":{"df":0,"docs":{},"o":{"d":{"df":1,"docs":{"12":{"tf":1.4142135623730951}}},"df":0,"docs":{},"s":{"df":0,"docs":{},"i":{"df":0,"docs":{},"o":{"df":0,"docs":{},"n":{")":{"df":0,"docs":{},"と":{"df":0,"docs":{},"呼":{"df":0,"docs":{},"び":{"df":0,"docs":{},"ま":{"df":0,"docs":{},"す":{"df":0,"docs":{},"が":{"df":0,"docs":{},"，":{"c":{"df":0,"docs":{},"o":{"df":0,"docs":{},"n":{"df":0,"docs":{},"t":{"df":0,"docs":{},"r":{"a":{"d":{"df":0,"docs":{},"i":{"c":{"df":0,"docs":{},"t":{"df":1,"docs":{"29":{"tf":1.0}}}},"df":0,"docs":{}}},"df":0,"docs":{}},"df":0,"docs":{}}}}}},"df":0,"docs":{}}}}}}}}},"df":0,"docs":{}}}}}}}},"t":{"df":1,"docs":{"37":{"tf":2.0}},"e":{"df":0,"docs":{},"n":{"df":0,"docs":{},"s":{"df":0,"docs":{},"i":{"df":0,"docs":{},"o":{"df":0,"docs":{},"n":{"df":1,"docs":{"37":{"tf":1.0}}}}}}}}}}},"f":{"a":{"c":{"df":2,"docs":{"44":{"tf":2.6457513110645907},"45":{"tf":1.7320508075688772}}},"df":0,"docs":{},"l":{"df":0,"docs":{},"s":{"df":7,"docs":{"16":{"tf":1.4142135623730951},"29":{"tf":1.4142135623730951},"49":{"tf":2.0},"5":{"tf":1.0},"52":{"tf":1.0},"7":{"tf":1.7320508075688772},"76":{"tf":1.0}}}}},"df":12,"docs":{"11":{"tf":2.23606797749979},"24":{"tf":2.8284271247461903},"25":{"tf":3.0},"26":{"tf":3.7416573867739413},"3":{"tf":2.23606797749979},"31":{"tf":1.7320508075688772},"37":{"tf":1.7320508075688772},"38":{"tf":2.449489742783178},"4":{"tf":1.7320508075688772},"63":{"tf":1.7320508075688772},"65":{"tf":2.23606797749979},"68":{"tf":3.605551275463989}},"e":{"df":0,"docs":{},"r":{"df":0,"docs":{},"m":{"a":{"df":0,"docs":{},"t":{"df":1,"docs":{"72":{"tf":1.0}},"l":{"a":{"df":0,"docs":{},"s":{"df":0,"docs":{},"t":{"df":0,"docs":{},"t":{"df":0,"docs":{},"h":{"df":0,"docs":{},"e":{"df":0,"docs":{},"o":{"df":0,"docs":{},"r":{"df":0,"docs":{},"e":{"df":0,"docs":{},"m":{"df":1,"docs":{"72":{"tf":1.4142135623730951}}}}}}}}}}}},"df":0,"docs":{}}}},"df":0,"docs":{}}}},"l":{"df":0,"docs":{},"t":{"df":1,"docs":{"72":{"tf":1.0}}}},"u":{"df":0,"docs":{},"n":{"df":4,"docs":{"17":{"tf":1.0},"18":{"tf":1.0},"25":{"tf":1.4142135623730951},"38":{"tf":1.4142135623730951}},"e":{"df":0,"docs":{},"x":{"df":0,"docs":{},"t":{"df":1,"docs":{"38":{"tf":1.7320508075688772}}}}}}}},"g":{"df":10,"docs":{"11":{"tf":1.7320508075688772},"24":{"tf":2.8284271247461903},"26":{"tf":2.23606797749979},"3":{"tf":1.7320508075688772},"37":{"tf":1.7320508075688772},"38":{"tf":2.449489742783178},"4":{"tf":1.4142135623730951},"64":{"tf":1.7320508075688772},"65":{"tf":1.7320508075688772},"68":{"tf":2.6457513110645907}},"e":{"_":{"df":0,"docs":{},"i":{"df":0,"docs":{},"f":{"df":0,"docs":{},"f":{"_":{"df":0,"docs":{},"l":{"df":1,"docs":{"73":{"tf":1.4142135623730951}}}},"df":0,"docs":{}}}}},"df":0,"docs":{},"n":{"df":0,"docs":{},"e":{"df":0,"docs":{},"r":{"a":{"df":0,"docs":{},"r":{"df":1,"docs":{"77":{"tf":1.0}}}},"df":1,"docs":{"46":{"tf":1.0}}}}}},"o":{"a":{"df":0,"docs":{},"l":{"df":1,"docs":{"27":{"tf":1.0}}}},"df":0,"docs":{}},"r":{"df":0,"docs":{},"o":{"df":0,"docs":{},"u":{"df":0,"docs":{},"p":{"df":2,"docs":{"11":{"tf":1.4142135623730951},"64":{"tf":1.0}}}}}},"u":{"a":{"df":0,"docs":{},"r":{"d":{"_":{"df":0,"docs":{},"h":{"df":0,"docs":{},"y":{"df":0,"docs":{},"p":{"df":8,"docs":{"15":{"tf":1.4142135623730951},"24":{"tf":1.4142135623730951},"39":{"tf":1.7320508075688772},"46":{"tf":1.7320508075688772},"47":{"tf":1.0},"59":{"tf":1.4142135623730951},"73":{"tf":1.4142135623730951},"77":{"tf":1.7320508075688772}}}}}},"df":0,"docs":{}},"df":0,"docs":{}}},"df":0,"docs":{}}},"h":{".":{"df":0,"docs":{},"l":{"df":0,"docs":{},"e":{"df":0,"docs":{},"f":{"df":0,"docs":{},"t":{"df":1,"docs":{"27":{"tf":1.4142135623730951}}}}}},"r":{"df":0,"docs":{},"i":{"df":0,"docs":{},"g":{"df":0,"docs":{},"h":{"df":0,"docs":{},"t":{"df":1,"docs":{"27":{"tf":1.0}}}}}}}},"1":{"df":4,"docs":{"51":{"tf":1.0},"52":{"tf":1.0},"58":{"tf":2.0},"63":{"tf":1.4142135623730951}}},"2":{"df":4,"docs":{"51":{"tf":1.0},"52":{"tf":1.0},"58":{"tf":1.4142135623730951},"63":{"tf":1.4142135623730951}}},"a":{"b":{"df":1,"docs":{"63":{"tf":1.7320508075688772}}},"df":0,"docs":{}},"c":{"df":1,"docs":{"31":{"tf":1.4142135623730951}}},"df":31,"docs":{"11":{"tf":1.4142135623730951},"12":{"tf":1.0},"15":{"tf":1.0},"16":{"tf":2.0},"17":{"tf":1.0},"20":{"tf":2.23606797749979},"21":{"tf":1.7320508075688772},"22":{"tf":1.4142135623730951},"23":{"tf":2.449489742783178},"24":{"tf":1.4142135623730951},"25":{"tf":1.7320508075688772},"26":{"tf":2.0},"27":{"tf":1.4142135623730951},"29":{"tf":1.7320508075688772},"31":{"tf":3.0},"40":{"tf":1.4142135623730951},"46":{"tf":1.7320508075688772},"48":{"tf":1.4142135623730951},"49":{"tf":1.7320508075688772},"53":{"tf":1.0},"54":{"tf":1.4142135623730951},"56":{"tf":1.7320508075688772},"59":{"tf":1.7320508075688772},"6":{"tf":2.8284271247461903},"63":{"tf":2.449489742783178},"68":{"tf":3.1622776601683795},"73":{"tf":3.1622776601683795},"75":{"tf":1.4142135623730951},"76":{"tf":1.0},"77":{"tf":2.23606797749979},"9":{"tf":1.4142135623730951}},"e":{"a":{"d":{"df":1,"docs":{"5":{"tf":1.4142135623730951}}},"df":0,"docs":{}},"df":0,"docs":{},"l":{"df":0,"docs":{},"p":{"df":1,"docs":{"1":{"tf":1.0}}}}},"f":{"df":2,"docs":{"24":{"tf":2.0},"26":{"tf":1.4142135623730951}}},"g":{"df":1,"docs":{"24":{"tf":1.7320508075688772}},"f":{"df":0,"docs":{},"i":{"df":0,"docs":{},"n":{"df":0,"docs":{},"j":{"df":3,"docs":{"3":{"tf":1.0},"4":{"tf":1.4142135623730951},"65":{"tf":1.4142135623730951}}}}}}},"k":{"df":1,"docs":{"59":{"tf":2.6457513110645907}}},"n":{"df":2,"docs":{"59":{"tf":1.4142135623730951},"7":{"tf":2.0}},"e":{"_":{"df":0,"docs":{},"s":{"df":0,"docs":{},"t":{"df":1,"docs":{"25":{"tf":1.4142135623730951}}}}},"df":0,"docs":{}},"n":{"df":0,"docs":{},"p":{"df":1,"docs":{"15":{"tf":1.0}}}},"p":{"df":1,"docs":{"29":{"tf":1.0}}},"q":{"df":2,"docs":{"16":{"tf":1.4142135623730951},"49":{"tf":1.4142135623730951}}}},"o":{"df":0,"docs":{},"g":{"df":0,"docs":{},"e":{"df":1,"docs":{"68":{"tf":1.0}}}},"m":{"df":1,"docs":{"68":{"tf":4.0}}}},"p":{"df":27,"docs":{"13":{"tf":1.0},"15":{"tf":1.7320508075688772},"16":{"tf":1.0},"17":{"tf":2.0},"18":{"tf":2.0},"20":{"tf":1.4142135623730951},"21":{"tf":1.4142135623730951},"22":{"tf":1.4142135623730951},"23":{"tf":2.23606797749979},"27":{"tf":1.4142135623730951},"29":{"tf":1.0},"33":{"tf":2.8284271247461903},"39":{"tf":1.7320508075688772},"40":{"tf":1.7320508075688772},"42":{"tf":1.0},"48":{"tf":1.7320508075688772},"49":{"tf":2.0},"5":{"tf":1.4142135623730951},"50":{"tf":1.4142135623730951},"55":{"tf":1.4142135623730951},"56":{"tf":1.4142135623730951},"57":{"tf":2.0},"6":{"tf":2.23606797749979},"65":{"tf":1.4142135623730951},"67":{"tf":1.4142135623730951},"7":{"tf":1.4142135623730951},"9":{"tf":1.4142135623730951}},"q":{"df":10,"docs":{"17":{"tf":2.0},"18":{"tf":1.7320508075688772},"35":{"tf":1.4142135623730951},"40":{"tf":1.7320508075688772},"42":{"tf":1.4142135623730951},"48":{"tf":1.7320508075688772},"5":{"tf":1.7320508075688772},"56":{"tf":1.4142135623730951},"63":{"tf":2.0},"65":{"tf":1.4142135623730951}}},"r":{"df":4,"docs":{"20":{"tf":1.4142135623730951},"21":{"tf":1.4142135623730951},"22":{"tf":1.4142135623730951},"23":{"tf":1.4142135623730951}}}},"q":{"df":15,"docs":{"20":{"tf":1.4142135623730951},"21":{"tf":1.4142135623730951},"22":{"tf":1.4142135623730951},"23":{"tf":2.23606797749979},"27":{"tf":1.4142135623730951},"33":{"tf":1.7320508075688772},"35":{"tf":1.4142135623730951},"40":{"tf":1.7320508075688772},"42":{"tf":1.0},"48":{"tf":1.7320508075688772},"49":{"tf":1.4142135623730951},"5":{"tf":1.0},"55":{"tf":1.4142135623730951},"57":{"tf":2.0},"67":{"tf":1.4142135623730951}},"n":{"df":1,"docs":{"5":{"tf":1.4142135623730951}}},"r":{"df":11,"docs":{"17":{"tf":2.0},"18":{"tf":1.7320508075688772},"20":{"tf":1.4142135623730951},"21":{"tf":1.4142135623730951},"22":{"tf":1.4142135623730951},"23":{"tf":1.4142135623730951},"35":{"tf":1.4142135623730951},"40":{"tf":1.7320508075688772},"48":{"tf":1.7320508075688772},"5":{"tf":1.0},"65":{"tf":1.4142135623730951}}}},"r":{"df":2,"docs":{"57":{"tf":2.0},"65":{"tf":1.4142135623730951}}},"x":{"df":3,"docs":{"28":{"tf":1.4142135623730951},"43":{"tf":2.0},"73":{"tf":1.7320508075688772}}},"y":{"df":1,"docs":{"43":{"tf":1.4142135623730951}},"p":{"df":1,"docs":{"48":{"tf":1.0}}}}},"i":{"d":{"_":{"c":{"df":0,"docs":{},"o":{"df":0,"docs":{},"m":{"df":0,"docs":{},"p":{"df":1,"docs":{"68":{"tf":1.4142135623730951}}}}}},"df":0,"docs":{}},"df":2,"docs":{"51":{"tf":1.7320508075688772},"68":{"tf":2.449489742783178}}},"df":0,"docs":{},"f":{"df":0,"docs":{},"f":{".":{"df":0,"docs":{},"m":{"df":0,"docs":{},"p":{"df":0,"docs":{},"r":{"df":1,"docs":{"74":{"tf":1.0}}}}}},"df":0,"docs":{}}},"h":{"df":4,"docs":{"44":{"tf":1.0},"45":{"tf":1.7320508075688772},"46":{"tf":1.4142135623730951},"47":{"tf":1.4142135623730951}}},"m":{"df":0,"docs":{},"p":{"df":0,"docs":{},"o":{"df":0,"docs":{},"r":{"df":0,"docs":{},"t":{"df":26,"docs":{"11":{"tf":1.0},"16":{"tf":1.0},"18":{"tf":1.0},"22":{"tf":1.0},"23":{"tf":1.0},"24":{"tf":1.0},"3":{"tf":1.0},"31":{"tf":1.0},"35":{"tf":1.0},"37":{"tf":1.0},"39":{"tf":1.0},"45":{"tf":1.0},"5":{"tf":1.0},"50":{"tf":1.0},"51":{"tf":1.0},"53":{"tf":1.0},"54":{"tf":1.0},"58":{"tf":1.0},"59":{"tf":1.0},"60":{"tf":1.7320508075688772},"61":{"tf":1.0},"62":{"tf":1.0},"64":{"tf":1.0},"65":{"tf":1.0},"75":{"tf":1.0},"77":{"tf":1.0}}}}}}},"n":{"d":{"df":0,"docs":{},"u":{"c":{"df":0,"docs":{},"t":{"df":5,"docs":{"44":{"tf":2.23606797749979},"45":{"tf":1.7320508075688772},"46":{"tf":1.4142135623730951},"47":{"tf":1.0},"60":{"tf":1.0}}}},"df":0,"docs":{}}},"df":0,"docs":{},"f":{"df":0,"docs":{},"i":{"df":0,"docs":{},"x":{"df":0,"docs":{},"r":{":":{"8":{"0":{"df":1,"docs":{"68":{"tf":1.0}}},"df":0,"docs":{}},"df":0,"docs":{}},"df":0,"docs":{}}}},"o":{"df":0,"docs":{},"v":{"df":0,"docs":{},"i":{"df":0,"docs":{},"e":{"df":0,"docs":{},"w":{"df":1,"docs":{"65":{"tf":1.0}}}}}}}},"j":{"df":0,"docs":{},"e":{"c":{"df":0,"docs":{},"t":{"df":3,"docs":{"3":{"tf":1.7320508075688772},"4":{"tf":1.7320508075688772},"65":{"tf":1.7320508075688772}}}},"df":0,"docs":{}}},"l":{"df":4,"docs":{"15":{"tf":1.0},"20":{"tf":1.7320508075688772},"21":{"tf":1.4142135623730951},"73":{"tf":1.0}}},"r":{"df":4,"docs":{"15":{"tf":1.0},"20":{"tf":1.7320508075688772},"21":{"tf":1.4142135623730951},"73":{"tf":1.0}}},"s":{"df":0,"docs":{},"e":{"df":0,"docs":{},"r":{"df":0,"docs":{},"t":{"df":1,"docs":{"20":{"tf":1.4142135623730951}}}}}},"t":{"df":5,"docs":{"26":{"tf":2.0},"54":{"tf":1.4142135623730951},"58":{"tf":1.4142135623730951},"59":{"tf":1.0},"73":{"tf":1.7320508075688772}},"r":{"df":0,"docs":{},"o":{"d":{"df":0,"docs":{},"u":{"c":{"df":1,"docs":{"48":{"tf":1.0}}},"df":0,"docs":{}}},"df":20,"docs":{"15":{"tf":1.0},"16":{"tf":1.0},"17":{"tf":1.0},"18":{"tf":1.0},"20":{"tf":1.0},"21":{"tf":1.0},"22":{"tf":1.0},"23":{"tf":1.4142135623730951},"25":{"tf":1.0},"28":{"tf":1.0},"3":{"tf":1.0},"37":{"tf":1.0},"4":{"tf":1.0},"40":{"tf":1.0},"48":{"tf":2.449489742783178},"49":{"tf":1.7320508075688772},"5":{"tf":1.0},"54":{"tf":1.0},"59":{"tf":1.0},"65":{"tf":1.0}}}}}},"t":{"df":0,"docs":{},"e":{"_":{"df":0,"docs":{},"f":{"a":{"df":0,"docs":{},"l":{"df":0,"docs":{},"s":{"df":1,"docs":{"73":{"tf":1.0}}}}},"df":0,"docs":{}},"t":{"df":0,"docs":{},"r":{"df":0,"docs":{},"u":{"df":1,"docs":{"73":{"tf":1.0}}}}}},"df":0,"docs":{}}}},"k":{"df":3,"docs":{"45":{"tf":1.4142135623730951},"47":{"tf":1.7320508075688772},"59":{"tf":3.3166247903554}}},"l":{".":{"df":0,"docs":{},"l":{"df":0,"docs":{},"e":{"df":0,"docs":{},"n":{"df":0,"docs":{},"g":{"df":0,"docs":{},"t":{"df":0,"docs":{},"h":{"df":1,"docs":{"46":{"tf":1.0}}}}}}}}},"df":1,"docs":{"46":{"tf":3.1622776601683795}},"e":{"a":{"df":0,"docs":{},"n":{".":{"df":0,"docs":{},"m":{"df":0,"docs":{},"v":{"a":{"df":0,"docs":{},"r":{"df":0,"docs":{},"i":{"d":{".":{"df":0,"docs":{},"r":{"df":0,"docs":{},"e":{"df":0,"docs":{},"f":{"df":0,"docs":{},"l":{"df":1,"docs":{"61":{"tf":1.0}}}}},"f":{"df":0,"docs":{},"l":{"df":1,"docs":{"61":{"tf":1.0}}}}}},"df":0,"docs":{}},"df":0,"docs":{}}}},"df":0,"docs":{}}}},"4":{"df":3,"docs":{"0":{"tf":1.0},"19":{"tf":1.0},"30":{"tf":1.0}}},"df":8,"docs":{"0":{"tf":1.0},"17":{"tf":1.0},"2":{"tf":2.0},"44":{"tf":1.0},"49":{"tf":1.0},"7":{"tf":1.0},"73":{"tf":1.0},"77":{"tf":1.0}}}},"df":0,"docs":{},"f":{"df":0,"docs":{},"t":{"df":3,"docs":{"20":{"tf":1.0},"27":{"tf":1.0},"50":{"tf":2.0}}}}},"i":{"df":0,"docs":{},"n":{"a":{"df":0,"docs":{},"r":{"df":0,"docs":{},"i":{"df":0,"docs":{},"t":{"df":0,"docs":{},"h":{"df":5,"docs":{"51":{"tf":3.0},"52":{"tf":1.4142135623730951},"53":{"tf":1.7320508075688772},"54":{"tf":1.0},"73":{"tf":1.4142135623730951}}}}}}},"df":0,"docs":{},"e":{"a":{"df":0,"docs":{},"r":{"df":2,"docs":{"51":{"tf":1.0},"53":{"tf":1.0}}}},"df":0,"docs":{}}},"s":{"df":0,"docs":{},"t":{".":{"df":0,"docs":{},"l":{"df":0,"docs":{},"e":{"df":0,"docs":{},"n":{"df":0,"docs":{},"g":{"df":0,"docs":{},"t":{"df":0,"docs":{},"h":{"df":1,"docs":{"46":{"tf":1.7320508075688772}}}}}}}}},"df":1,"docs":{"46":{"tf":1.7320508075688772}}}}},"o":{"df":0,"docs":{},"s":{"df":0,"docs":{},"s":{"df":1,"docs":{"77":{"tf":1.0}}}}}},"m":{"a":{"df":0,"docs":{},"t":{"c":{"df":0,"docs":{},"h":{"df":1,"docs":{"47":{"tf":1.0}}}},"df":0,"docs":{},"h":{"df":0,"docs":{},"e":{"df":0,"docs":{},"m":{"a":{"df":0,"docs":{},"t":{"df":1,"docs":{"2":{"tf":1.0}}}},"df":0,"docs":{}}},"l":{"df":0,"docs":{},"i":{"b":{".":{"d":{"a":{"df":0,"docs":{},"t":{"a":{".":{"df":0,"docs":{},"n":{"a":{"df":0,"docs":{},"t":{".":{"b":{"a":{"df":0,"docs":{},"s":{"df":1,"docs":{"60":{"tf":1.0}}}},"df":0,"docs":{}},"df":0,"docs":{}},"df":0,"docs":{}}},"df":0,"docs":{}},"s":{"df":0,"docs":{},"e":{"df":0,"docs":{},"t":{"df":0,"docs":{},"l":{"df":0,"docs":{},"i":{"df":0,"docs":{},"k":{"df":0,"docs":{},"e":{".":{"b":{"a":{"df":0,"docs":{},"s":{"df":1,"docs":{"37":{"tf":1.0}}}},"df":0,"docs":{}},"df":0,"docs":{}},"df":0,"docs":{}}}}}}}}},"df":0,"docs":{}},"df":0,"docs":{}}},"df":0,"docs":{}},"df":0,"docs":{},"t":{"a":{"c":{"df":0,"docs":{},"t":{"df":0,"docs":{},"i":{"c":{".":{"b":{"df":0,"docs":{},"y":{"c":{"df":0,"docs":{},"o":{"df":0,"docs":{},"n":{"df":0,"docs":{},"t":{"df":0,"docs":{},"r":{"a":{"df":1,"docs":{"16":{"tf":1.0}}},"df":0,"docs":{}}}}}},"df":0,"docs":{}}},"c":{"a":{"df":0,"docs":{},"s":{"df":2,"docs":{"22":{"tf":1.0},"45":{"tf":1.0}}}},"df":0,"docs":{},"h":{"df":0,"docs":{},"o":{"df":0,"docs":{},"o":{"df":0,"docs":{},"s":{"df":1,"docs":{"24":{"tf":1.0}}}}}},"o":{"df":0,"docs":{},"n":{"df":0,"docs":{},"v":{"df":0,"docs":{},"e":{"df":0,"docs":{},"r":{"df":0,"docs":{},"t":{"df":1,"docs":{"31":{"tf":1.0}}}}}}}}},"df":0,"docs":{},"g":{"c":{"df":0,"docs":{},"o":{"df":0,"docs":{},"n":{"df":0,"docs":{},"g":{"df":0,"docs":{},"r":{"df":1,"docs":{"58":{"tf":1.0}}}}}}},"df":0,"docs":{}},"l":{"df":0,"docs":{},"e":{"df":0,"docs":{},"f":{"df":0,"docs":{},"t":{"df":0,"docs":{},"r":{"df":0,"docs":{},"i":{"df":0,"docs":{},"g":{"df":0,"docs":{},"h":{"df":0,"docs":{},"t":{"df":1,"docs":{"50":{"tf":1.0}}}}}}}}}},"i":{"b":{"df":0,"docs":{},"r":{"a":{"df":0,"docs":{},"r":{"df":0,"docs":{},"y":{"df":0,"docs":{},"s":{"df":0,"docs":{},"e":{"a":{"df":0,"docs":{},"r":{"c":{"df":0,"docs":{},"h":{"df":2,"docs":{"11":{"tf":1.0},"35":{"tf":1.0}}}},"df":0,"docs":{}}},"df":0,"docs":{}}}}}},"df":0,"docs":{}}},"df":0,"docs":{},"n":{"a":{"df":0,"docs":{},"r":{"df":0,"docs":{},"i":{"df":0,"docs":{},"t":{"df":0,"docs":{},"h":{"df":2,"docs":{"51":{"tf":1.0},"53":{"tf":1.0}}}}}}},"df":0,"docs":{}}}},"n":{"df":0,"docs":{},"t":{"df":0,"docs":{},"h":{"df":0,"docs":{},"r":{"df":0,"docs":{},"e":{"df":0,"docs":{},"w":{"df":0,"docs":{},"r":{"df":0,"docs":{},"i":{"df":0,"docs":{},"t":{"df":1,"docs":{"64":{"tf":1.0}}}}}}}}}}},"p":{"df":0,"docs":{},"u":{"df":0,"docs":{},"s":{"df":0,"docs":{},"h":{"df":0,"docs":{},"n":{"df":0,"docs":{},"e":{"df":0,"docs":{},"g":{"df":1,"docs":{"54":{"tf":1.0}}}}}}}}},"r":{"df":1,"docs":{"62":{"tf":1.0}},"e":{"df":0,"docs":{},"l":{"a":{"df":0,"docs":{},"t":{"df":0,"docs":{},"i":{"df":0,"docs":{},"o":{"df":0,"docs":{},"n":{".":{"df":0,"docs":{},"r":{"df":0,"docs":{},"f":{"df":0,"docs":{},"l":{"df":2,"docs":{"60":{"tf":1.0},"61":{"tf":1.4142135623730951}}}}}},"df":0,"docs":{}}}}}},"df":0,"docs":{}}}},"s":{"a":{"df":0,"docs":{},"y":{"df":1,"docs":{"65":{"tf":1.0}}}},"df":0,"docs":{},"o":{"df":0,"docs":{},"l":{"df":0,"docs":{},"v":{"df":0,"docs":{},"e":{"b":{"df":0,"docs":{},"y":{"df":0,"docs":{},"e":{"df":0,"docs":{},"l":{"df":0,"docs":{},"i":{"df":0,"docs":{},"m":{"df":1,"docs":{"5":{"tf":1.0}}}}}}}},"df":0,"docs":{}}}}}},"t":{"a":{"df":0,"docs":{},"u":{"df":0,"docs":{},"t":{"df":0,"docs":{},"o":{"df":1,"docs":{"75":{"tf":1.0}}}}}},"df":0,"docs":{}},"w":{"df":0,"docs":{},"l":{"df":0,"docs":{},"o":{"df":0,"docs":{},"g":{"df":1,"docs":{"77":{"tf":1.0}}}}}}},"df":0,"docs":{}},"df":0,"docs":{}}}},"df":0,"docs":{}},"df":0,"docs":{}}},"4":{"df":2,"docs":{"2":{"tf":1.0},"50":{"tf":1.0}}},"df":0,"docs":{}},"df":0,"docs":{}}}}}},"df":1,"docs":{"47":{"tf":1.7320508075688772}},"o":{"df":0,"docs":{},"n":{"df":0,"docs":{},"o":{"df":0,"docs":{},"i":{"d":{"df":0,"docs":{},"h":{"df":0,"docs":{},"o":{"df":0,"docs":{},"m":{".":{"df":0,"docs":{},"m":{"a":{"df":0,"docs":{},"p":{"_":{"df":0,"docs":{},"m":{"df":0,"docs":{},"u":{"df":0,"docs":{},"l":{"df":1,"docs":{"11":{"tf":1.0}}}}}},"df":0,"docs":{}}},"df":0,"docs":{}}},"df":0,"docs":{}}}}},"df":0,"docs":{}}}}},"u":{"df":0,"docs":{},"l":{"_":{"df":0,"docs":{},"i":{"df":0,"docs":{},"n":{"df":0,"docs":{},"v":{"_":{"df":0,"docs":{},"e":{"df":0,"docs":{},"q":{"_":{"df":0,"docs":{},"i":{"df":0,"docs":{},"f":{"df":0,"docs":{},"f":{"_":{"df":0,"docs":{},"e":{"df":0,"docs":{},"q":{"_":{"df":0,"docs":{},"m":{"df":0,"docs":{},"u":{"df":0,"docs":{},"l":{"df":1,"docs":{"64":{"tf":1.4142135623730951}}}}}},"df":0,"docs":{}}}},"df":0,"docs":{}}}}},"df":0,"docs":{}}}},"df":0,"docs":{}}}},"n":{"df":0,"docs":{},"e":{"df":0,"docs":{},"g":{"df":1,"docs":{"73":{"tf":1.0}}}}}},"df":0,"docs":{}}},"y":{"a":{"b":{"df":1,"docs":{"73":{"tf":2.23606797749979}}},"df":0,"docs":{}},"df":0,"docs":{},"e":{"df":0,"docs":{},"q":{".":{"df":0,"docs":{},"r":{"df":0,"docs":{},"e":{"df":0,"docs":{},"f":{"df":0,"docs":{},"l":{"df":1,"docs":{"60":{"tf":1.0}}}}}}},"df":1,"docs":{"60":{"tf":1.7320508075688772}}}}}},"n":{"a":{"df":0,"docs":{},"m":{"df":0,"docs":{},"e":{"df":11,"docs":{"23":{"tf":1.0},"26":{"tf":1.0},"37":{"tf":1.0},"48":{"tf":1.0},"51":{"tf":1.0},"53":{"tf":1.0},"54":{"tf":1.0},"58":{"tf":1.0},"60":{"tf":1.0},"75":{"tf":1.0},"77":{"tf":1.0}}}},"t":{".":{"d":{"df":0,"docs":{},"v":{"d":{"_":{"df":0,"docs":{},"i":{"df":0,"docs":{},"f":{"df":0,"docs":{},"f":{"_":{"d":{"df":0,"docs":{},"i":{"df":0,"docs":{},"v":{"_":{"df":0,"docs":{},"m":{"df":0,"docs":{},"u":{"df":0,"docs":{},"l":{"_":{"df":0,"docs":{},"e":{"df":0,"docs":{},"q":{"df":1,"docs":{"74":{"tf":1.0}}}}},"df":0,"docs":{}}}}},"df":0,"docs":{}}}},"df":0,"docs":{}},"df":0,"docs":{}}}}},"df":0,"docs":{}},"df":0,"docs":{}}},"df":0,"docs":{},"l":{"df":0,"docs":{},"t":{".":{"b":{"a":{"df":0,"docs":{},"s":{"df":1,"docs":{"35":{"tf":1.0}}}},"df":0,"docs":{}},"df":0,"docs":{}},"df":0,"docs":{}}},"m":{"df":0,"docs":{},"u":{"df":0,"docs":{},"l":{"_":{"a":{"df":0,"docs":{},"s":{"df":0,"docs":{},"s":{"df":0,"docs":{},"o":{"c":{"df":1,"docs":{"63":{"tf":1.4142135623730951}}},"df":0,"docs":{}}}}},"df":0,"docs":{}},"df":0,"docs":{}}}},"s":{"df":0,"docs":{},"t":{"df":0,"docs":{},"r":{"df":0,"docs":{},"o":{"df":0,"docs":{},"n":{"df":0,"docs":{},"g":{"_":{"df":0,"docs":{},"i":{"df":0,"docs":{},"n":{"d":{"df":0,"docs":{},"u":{"c":{"df":0,"docs":{},"t":{"df":0,"docs":{},"i":{"df":0,"docs":{},"o":{"df":0,"docs":{},"n":{"_":{"df":0,"docs":{},"o":{"df":0,"docs":{},"n":{"df":1,"docs":{"47":{"tf":1.0}}}}},"df":0,"docs":{}}}}}},"df":0,"docs":{}}},"df":0,"docs":{}}}},"df":0,"docs":{}}}}}}}},"df":15,"docs":{"12":{"tf":1.0},"28":{"tf":1.0},"29":{"tf":1.0},"31":{"tf":1.4142135623730951},"36":{"tf":1.0},"38":{"tf":1.4142135623730951},"44":{"tf":2.8284271247461903},"45":{"tf":1.0},"47":{"tf":1.4142135623730951},"48":{"tf":1.0},"53":{"tf":1.0},"60":{"tf":1.0},"63":{"tf":1.0},"72":{"tf":1.0},"77":{"tf":1.4142135623730951}}}},"df":8,"docs":{"44":{"tf":3.872983346207417},"45":{"tf":1.7320508075688772},"46":{"tf":2.0},"47":{"tf":3.3166247903554},"48":{"tf":1.7320508075688772},"59":{"tf":3.7416573867739413},"60":{"tf":2.449489742783178},"72":{"tf":2.23606797749979}},"e":{"df":0,"docs":{},"e":{"d":{"df":25,"docs":{"11":{"tf":1.0},"16":{"tf":1.0},"18":{"tf":1.0},"22":{"tf":1.0},"23":{"tf":1.0},"24":{"tf":1.0},"3":{"tf":1.0},"31":{"tf":1.0},"35":{"tf":1.0},"37":{"tf":1.0},"39":{"tf":1.0},"45":{"tf":1.0},"5":{"tf":1.0},"50":{"tf":1.0},"51":{"tf":1.0},"53":{"tf":1.0},"54":{"tf":1.0},"58":{"tf":1.0},"59":{"tf":1.0},"60":{"tf":1.0},"62":{"tf":1.0},"64":{"tf":1.0},"65":{"tf":1.0},"75":{"tf":1.0},"77":{"tf":1.0}}},"df":0,"docs":{}},"g":{"a":{"df":0,"docs":{},"t":{"df":1,"docs":{"54":{"tf":1.0}}}},"df":0,"docs":{}}},"l":{"df":0,"docs":{},"i":{"df":0,"docs":{},"n":{"a":{"df":0,"docs":{},"r":{"df":0,"docs":{},"i":{"df":0,"docs":{},"t":{"df":0,"docs":{},"h":{"df":1,"docs":{"53":{"tf":1.7320508075688772}}}}}}},"df":0,"docs":{}}}},"o":{"df":0,"docs":{},"n":{"c":{"df":0,"docs":{},"o":{"df":0,"docs":{},"m":{"df":0,"docs":{},"p":{"df":0,"docs":{},"u":{"df":0,"docs":{},"t":{"df":1,"docs":{"25":{"tf":1.0}}}}}}}},"df":1,"docs":{"53":{"tf":1.0}},"e":{"df":0,"docs":{},"m":{"df":0,"docs":{},"p":{"df":0,"docs":{},"t":{"df":0,"docs":{},"i":{"df":1,"docs":{"25":{"tf":1.0}}}}}}}}},"t":{"df":0,"docs":{},"h":{"_":{"df":0,"docs":{},"r":{"df":0,"docs":{},"e":{"df":0,"docs":{},"w":{"df":0,"docs":{},"r":{"df":0,"docs":{},"i":{"df":0,"docs":{},"t":{"df":2,"docs":{"59":{"tf":1.0},"64":{"tf":1.4142135623730951}}}}}}}}},"df":0,"docs":{}}}},"o":{"b":{"df":0,"docs":{},"t":{"a":{"df":0,"docs":{},"i":{"df":0,"docs":{},"n":{"df":1,"docs":{"59":{"tf":1.0}}}}},"df":0,"docs":{}}},"df":0,"docs":{},"n":{"df":0,"docs":{},"e":{"_":{"df":0,"docs":{},"m":{"df":0,"docs":{},"u":{"df":0,"docs":{},"l":{"df":1,"docs":{"64":{"tf":1.4142135623730951}}}}}},"df":0,"docs":{}}},"p":{"df":0,"docs":{},"e":{"df":0,"docs":{},"n":{"df":1,"docs":{"68":{"tf":1.0}}}},"t":{"df":0,"docs":{},"i":{"df":0,"docs":{},"o":{"df":0,"docs":{},"n":{"df":1,"docs":{"1":{"tf":1.0}}}}}}},"r":{".":{"df":0,"docs":{},"i":{"df":0,"docs":{},"n":{"df":0,"docs":{},"l":{"df":1,"docs":{"50":{"tf":1.4142135623730951}}},"r":{"df":1,"docs":{"50":{"tf":1.0}}}}}},"df":0,"docs":{}}},"p":{"(":{"0":{"df":1,"docs":{"47":{"tf":1.0}}},"df":0,"docs":{},"x":{"df":2,"docs":{"24":{"tf":1.4142135623730951},"48":{"tf":1.0}}}},"df":43,"docs":{"13":{"tf":1.7320508075688772},"15":{"tf":3.3166247903554},"16":{"tf":2.6457513110645907},"17":{"tf":2.8284271247461903},"18":{"tf":1.4142135623730951},"20":{"tf":2.449489742783178},"21":{"tf":1.7320508075688772},"22":{"tf":1.4142135623730951},"23":{"tf":3.0},"25":{"tf":2.449489742783178},"27":{"tf":3.0},"28":{"tf":1.0},"29":{"tf":2.6457513110645907},"33":{"tf":2.449489742783178},"35":{"tf":1.4142135623730951},"36":{"tf":1.7320508075688772},"39":{"tf":1.7320508075688772},"40":{"tf":3.0},"42":{"tf":2.23606797749979},"43":{"tf":1.4142135623730951},"44":{"tf":2.0},"46":{"tf":2.23606797749979},"47":{"tf":2.449489742783178},"48":{"tf":4.242640687119285},"49":{"tf":3.3166247903554},"5":{"tf":2.23606797749979},"50":{"tf":2.449489742783178},"54":{"tf":3.4641016151377544},"55":{"tf":2.0},"56":{"tf":2.23606797749979},"57":{"tf":2.6457513110645907},"59":{"tf":1.0},"6":{"tf":3.7416573867739413},"63":{"tf":1.7320508075688772},"65":{"tf":1.4142135623730951},"67":{"tf":2.23606797749979},"68":{"tf":1.4142135623730951},"7":{"tf":2.6457513110645907},"73":{"tf":1.7320508075688772},"74":{"tf":1.0},"75":{"tf":3.0},"76":{"tf":1.0},"9":{"tf":2.0}},"h":{"df":0,"docs":{},"r":{"a":{"df":0,"docs":{},"s":{"df":0,"docs":{},"e":{"b":{"df":0,"docs":{},"o":{"df":0,"docs":{},"o":{"df":0,"docs":{},"k":{"df":1,"docs":{"2":{"tf":1.0}}}}}},"df":0,"docs":{}}}},"df":0,"docs":{}}},"o":{"df":0,"docs":{},"s":{"df":0,"docs":{},"i":{"df":0,"docs":{},"t":{"df":2,"docs":{"44":{"tf":1.0},"45":{"tf":1.0}}}}}},"r":{"df":0,"docs":{},"o":{"df":0,"docs":{},"p":{"df":7,"docs":{"15":{"tf":1.0},"23":{"tf":1.0},"25":{"tf":1.0},"46":{"tf":1.0},"47":{"tf":1.0},"48":{"tf":1.0},"60":{"tf":1.0}}},"v":{"df":0,"docs":{},"e":{"df":2,"docs":{"19":{"tf":1.0},"30":{"tf":1.0}}}}}},"u":{"df":0,"docs":{},"s":{"df":0,"docs":{},"h":{"_":{"df":0,"docs":{},"n":{"df":0,"docs":{},"e":{"df":0,"docs":{},"g":{"df":1,"docs":{"54":{"tf":2.0}}}}}},"df":1,"docs":{"54":{"tf":1.0}}}}},"y":{"df":1,"docs":{"25":{"tf":1.4142135623730951}}}},"q":{"(":{"df":0,"docs":{},"i":{"df":1,"docs":{"48":{"tf":1.0}}}},"df":32,"docs":{"13":{"tf":1.0},"16":{"tf":2.23606797749979},"17":{"tf":2.0},"18":{"tf":1.4142135623730951},"20":{"tf":2.449489742783178},"21":{"tf":1.7320508075688772},"22":{"tf":1.4142135623730951},"23":{"tf":3.0},"27":{"tf":2.8284271247461903},"28":{"tf":1.0},"29":{"tf":1.0},"33":{"tf":1.4142135623730951},"35":{"tf":1.4142135623730951},"40":{"tf":2.6457513110645907},"42":{"tf":2.23606797749979},"44":{"tf":2.0},"48":{"tf":3.872983346207417},"49":{"tf":3.0},"5":{"tf":2.23606797749979},"50":{"tf":2.0},"54":{"tf":3.1622776601683795},"55":{"tf":1.4142135623730951},"56":{"tf":2.0},"57":{"tf":2.8284271247461903},"6":{"tf":3.4641016151377544},"63":{"tf":1.4142135623730951},"65":{"tf":1.4142135623730951},"67":{"tf":1.7320508075688772},"73":{"tf":1.7320508075688772},"74":{"tf":2.6457513110645907},"75":{"tf":2.23606797749979},"9":{"tf":2.0}}},"r":{"c":{"a":{"df":0,"docs":{},"s":{"df":0,"docs":{},"e":{"df":1,"docs":{"23":{"tf":2.0}}}}},"df":0,"docs":{}},"df":13,"docs":{"17":{"tf":2.449489742783178},"18":{"tf":1.4142135623730951},"20":{"tf":1.7320508075688772},"21":{"tf":1.7320508075688772},"22":{"tf":1.7320508075688772},"23":{"tf":2.0},"35":{"tf":1.4142135623730951},"40":{"tf":2.23606797749979},"48":{"tf":2.6457513110645907},"5":{"tf":1.4142135623730951},"57":{"tf":2.8284271247461903},"65":{"tf":1.4142135623730951},"75":{"tf":1.4142135623730951}},"e":{"c":{"df":0,"docs":{},"u":{"df":0,"docs":{},"r":{"df":0,"docs":{},"s":{"df":1,"docs":{"23":{"tf":1.0}}}}}},"df":0,"docs":{},"f":{"df":0,"docs":{},"i":{"df":0,"docs":{},"n":{"df":3,"docs":{"55":{"tf":1.7320508075688772},"56":{"tf":2.0},"57":{"tf":1.7320508075688772}}}},"l":{"df":2,"docs":{"60":{"tf":2.0},"61":{"tf":1.0}},"e":{"df":0,"docs":{},"x":{"df":1,"docs":{"60":{"tf":1.0}}}}}},"l":{"a":{"df":0,"docs":{},"t":{"df":1,"docs":{"58":{"tf":1.0}}}},"df":1,"docs":{"58":{"tf":2.23606797749979}}},"p":{"df":0,"docs":{},"e":{"a":{"df":0,"docs":{},"t":{"df":1,"docs":{"5":{"tf":1.4142135623730951}}}},"df":0,"docs":{}},"l":{"a":{"c":{"df":2,"docs":{"59":{"tf":2.0},"73":{"tf":1.0}}},"df":0,"docs":{}},"df":0,"docs":{}}}},"f":{"df":0,"docs":{},"l":{"df":5,"docs":{"51":{"tf":1.0},"60":{"tf":2.0},"61":{"tf":2.0},"74":{"tf":1.4142135623730951},"76":{"tf":1.0}}}},"i":{"df":0,"docs":{},"g":{"df":0,"docs":{},"h":{"df":0,"docs":{},"t":{"df":3,"docs":{"20":{"tf":1.0},"27":{"tf":1.0},"50":{"tf":1.7320508075688772}}}}},"n":{"df":0,"docs":{},"g":{"df":4,"docs":{"38":{"tf":1.0},"43":{"tf":1.0},"59":{"tf":2.0},"62":{"tf":2.23606797749979}}}}},"w":{"df":11,"docs":{"28":{"tf":1.0},"3":{"tf":1.0},"31":{"tf":1.0},"4":{"tf":1.0},"43":{"tf":1.0},"48":{"tf":1.0},"59":{"tf":1.4142135623730951},"63":{"tf":3.4641016151377544},"64":{"tf":1.0},"65":{"tf":1.0},"69":{"tf":1.0}}}},"s":{"a":{"df":0,"docs":{},"y":{"df":0,"docs":{},"s":{".":{"df":0,"docs":{},"n":{"df":0,"docs":{},"o":{"_":{"df":0,"docs":{},"v":{"df":0,"docs":{},"e":{"df":0,"docs":{},"r":{"df":0,"docs":{},"i":{"df":0,"docs":{},"f":{"df":0,"docs":{},"y":{"_":{"df":0,"docs":{},"i":{"df":0,"docs":{},"n":{"_":{"c":{"df":0,"docs":{},"i":{"df":1,"docs":{"66":{"tf":1.0}}}},"df":0,"docs":{}},"df":0,"docs":{}}}},"df":0,"docs":{}}}}}}}},"df":0,"docs":{}}},"v":{"df":0,"docs":{},"e":{"df":0,"docs":{},"r":{"df":0,"docs":{},"i":{"df":0,"docs":{},"f":{"df":0,"docs":{},"i":{"df":1,"docs":{"66":{"tf":1.0}}}}}}}}},"df":0,"docs":{}}}},"df":2,"docs":{"37":{"tf":2.449489742783178},"65":{"tf":1.4142135623730951}},"e":{"df":0,"docs":{},"t":{"_":{"df":0,"docs":{},"o":{"df":0,"docs":{},"p":{"df":0,"docs":{},"t":{"df":1,"docs":{"1":{"tf":1.0}}}}}},"df":1,"docs":{"37":{"tf":1.0}}}},"h":{"df":0,"docs":{},"o":{"df":0,"docs":{},"w":{"_":{"df":0,"docs":{},"t":{"df":0,"docs":{},"e":{"df":0,"docs":{},"r":{"df":0,"docs":{},"m":{"df":1,"docs":{"62":{"tf":1.4142135623730951}}}}}}},"df":15,"docs":{"16":{"tf":1.0},"26":{"tf":1.4142135623730951},"31":{"tf":1.0},"46":{"tf":1.4142135623730951},"48":{"tf":1.4142135623730951},"49":{"tf":1.0},"5":{"tf":1.7320508075688772},"54":{"tf":1.4142135623730951},"55":{"tf":1.0},"56":{"tf":1.0},"57":{"tf":2.6457513110645907},"6":{"tf":1.0},"67":{"tf":2.0},"73":{"tf":1.7320508075688772},"77":{"tf":1.4142135623730951}}}}},"i":{"df":0,"docs":{},"m":{"df":0,"docs":{},"p":{"_":{"a":{"df":0,"docs":{},"l":{"df":4,"docs":{"28":{"tf":1.0},"4":{"tf":1.0},"65":{"tf":1.0},"70":{"tf":1.4142135623730951}}}},"df":0,"docs":{}},"df":11,"docs":{"26":{"tf":1.4142135623730951},"3":{"tf":1.0},"44":{"tf":1.4142135623730951},"45":{"tf":1.4142135623730951},"62":{"tf":1.0},"65":{"tf":1.0},"68":{"tf":2.8284271247461903},"69":{"tf":1.4142135623730951},"70":{"tf":1.0},"71":{"tf":1.0},"73":{"tf":2.449489742783178}}}}},"o":{"df":0,"docs":{},"r":{"df":0,"docs":{},"r":{"df":0,"docs":{},"i":{"df":4,"docs":{"12":{"tf":2.0},"46":{"tf":1.4142135623730951},"47":{"tf":1.4142135623730951},"72":{"tf":2.0}}},"y":{"a":{"df":0,"docs":{},"x":{"df":1,"docs":{"12":{"tf":1.4142135623730951}}}},"df":0,"docs":{}}}}},"p":{"df":0,"docs":{},"l":{"df":0,"docs":{},"i":{"df":0,"docs":{},"t":{"df":1,"docs":{"73":{"tf":2.23606797749979}}}}}},"t":{"d":{".":{"df":0,"docs":{},"t":{"a":{"c":{"df":0,"docs":{},"t":{"df":0,"docs":{},"i":{"c":{".":{"df":0,"docs":{},"e":{"df":0,"docs":{},"x":{"df":0,"docs":{},"t":{"df":1,"docs":{"37":{"tf":1.0}}}}},"g":{"df":0,"docs":{},"u":{"a":{"df":0,"docs":{},"r":{"d":{"df":0,"docs":{},"e":{"df":0,"docs":{},"x":{"df":0,"docs":{},"p":{"df":0,"docs":{},"r":{"df":1,"docs":{"39":{"tf":1.0}}}}}}},"df":0,"docs":{}}},"df":0,"docs":{}}},"r":{"c":{"a":{"df":0,"docs":{},"s":{"df":1,"docs":{"23":{"tf":1.0}}}},"df":0,"docs":{}},"df":0,"docs":{},"e":{"df":0,"docs":{},"p":{"df":0,"docs":{},"l":{"a":{"c":{"df":1,"docs":{"59":{"tf":1.0}}},"df":0,"docs":{}},"df":0,"docs":{}}}}},"s":{"df":0,"docs":{},"h":{"df":0,"docs":{},"o":{"df":0,"docs":{},"w":{"df":0,"docs":{},"t":{"df":0,"docs":{},"e":{"df":0,"docs":{},"r":{"df":0,"docs":{},"m":{"df":1,"docs":{"18":{"tf":1.0}}}}}}}}}}},"df":0,"docs":{}},"df":0,"docs":{}}}},"df":0,"docs":{}},"df":0,"docs":{}}},"df":0,"docs":{}},"df":0,"docs":{}},"u":{"c":{"c":{"df":2,"docs":{"44":{"tf":2.6457513110645907},"46":{"tf":1.0}}},"df":0,"docs":{}},"df":0,"docs":{},"f":{"df":0,"docs":{},"f":{"df":0,"docs":{},"i":{"c":{"df":1,"docs":{"74":{"tf":2.6457513110645907}}},"df":0,"docs":{}}}}}},"t":{"a":{"c":{"df":0,"docs":{},"t":{"df":0,"docs":{},"i":{"c":{"df":1,"docs":{"2":{"tf":1.0}}},"df":0,"docs":{}}}},"df":0,"docs":{},"u":{"df":0,"docs":{},"t":{"df":0,"docs":{},"o":{"df":1,"docs":{"75":{"tf":2.449489742783178}},"l":{"df":0,"docs":{},"o":{"df":0,"docs":{},"g":{"df":1,"docs":{"75":{"tf":1.0}}}}}}}}},"df":2,"docs":{"12":{"tf":1.7320508075688772},"37":{"tf":2.449489742783178}},"h":{"df":0,"docs":{},"e":{"df":0,"docs":{},"o":{"df":0,"docs":{},"r":{"df":0,"docs":{},"e":{"df":0,"docs":{},"m":{"df":4,"docs":{"12":{"tf":1.0},"19":{"tf":1.0},"30":{"tf":1.0},"72":{"tf":1.0}}}},"i":{"df":1,"docs":{"2":{"tf":1.0}}}}}}},"r":{"df":0,"docs":{},"i":{"df":7,"docs":{"18":{"tf":1.0},"31":{"tf":1.0},"35":{"tf":1.4142135623730951},"51":{"tf":1.0},"53":{"tf":1.0},"65":{"tf":1.7320508075688772},"75":{"tf":1.4142135623730951}},"v":{"df":0,"docs":{},"i":{"a":{"df":0,"docs":{},"l":{"df":1,"docs":{"76":{"tf":2.449489742783178}}}},"df":0,"docs":{}}}},"u":{"df":0,"docs":{},"e":{"df":2,"docs":{"1":{"tf":1.0},"66":{"tf":1.4142135623730951}}}}},"y":{"df":0,"docs":{},"p":{"df":0,"docs":{},"e":{"df":5,"docs":{"2":{"tf":1.0},"37":{"tf":1.0},"60":{"tf":1.0},"61":{"tf":1.0},"68":{"tf":1.7320508075688772}}}}}},"u":{"df":2,"docs":{"60":{"tf":1.0},"68":{"tf":1.7320508075688772}},"n":{"df":0,"docs":{},"f":{"df":0,"docs":{},"o":{"df":0,"docs":{},"l":{"d":{"df":1,"docs":{"73":{"tf":1.0}}},"df":0,"docs":{}}}},"i":{"df":0,"docs":{},"v":{"df":0,"docs":{},"e":{"df":0,"docs":{},"r":{"df":0,"docs":{},"s":{"df":1,"docs":{"68":{"tf":1.0}}}}}}}},"s":{"df":2,"docs":{"24":{"tf":1.4142135623730951},"47":{"tf":1.0}}}},"v":{"a":{"df":0,"docs":{},"r":{"df":0,"docs":{},"i":{"a":{"b":{"df":0,"docs":{},"l":{"df":7,"docs":{"23":{"tf":1.0},"25":{"tf":1.0},"37":{"tf":1.4142135623730951},"47":{"tf":1.0},"61":{"tf":1.0},"64":{"tf":1.0},"68":{"tf":1.0}}}},"df":0,"docs":{}},"df":0,"docs":{}}}},"df":1,"docs":{"68":{"tf":1.7320508075688772}}},"w":{"a":{"df":0,"docs":{},"r":{"df":0,"docs":{},"n":{"df":1,"docs":{"1":{"tf":1.0}},"i":{"df":0,"docs":{},"n":{"df":0,"docs":{},"g":{"a":{"df":0,"docs":{},"s":{"df":0,"docs":{},"e":{"df":0,"docs":{},"r":{"df":0,"docs":{},"r":{"df":0,"docs":{},"o":{"df":0,"docs":{},"r":{"df":1,"docs":{"1":{"tf":1.0}}}}}}}}},"df":0,"docs":{}}}}}}},"df":0,"docs":{},"i":{"df":0,"docs":{},"t":{"df":0,"docs":{},"h":{"df":0,"docs":{},"o":{"df":0,"docs":{},"u":{"df":0,"docs":{},"t":{"df":1,"docs":{"77":{"tf":1.0}}}}}}}},"l":{"df":0,"docs":{},"o":{"df":0,"docs":{},"g":{"df":1,"docs":{"77":{"tf":1.7320508075688772}}}}}},"x":{")":{".":{"df":0,"docs":{},"p":{"df":0,"docs":{},"r":{"df":0,"docs":{},"o":{"df":0,"docs":{},"p":{"df":0,"docs":{},"e":{"df":0,"docs":{},"r":{"df":0,"docs":{},"t":{"df":0,"docs":{},"i":{"df":1,"docs":{"25":{"tf":1.0}}}}}}}}}},"v":{"a":{"df":0,"docs":{},"l":{"df":1,"docs":{"25":{"tf":1.0}}}},"df":0,"docs":{}}},"df":0,"docs":{}},"`":{"df":0,"docs":{},"が":{"df":0,"docs":{},"偶":{"df":0,"docs":{},"数":{"df":0,"docs":{},"の":{"df":0,"docs":{},"と":{"df":0,"docs":{},"き":{"`":{"3":{"df":1,"docs":{"43":{"tf":1.0}}},"df":0,"docs":{}},"df":0,"docs":{}}}}}}}},"df":24,"docs":{"12":{"tf":3.4641016151377544},"24":{"tf":3.1622776601683795},"25":{"tf":4.358898943540674},"26":{"tf":3.4641016151377544},"28":{"tf":2.6457513110645907},"29":{"tf":1.7320508075688772},"3":{"tf":1.0},"35":{"tf":1.7320508075688772},"36":{"tf":3.3166247903554},"37":{"tf":2.6457513110645907},"38":{"tf":3.872983346207417},"4":{"tf":1.0},"43":{"tf":3.4641016151377544},"48":{"tf":2.449489742783178},"51":{"tf":2.8284271247461903},"52":{"tf":1.4142135623730951},"54":{"tf":3.1622776601683795},"58":{"tf":2.23606797749979},"61":{"tf":1.7320508075688772},"62":{"tf":2.449489742783178},"65":{"tf":2.8284271247461903},"66":{"tf":1.4142135623730951},"72":{"tf":1.7320508075688772},"73":{"tf":5.196152422706632}}},"y":{"df":14,"docs":{"12":{"tf":3.4641016151377544},"24":{"tf":4.0},"25":{"tf":3.3166247903554},"3":{"tf":1.4142135623730951},"4":{"tf":1.4142135623730951},"43":{"tf":2.449489742783178},"48":{"tf":3.3166247903554},"51":{"tf":1.4142135623730951},"52":{"tf":1.4142135623730951},"54":{"tf":2.0},"62":{"tf":2.449489742783178},"65":{"tf":2.6457513110645907},"66":{"tf":2.0},"72":{"tf":1.7320508075688772}}},"z":{"df":6,"docs":{"3":{"tf":1.0},"4":{"tf":1.0},"43":{"tf":1.4142135623730951},"51":{"tf":1.4142135623730951},"65":{"tf":1.0},"72":{"tf":1.7320508075688772}},"e":{"df":0,"docs":{},"r":{"df":0,"docs":{},"o":{"df":2,"docs":{"44":{"tf":1.7320508075688772},"46":{"tf":1.0}}}}}}}},"breadcrumbs":{"root":{"0":{"df":15,"docs":{"12":{"tf":1.0},"26":{"tf":1.4142135623730951},"28":{"tf":1.7320508075688772},"31":{"tf":1.4142135623730951},"44":{"tf":2.0},"45":{"tf":1.0},"46":{"tf":1.4142135623730951},"47":{"tf":1.0},"51":{"tf":1.4142135623730951},"54":{"tf":1.4142135623730951},"58":{"tf":1.0},"61":{"tf":1.0},"72":{"tf":1.0},"73":{"tf":3.3166247903554},"74":{"tf":1.0}}},"1":{"0":{"0":{"df":1,"docs":{"62":{"tf":1.0}}},"df":0,"docs":{}},"2":{"df":1,"docs":{"51":{"tf":1.0}}},"3":{"df":2,"docs":{"61":{"tf":1.0},"74":{"tf":1.7320508075688772}}},"df":16,"docs":{"12":{"tf":1.7320508075688772},"26":{"tf":1.0},"28":{"tf":2.449489742783178},"35":{"tf":1.0},"36":{"tf":1.0},"44":{"tf":2.0},"46":{"tf":1.4142135623730951},"47":{"tf":1.0},"48":{"tf":2.8284271247461903},"52":{"tf":1.0},"54":{"tf":1.7320508075688772},"59":{"tf":1.0},"61":{"tf":1.4142135623730951},"64":{"tf":1.7320508075688772},"73":{"tf":1.4142135623730951},"76":{"tf":1.4142135623730951}}},"2":{"df":19,"docs":{"12":{"tf":3.0},"26":{"tf":3.1622776601683795},"29":{"tf":1.4142135623730951},"36":{"tf":1.0},"37":{"tf":1.0},"38":{"tf":1.4142135623730951},"43":{"tf":1.7320508075688772},"51":{"tf":1.4142135623730951},"52":{"tf":1.4142135623730951},"53":{"tf":1.4142135623730951},"58":{"tf":1.7320508075688772},"59":{"tf":2.6457513110645907},"61":{"tf":1.4142135623730951},"62":{"tf":2.8284271247461903},"64":{"tf":1.0},"72":{"tf":1.0},"73":{"tf":3.872983346207417},"74":{"tf":1.7320508075688772},"76":{"tf":1.0}},"回":{"df":0,"docs":{},"出":{"df":0,"docs":{},"現":{"df":0,"docs":{},"す":{"df":0,"docs":{},"る":{"df":0,"docs":{},"が":{"df":0,"docs":{},"，":{"2":{"df":1,"docs":{"64":{"tf":1.0}}},"df":0,"docs":{}}}}}}}}},"3":{"df":8,"docs":{"12":{"tf":1.0},"29":{"tf":1.0},"36":{"tf":1.0},"43":{"tf":1.4142135623730951},"51":{"tf":1.0},"61":{"tf":1.0},"74":{"tf":1.7320508075688772},"75":{"tf":1.0}}},"4":{"df":2,"docs":{"51":{"tf":1.4142135623730951},"59":{"tf":1.4142135623730951}},"│":{"0":{",":{"1":{",":{"2":{",":{"3":{"df":1,"docs":{"12":{"tf":1.0}}},"df":0,"docs":{}},"df":0,"docs":{}},"df":0,"docs":{}},"df":0,"docs":{}},"df":0,"docs":{}},"df":0,"docs":{}},"df":0,"docs":{}}},"5":{"df":1,"docs":{"59":{"tf":2.449489742783178}}},"7":{"0":{"df":2,"docs":{"61":{"tf":1.4142135623730951},"74":{"tf":2.449489742783178}}},"df":1,"docs":{"36":{"tf":1.0}}},"_":{"df":9,"docs":{"12":{"tf":1.0},"13":{"tf":1.0},"26":{"tf":1.0},"42":{"tf":1.0},"5":{"tf":1.0},"55":{"tf":1.0},"56":{"tf":1.4142135623730951},"57":{"tf":1.7320508075688772},"59":{"tf":1.7320508075688772}}},"a":{"b":{"df":0,"docs":{},"e":{"df":0,"docs":{},"l":{"df":1,"docs":{"77":{"tf":1.4142135623730951}}}}},"d":{"d":{"_":{"df":0,"docs":{},"z":{"df":0,"docs":{},"e":{"df":0,"docs":{},"r":{"df":0,"docs":{},"o":{"df":1,"docs":{"26":{"tf":1.4142135623730951}}}}}}},"df":0,"docs":{}},"df":0,"docs":{}},"df":0,"docs":{},"e":{"df":0,"docs":{},"s":{"df":0,"docs":{},"o":{"df":0,"docs":{},"p":{"df":6,"docs":{"3":{"tf":2.449489742783178},"37":{"tf":1.0},"4":{"tf":2.449489742783178},"65":{"tf":1.4142135623730951},"75":{"tf":1.4142135623730951},"76":{"tf":1.0}}}}}},"p":{"df":0,"docs":{},"p":{"df":0,"docs":{},"l":{"df":0,"docs":{},"i":{"df":16,"docs":{"10":{"tf":1.7320508075688772},"11":{"tf":2.23606797749979},"12":{"tf":2.23606797749979},"22":{"tf":1.4142135623730951},"23":{"tf":1.4142135623730951},"35":{"tf":1.4142135623730951},"4":{"tf":1.0},"5":{"tf":1.0},"50":{"tf":1.0},"56":{"tf":2.0},"6":{"tf":2.6457513110645907},"65":{"tf":2.0},"7":{"tf":1.7320508075688772},"74":{"tf":1.4142135623730951},"8":{"tf":1.4142135623730951},"9":{"tf":2.0}}},"y":{"_":{"a":{"df":0,"docs":{},"s":{"df":0,"docs":{},"s":{"df":0,"docs":{},"u":{"df":0,"docs":{},"m":{"df":0,"docs":{},"p":{"df":0,"docs":{},"t":{"df":2,"docs":{"10":{"tf":1.7320508075688772},"5":{"tf":2.8284271247461903}}}}}}}}},"df":0,"docs":{}},"df":0,"docs":{}}}}},"r":{"df":0,"docs":{},"i":{"df":0,"docs":{},"t":{"df":0,"docs":{},"h":{"df":0,"docs":{},"m":{"df":0,"docs":{},"e":{"df":0,"docs":{},"t":{"df":2,"docs":{"51":{"tf":1.0},"53":{"tf":1.0}}}}}}}}},"s":{"df":0,"docs":{},"s":{"df":0,"docs":{},"o":{"c":{"df":1,"docs":{"68":{"tf":1.4142135623730951}}},"df":0,"docs":{}},"u":{"df":0,"docs":{},"m":{"df":0,"docs":{},"p":{"df":0,"docs":{},"t":{"df":7,"docs":{"13":{"tf":2.23606797749979},"14":{"tf":1.4142135623730951},"15":{"tf":1.0},"34":{"tf":1.7320508075688772},"42":{"tf":1.0},"48":{"tf":1.0},"50":{"tf":1.4142135623730951}}}}}}}},"t":{"df":0,"docs":{},"t":{"df":0,"docs":{},"r":{"df":0,"docs":{},"i":{"b":{"df":0,"docs":{},"u":{"df":0,"docs":{},"t":{"df":2,"docs":{"60":{"tf":1.4142135623730951},"68":{"tf":1.0}}}}},"df":0,"docs":{}}}}}},"b":{"`":{"df":0,"docs":{},"と":{"`":{"df":0,"docs":{},"g":{"df":1,"docs":{"68":{"tf":1.0}}}},"df":0,"docs":{}}},"df":10,"docs":{"11":{"tf":2.0},"31":{"tf":2.0},"37":{"tf":2.449489742783178},"53":{"tf":1.7320508075688772},"58":{"tf":2.0},"63":{"tf":2.449489742783178},"64":{"tf":3.3166247903554},"68":{"tf":4.0},"73":{"tf":1.4142135623730951},"77":{"tf":4.123105625617661}},"o":{"df":0,"docs":{},"o":{"df":0,"docs":{},"l":{"df":1,"docs":{"66":{"tf":1.4142135623730951}}}}},"s":{"df":1,"docs":{"26":{"tf":1.7320508075688772}}},"y":{"_":{"c":{"a":{"df":0,"docs":{},"s":{"df":1,"docs":{"15":{"tf":2.449489742783178}}}},"df":0,"docs":{},"o":{"df":0,"docs":{},"n":{"df":0,"docs":{},"t":{"df":0,"docs":{},"r":{"a":{"df":1,"docs":{"16":{"tf":2.449489742783178}}},"df":0,"docs":{}}}}}},"df":0,"docs":{}},"df":0,"docs":{}}},"c":{"`":{"df":0,"docs":{},"の":{"df":0,"docs":{},"合":{"df":0,"docs":{},"成":{"df":0,"docs":{},"を":{"`":{"df":0,"docs":{},"f":{"df":1,"docs":{"68":{"tf":1.0}}}},"df":0,"docs":{}}}}}},"a":{"df":0,"docs":{},"l":{"c":{"df":2,"docs":{"19":{"tf":2.0},"59":{"tf":1.0}}},"df":0,"docs":{}},"s":{"df":0,"docs":{},"e":{"df":7,"docs":{"15":{"tf":1.4142135623730951},"20":{"tf":3.1622776601683795},"21":{"tf":2.8284271247461903},"22":{"tf":2.23606797749979},"23":{"tf":1.7320508075688772},"46":{"tf":1.4142135623730951},"73":{"tf":1.4142135623730951}}}},"t":{"df":0,"docs":{},"e":{"df":0,"docs":{},"g":{"df":0,"docs":{},"o":{"df":0,"docs":{},"r":{"df":0,"docs":{},"i":{"df":1,"docs":{"68":{"tf":1.4142135623730951}}},"y":{".":{"c":{"df":0,"docs":{},"o":{"df":0,"docs":{},"m":{"df":0,"docs":{},"p":{"df":1,"docs":{"68":{"tf":1.0}}}}}},"df":0,"docs":{},"h":{"df":0,"docs":{},"o":{"df":0,"docs":{},"g":{"df":1,"docs":{"68":{"tf":1.0}}}}},"{":{"df":0,"docs":{},"u":{"df":1,"docs":{"68":{"tf":1.0}}}}},"df":0,"docs":{}}}}}}}},"df":5,"docs":{"31":{"tf":2.0},"58":{"tf":1.4142135623730951},"63":{"tf":1.7320508075688772},"64":{"tf":1.4142135623730951},"68":{"tf":4.58257569495584}},"h":{"df":0,"docs":{},"o":{"df":0,"docs":{},"o":{"df":0,"docs":{},"s":{"df":2,"docs":{"24":{"tf":2.23606797749979},"25":{"tf":1.4142135623730951}}}}}},"i":{"df":1,"docs":{"66":{"tf":1.0}}},"l":{"a":{"df":0,"docs":{},"s":{"df":0,"docs":{},"s":{"df":1,"docs":{"68":{"tf":1.0}},"i":{"c":{"a":{"df":0,"docs":{},"l":{".":{"c":{"df":0,"docs":{},"h":{"df":0,"docs":{},"o":{"df":0,"docs":{},"i":{"c":{"df":1,"docs":{"25":{"tf":1.4142135623730951}}},"df":0,"docs":{}}}}},"df":0,"docs":{}},"df":0,"docs":{}}},"df":0,"docs":{}},"df":0,"docs":{}}}}},"df":0,"docs":{}},"o":{"df":0,"docs":{},"m":{"df":0,"docs":{},"p":{"_":{"a":{"df":0,"docs":{},"p":{"df":0,"docs":{},"p":{"df":0,"docs":{},"l":{"df":0,"docs":{},"i":{"df":2,"docs":{"4":{"tf":1.0},"65":{"tf":1.0}}}}}}},"df":0,"docs":{},"i":{"d":{"df":1,"docs":{"68":{"tf":1.4142135623730951}}},"df":0,"docs":{}}},"df":1,"docs":{"68":{"tf":2.6457513110645907}}}},"n":{"df":0,"docs":{},"g":{"df":0,"docs":{},"r":{"df":1,"docs":{"26":{"tf":3.0}},"u":{"df":0,"docs":{},"e":{"df":0,"docs":{},"n":{"c":{"df":1,"docs":{"26":{"tf":1.0}}},"df":0,"docs":{}}}}}},"s":{"df":0,"docs":{},"t":{"df":0,"docs":{},"r":{"df":0,"docs":{},"u":{"c":{"df":0,"docs":{},"t":{"df":0,"docs":{},"o":{"df":0,"docs":{},"r":{"df":4,"docs":{"27":{"tf":2.23606797749979},"28":{"tf":1.7320508075688772},"57":{"tf":2.8284271247461903},"67":{"tf":1.0}}}}}},"df":0,"docs":{}}}}},"t":{"df":0,"docs":{},"r":{"a":{"d":{"df":0,"docs":{},"i":{"c":{"df":0,"docs":{},"t":{"df":5,"docs":{"15":{"tf":1.0},"16":{"tf":1.0},"29":{"tf":2.6457513110645907},"49":{"tf":1.0},"76":{"tf":1.0}}}},"df":0,"docs":{}}},"df":0,"docs":{}},"df":0,"docs":{}}},"v":{"df":1,"docs":{"30":{"tf":2.0}},"e":{"df":0,"docs":{},"r":{"df":0,"docs":{},"t":{"df":1,"docs":{"31":{"tf":2.23606797749979}}}}}}}}},"d":{"df":3,"docs":{"58":{"tf":1.4142135623730951},"63":{"tf":1.7320508075688772},"68":{"tf":2.23606797749979}},"e":{"df":0,"docs":{},"f":{"df":4,"docs":{"38":{"tf":1.4142135623730951},"44":{"tf":1.0},"72":{"tf":1.0},"73":{"tf":1.0}}}},"o":{"df":0,"docs":{},"n":{"df":0,"docs":{},"e":{"df":4,"docs":{"12":{"tf":1.4142135623730951},"32":{"tf":2.0},"35":{"tf":1.0},"5":{"tf":1.0}}}}},"s":{"df":0,"docs":{},"i":{"df":0,"docs":{},"m":{"df":0,"docs":{},"p":{"df":2,"docs":{"38":{"tf":1.0},"71":{"tf":1.7320508075688772}}}}}}},"df":0,"docs":{},"e":{"df":2,"docs":{"63":{"tf":1.7320508075688772},"68":{"tf":1.4142135623730951}},"v":{"df":0,"docs":{},"e":{"df":0,"docs":{},"n":{"df":1,"docs":{"59":{"tf":1.7320508075688772}}}}},"x":{"a":{"c":{"df":0,"docs":{},"t":{"df":30,"docs":{"11":{"tf":1.0},"14":{"tf":1.7320508075688772},"17":{"tf":1.0},"18":{"tf":1.0},"20":{"tf":1.4142135623730951},"21":{"tf":1.4142135623730951},"23":{"tf":1.0},"24":{"tf":1.0},"25":{"tf":1.0},"26":{"tf":1.0},"27":{"tf":1.7320508075688772},"31":{"tf":1.4142135623730951},"33":{"tf":2.6457513110645907},"34":{"tf":1.7320508075688772},"35":{"tf":3.3166247903554},"39":{"tf":1.0},"40":{"tf":1.4142135623730951},"48":{"tf":1.0},"5":{"tf":1.0},"54":{"tf":1.0},"55":{"tf":1.4142135623730951},"57":{"tf":2.449489742783178},"6":{"tf":1.7320508075688772},"64":{"tf":1.0},"65":{"tf":2.23606797749979},"67":{"tf":1.4142135623730951},"7":{"tf":1.0},"74":{"tf":1.0},"75":{"tf":1.4142135623730951},"9":{"tf":1.7320508075688772}}}},"df":0,"docs":{},"m":{"df":0,"docs":{},"p":{"df":0,"docs":{},"l":{"df":61,"docs":{"11":{"tf":1.0},"13":{"tf":1.0},"15":{"tf":1.0},"16":{"tf":1.0},"17":{"tf":1.4142135623730951},"18":{"tf":1.0},"20":{"tf":1.0},"21":{"tf":1.0},"22":{"tf":1.0},"23":{"tf":1.4142135623730951},"24":{"tf":1.0},"25":{"tf":1.0},"26":{"tf":1.4142135623730951},"27":{"tf":1.4142135623730951},"28":{"tf":1.0},"29":{"tf":2.0},"3":{"tf":1.0},"31":{"tf":1.0},"33":{"tf":1.4142135623730951},"35":{"tf":1.4142135623730951},"36":{"tf":1.0},"37":{"tf":1.0},"38":{"tf":1.0},"39":{"tf":1.0},"4":{"tf":1.0},"40":{"tf":1.0},"42":{"tf":1.0},"43":{"tf":1.0},"44":{"tf":1.0},"45":{"tf":1.0},"46":{"tf":1.0},"47":{"tf":1.0},"48":{"tf":1.4142135623730951},"49":{"tf":1.0},"5":{"tf":1.4142135623730951},"50":{"tf":1.4142135623730951},"51":{"tf":1.4142135623730951},"52":{"tf":1.0},"53":{"tf":1.0},"54":{"tf":1.4142135623730951},"55":{"tf":1.0},"56":{"tf":1.0},"57":{"tf":1.4142135623730951},"58":{"tf":1.4142135623730951},"59":{"tf":1.0},"6":{"tf":1.4142135623730951},"60":{"tf":1.4142135623730951},"61":{"tf":1.7320508075688772},"62":{"tf":1.4142135623730951},"63":{"tf":1.0},"64":{"tf":1.0},"65":{"tf":1.4142135623730951},"67":{"tf":1.0},"68":{"tf":1.0},"7":{"tf":1.0},"73":{"tf":1.0},"74":{"tf":1.0},"75":{"tf":2.0},"76":{"tf":1.4142135623730951},"77":{"tf":1.0},"9":{"tf":1.0}}}}}},"df":0,"docs":{},"i":{"df":0,"docs":{},"s":{"df":0,"docs":{},"t":{"df":5,"docs":{"25":{"tf":1.0},"36":{"tf":2.449489742783178},"43":{"tf":1.0},"54":{"tf":1.0},"59":{"tf":1.0}}}}},"p":{"df":0,"docs":{},"l":{"df":0,"docs":{},"o":{"d":{"df":1,"docs":{"12":{"tf":1.4142135623730951}}},"df":0,"docs":{},"s":{"df":0,"docs":{},"i":{"df":0,"docs":{},"o":{"df":0,"docs":{},"n":{")":{"df":0,"docs":{},"と":{"df":0,"docs":{},"呼":{"df":0,"docs":{},"び":{"df":0,"docs":{},"ま":{"df":0,"docs":{},"す":{"df":0,"docs":{},"が":{"df":0,"docs":{},"，":{"c":{"df":0,"docs":{},"o":{"df":0,"docs":{},"n":{"df":0,"docs":{},"t":{"df":0,"docs":{},"r":{"a":{"d":{"df":0,"docs":{},"i":{"c":{"df":0,"docs":{},"t":{"df":1,"docs":{"29":{"tf":1.0}}}},"df":0,"docs":{}}},"df":0,"docs":{}},"df":0,"docs":{}}}}}},"df":0,"docs":{}}}}}}}}},"df":0,"docs":{}}}}}}}},"t":{"df":1,"docs":{"37":{"tf":2.449489742783178}},"e":{"df":0,"docs":{},"n":{"df":0,"docs":{},"s":{"df":0,"docs":{},"i":{"df":0,"docs":{},"o":{"df":0,"docs":{},"n":{"df":1,"docs":{"37":{"tf":1.0}}}}}}}}}}},"f":{"a":{"c":{"df":2,"docs":{"44":{"tf":2.6457513110645907},"45":{"tf":1.7320508075688772}}},"df":0,"docs":{},"l":{"df":0,"docs":{},"s":{"df":7,"docs":{"16":{"tf":1.4142135623730951},"29":{"tf":1.4142135623730951},"49":{"tf":2.0},"5":{"tf":1.0},"52":{"tf":1.0},"7":{"tf":1.7320508075688772},"76":{"tf":1.0}}}}},"df":12,"docs":{"11":{"tf":2.23606797749979},"24":{"tf":2.8284271247461903},"25":{"tf":3.0},"26":{"tf":3.7416573867739413},"3":{"tf":2.23606797749979},"31":{"tf":1.7320508075688772},"37":{"tf":1.7320508075688772},"38":{"tf":2.449489742783178},"4":{"tf":1.7320508075688772},"63":{"tf":1.7320508075688772},"65":{"tf":2.23606797749979},"68":{"tf":3.605551275463989}},"e":{"df":0,"docs":{},"r":{"df":0,"docs":{},"m":{"a":{"df":0,"docs":{},"t":{"df":1,"docs":{"72":{"tf":1.0}},"l":{"a":{"df":0,"docs":{},"s":{"df":0,"docs":{},"t":{"df":0,"docs":{},"t":{"df":0,"docs":{},"h":{"df":0,"docs":{},"e":{"df":0,"docs":{},"o":{"df":0,"docs":{},"r":{"df":0,"docs":{},"e":{"df":0,"docs":{},"m":{"df":1,"docs":{"72":{"tf":1.4142135623730951}}}}}}}}}}}},"df":0,"docs":{}}}},"df":0,"docs":{}}}},"l":{"df":0,"docs":{},"t":{"df":1,"docs":{"72":{"tf":1.0}}}},"u":{"df":0,"docs":{},"n":{"df":4,"docs":{"17":{"tf":1.0},"18":{"tf":1.0},"25":{"tf":1.4142135623730951},"38":{"tf":1.4142135623730951}},"e":{"df":0,"docs":{},"x":{"df":0,"docs":{},"t":{"df":1,"docs":{"38":{"tf":2.23606797749979}}}}}}}},"g":{"df":10,"docs":{"11":{"tf":1.7320508075688772},"24":{"tf":2.8284271247461903},"26":{"tf":2.23606797749979},"3":{"tf":1.7320508075688772},"37":{"tf":1.7320508075688772},"38":{"tf":2.449489742783178},"4":{"tf":1.4142135623730951},"64":{"tf":1.7320508075688772},"65":{"tf":1.7320508075688772},"68":{"tf":2.6457513110645907}},"e":{"_":{"df":0,"docs":{},"i":{"df":0,"docs":{},"f":{"df":0,"docs":{},"f":{"_":{"df":0,"docs":{},"l":{"df":1,"docs":{"73":{"tf":1.4142135623730951}}}},"df":0,"docs":{}}}}},"df":0,"docs":{},"n":{"df":0,"docs":{},"e":{"df":0,"docs":{},"r":{"a":{"df":0,"docs":{},"r":{"df":1,"docs":{"77":{"tf":1.0}}}},"df":1,"docs":{"46":{"tf":1.0}}}}}},"o":{"a":{"df":0,"docs":{},"l":{"df":1,"docs":{"27":{"tf":1.0}}}},"df":0,"docs":{}},"r":{"df":0,"docs":{},"o":{"df":0,"docs":{},"u":{"df":0,"docs":{},"p":{"df":2,"docs":{"11":{"tf":1.4142135623730951},"64":{"tf":1.0}}}}}},"u":{"a":{"df":0,"docs":{},"r":{"d":{"_":{"df":0,"docs":{},"h":{"df":0,"docs":{},"y":{"df":0,"docs":{},"p":{"df":8,"docs":{"15":{"tf":1.4142135623730951},"24":{"tf":1.4142135623730951},"39":{"tf":2.23606797749979},"46":{"tf":1.7320508075688772},"47":{"tf":1.0},"59":{"tf":1.4142135623730951},"73":{"tf":1.4142135623730951},"77":{"tf":1.7320508075688772}}}}}},"df":0,"docs":{}},"df":0,"docs":{}}},"df":0,"docs":{}}},"h":{".":{"df":0,"docs":{},"l":{"df":0,"docs":{},"e":{"df":0,"docs":{},"f":{"df":0,"docs":{},"t":{"df":1,"docs":{"27":{"tf":1.4142135623730951}}}}}},"r":{"df":0,"docs":{},"i":{"df":0,"docs":{},"g":{"df":0,"docs":{},"h":{"df":0,"docs":{},"t":{"df":1,"docs":{"27":{"tf":1.0}}}}}}}},"1":{"df":4,"docs":{"51":{"tf":1.0},"52":{"tf":1.0},"58":{"tf":2.0},"63":{"tf":1.4142135623730951}}},"2":{"df":4,"docs":{"51":{"tf":1.0},"52":{"tf":1.0},"58":{"tf":1.4142135623730951},"63":{"tf":1.4142135623730951}}},"a":{"b":{"df":1,"docs":{"63":{"tf":1.7320508075688772}}},"df":0,"docs":{}},"c":{"df":1,"docs":{"31":{"tf":1.4142135623730951}}},"df":31,"docs":{"11":{"tf":1.4142135623730951},"12":{"tf":1.0},"15":{"tf":1.0},"16":{"tf":2.0},"17":{"tf":1.0},"20":{"tf":2.23606797749979},"21":{"tf":1.7320508075688772},"22":{"tf":1.4142135623730951},"23":{"tf":2.449489742783178},"24":{"tf":1.4142135623730951},"25":{"tf":1.7320508075688772},"26":{"tf":2.0},"27":{"tf":1.4142135623730951},"29":{"tf":1.7320508075688772},"31":{"tf":3.0},"40":{"tf":1.4142135623730951},"46":{"tf":1.7320508075688772},"48":{"tf":1.4142135623730951},"49":{"tf":1.7320508075688772},"53":{"tf":1.0},"54":{"tf":1.4142135623730951},"56":{"tf":1.7320508075688772},"59":{"tf":1.7320508075688772},"6":{"tf":2.8284271247461903},"63":{"tf":2.449489742783178},"68":{"tf":3.1622776601683795},"73":{"tf":3.1622776601683795},"75":{"tf":1.4142135623730951},"76":{"tf":1.0},"77":{"tf":2.23606797749979},"9":{"tf":1.4142135623730951}},"e":{"a":{"d":{"df":1,"docs":{"5":{"tf":1.4142135623730951}}},"df":0,"docs":{}},"df":0,"docs":{},"l":{"df":0,"docs":{},"p":{"df":1,"docs":{"1":{"tf":1.0}}}}},"f":{"df":2,"docs":{"24":{"tf":2.0},"26":{"tf":1.4142135623730951}}},"g":{"df":1,"docs":{"24":{"tf":1.7320508075688772}},"f":{"df":0,"docs":{},"i":{"df":0,"docs":{},"n":{"df":0,"docs":{},"j":{"df":3,"docs":{"3":{"tf":1.0},"4":{"tf":1.4142135623730951},"65":{"tf":1.4142135623730951}}}}}}},"k":{"df":1,"docs":{"59":{"tf":2.6457513110645907}}},"n":{"df":2,"docs":{"59":{"tf":1.4142135623730951},"7":{"tf":2.0}},"e":{"_":{"df":0,"docs":{},"s":{"df":0,"docs":{},"t":{"df":1,"docs":{"25":{"tf":1.4142135623730951}}}}},"df":0,"docs":{}},"n":{"df":0,"docs":{},"p":{"df":1,"docs":{"15":{"tf":1.0}}}},"p":{"df":1,"docs":{"29":{"tf":1.0}}},"q":{"df":2,"docs":{"16":{"tf":1.4142135623730951},"49":{"tf":1.4142135623730951}}}},"o":{"df":0,"docs":{},"g":{"df":0,"docs":{},"e":{"df":1,"docs":{"68":{"tf":1.0}}}},"m":{"df":1,"docs":{"68":{"tf":4.0}}}},"p":{"df":27,"docs":{"13":{"tf":1.0},"15":{"tf":1.7320508075688772},"16":{"tf":1.0},"17":{"tf":2.0},"18":{"tf":2.0},"20":{"tf":1.4142135623730951},"21":{"tf":1.4142135623730951},"22":{"tf":1.4142135623730951},"23":{"tf":2.23606797749979},"27":{"tf":1.4142135623730951},"29":{"tf":1.0},"33":{"tf":2.8284271247461903},"39":{"tf":1.7320508075688772},"40":{"tf":1.7320508075688772},"42":{"tf":1.0},"48":{"tf":1.7320508075688772},"49":{"tf":2.0},"5":{"tf":1.4142135623730951},"50":{"tf":1.4142135623730951},"55":{"tf":1.4142135623730951},"56":{"tf":1.4142135623730951},"57":{"tf":2.0},"6":{"tf":2.23606797749979},"65":{"tf":1.4142135623730951},"67":{"tf":1.4142135623730951},"7":{"tf":1.4142135623730951},"9":{"tf":1.4142135623730951}},"q":{"df":10,"docs":{"17":{"tf":2.0},"18":{"tf":1.7320508075688772},"35":{"tf":1.4142135623730951},"40":{"tf":1.7320508075688772},"42":{"tf":1.4142135623730951},"48":{"tf":1.7320508075688772},"5":{"tf":1.7320508075688772},"56":{"tf":1.4142135623730951},"63":{"tf":2.0},"65":{"tf":1.4142135623730951}}},"r":{"df":4,"docs":{"20":{"tf":1.4142135623730951},"21":{"tf":1.4142135623730951},"22":{"tf":1.4142135623730951},"23":{"tf":1.4142135623730951}}}},"q":{"df":15,"docs":{"20":{"tf":1.4142135623730951},"21":{"tf":1.4142135623730951},"22":{"tf":1.4142135623730951},"23":{"tf":2.23606797749979},"27":{"tf":1.4142135623730951},"33":{"tf":1.7320508075688772},"35":{"tf":1.4142135623730951},"40":{"tf":1.7320508075688772},"42":{"tf":1.0},"48":{"tf":1.7320508075688772},"49":{"tf":1.4142135623730951},"5":{"tf":1.0},"55":{"tf":1.4142135623730951},"57":{"tf":2.0},"67":{"tf":1.4142135623730951}},"n":{"df":1,"docs":{"5":{"tf":1.4142135623730951}}},"r":{"df":11,"docs":{"17":{"tf":2.0},"18":{"tf":1.7320508075688772},"20":{"tf":1.4142135623730951},"21":{"tf":1.4142135623730951},"22":{"tf":1.4142135623730951},"23":{"tf":1.4142135623730951},"35":{"tf":1.4142135623730951},"40":{"tf":1.7320508075688772},"48":{"tf":1.7320508075688772},"5":{"tf":1.0},"65":{"tf":1.4142135623730951}}}},"r":{"df":2,"docs":{"57":{"tf":2.0},"65":{"tf":1.4142135623730951}}},"x":{"df":3,"docs":{"28":{"tf":1.4142135623730951},"43":{"tf":2.0},"73":{"tf":1.7320508075688772}}},"y":{"df":1,"docs":{"43":{"tf":1.4142135623730951}},"p":{"df":1,"docs":{"48":{"tf":1.0}}}}},"i":{"d":{"_":{"c":{"df":0,"docs":{},"o":{"df":0,"docs":{},"m":{"df":0,"docs":{},"p":{"df":1,"docs":{"68":{"tf":1.4142135623730951}}}}}},"df":0,"docs":{}},"df":2,"docs":{"51":{"tf":1.7320508075688772},"68":{"tf":2.449489742783178}}},"df":0,"docs":{},"f":{"df":0,"docs":{},"f":{".":{"df":0,"docs":{},"m":{"df":0,"docs":{},"p":{"df":0,"docs":{},"r":{"df":1,"docs":{"74":{"tf":1.0}}}}}},"df":0,"docs":{}}},"h":{"df":4,"docs":{"44":{"tf":1.0},"45":{"tf":1.7320508075688772},"46":{"tf":1.4142135623730951},"47":{"tf":1.4142135623730951}}},"m":{"df":0,"docs":{},"p":{"df":0,"docs":{},"o":{"df":0,"docs":{},"r":{"df":0,"docs":{},"t":{"df":26,"docs":{"11":{"tf":1.0},"16":{"tf":1.0},"18":{"tf":1.0},"22":{"tf":1.0},"23":{"tf":1.0},"24":{"tf":1.0},"3":{"tf":1.0},"31":{"tf":1.0},"35":{"tf":1.0},"37":{"tf":1.0},"39":{"tf":1.0},"45":{"tf":1.0},"5":{"tf":1.0},"50":{"tf":1.0},"51":{"tf":1.0},"53":{"tf":1.0},"54":{"tf":1.0},"58":{"tf":1.0},"59":{"tf":1.0},"60":{"tf":1.7320508075688772},"61":{"tf":1.0},"62":{"tf":1.0},"64":{"tf":1.0},"65":{"tf":1.0},"75":{"tf":1.0},"77":{"tf":1.0}}}}}}},"n":{"d":{"df":0,"docs":{},"u":{"c":{"df":0,"docs":{},"t":{"df":5,"docs":{"44":{"tf":2.6457513110645907},"45":{"tf":2.23606797749979},"46":{"tf":1.7320508075688772},"47":{"tf":1.4142135623730951},"60":{"tf":1.0}}}},"df":0,"docs":{}}},"df":0,"docs":{},"f":{"df":0,"docs":{},"i":{"df":0,"docs":{},"x":{"df":0,"docs":{},"r":{":":{"8":{"0":{"df":1,"docs":{"68":{"tf":1.0}}},"df":0,"docs":{}},"df":0,"docs":{}},"df":0,"docs":{}}}},"o":{"df":0,"docs":{},"v":{"df":0,"docs":{},"i":{"df":0,"docs":{},"e":{"df":0,"docs":{},"w":{"df":1,"docs":{"65":{"tf":1.0}}}}}}}},"j":{"df":0,"docs":{},"e":{"c":{"df":0,"docs":{},"t":{"df":3,"docs":{"3":{"tf":1.7320508075688772},"4":{"tf":1.7320508075688772},"65":{"tf":1.7320508075688772}}}},"df":0,"docs":{}}},"l":{"df":4,"docs":{"15":{"tf":1.0},"20":{"tf":1.7320508075688772},"21":{"tf":1.4142135623730951},"73":{"tf":1.0}}},"r":{"df":4,"docs":{"15":{"tf":1.0},"20":{"tf":1.7320508075688772},"21":{"tf":1.4142135623730951},"73":{"tf":1.0}}},"s":{"df":0,"docs":{},"e":{"df":0,"docs":{},"r":{"df":0,"docs":{},"t":{"df":1,"docs":{"20":{"tf":1.4142135623730951}}}}}},"t":{"df":5,"docs":{"26":{"tf":2.0},"54":{"tf":1.4142135623730951},"58":{"tf":1.4142135623730951},"59":{"tf":1.0},"73":{"tf":1.7320508075688772}},"r":{"df":0,"docs":{},"o":{"d":{"df":0,"docs":{},"u":{"c":{"df":1,"docs":{"48":{"tf":1.0}}},"df":0,"docs":{}}},"df":20,"docs":{"15":{"tf":1.0},"16":{"tf":1.0},"17":{"tf":1.0},"18":{"tf":1.0},"20":{"tf":1.0},"21":{"tf":1.0},"22":{"tf":1.0},"23":{"tf":1.4142135623730951},"25":{"tf":1.0},"28":{"tf":1.0},"3":{"tf":1.0},"37":{"tf":1.0},"4":{"tf":1.0},"40":{"tf":1.0},"48":{"tf":2.8284271247461903},"49":{"tf":2.0},"5":{"tf":1.0},"54":{"tf":1.0},"59":{"tf":1.0},"65":{"tf":1.0}}}}}},"t":{"df":0,"docs":{},"e":{"_":{"df":0,"docs":{},"f":{"a":{"df":0,"docs":{},"l":{"df":0,"docs":{},"s":{"df":1,"docs":{"73":{"tf":1.0}}}}},"df":0,"docs":{}},"t":{"df":0,"docs":{},"r":{"df":0,"docs":{},"u":{"df":1,"docs":{"73":{"tf":1.0}}}}}},"df":0,"docs":{}}}},"k":{"df":3,"docs":{"45":{"tf":1.4142135623730951},"47":{"tf":1.7320508075688772},"59":{"tf":3.3166247903554}}},"l":{".":{"df":0,"docs":{},"l":{"df":0,"docs":{},"e":{"df":0,"docs":{},"n":{"df":0,"docs":{},"g":{"df":0,"docs":{},"t":{"df":0,"docs":{},"h":{"df":1,"docs":{"46":{"tf":1.0}}}}}}}}},"df":1,"docs":{"46":{"tf":3.1622776601683795}},"e":{"a":{"df":0,"docs":{},"n":{".":{"df":0,"docs":{},"m":{"df":0,"docs":{},"v":{"a":{"df":0,"docs":{},"r":{"df":0,"docs":{},"i":{"d":{".":{"df":0,"docs":{},"r":{"df":0,"docs":{},"e":{"df":0,"docs":{},"f":{"df":0,"docs":{},"l":{"df":1,"docs":{"61":{"tf":1.0}}}}},"f":{"df":0,"docs":{},"l":{"df":1,"docs":{"61":{"tf":1.0}}}}}},"df":0,"docs":{}},"df":0,"docs":{}}}},"df":0,"docs":{}}}},"4":{"df":5,"docs":{"0":{"tf":1.7320508075688772},"1":{"tf":1.0},"19":{"tf":1.0},"2":{"tf":1.0},"30":{"tf":1.0}}},"df":8,"docs":{"0":{"tf":1.0},"17":{"tf":1.0},"2":{"tf":2.0},"44":{"tf":1.0},"49":{"tf":1.0},"7":{"tf":1.0},"73":{"tf":1.0},"77":{"tf":1.0}}}},"df":0,"docs":{},"f":{"df":0,"docs":{},"t":{"df":3,"docs":{"20":{"tf":1.0},"27":{"tf":1.0},"50":{"tf":2.449489742783178}}}}},"i":{"df":0,"docs":{},"n":{"a":{"df":0,"docs":{},"r":{"df":0,"docs":{},"i":{"df":0,"docs":{},"t":{"df":0,"docs":{},"h":{"df":5,"docs":{"51":{"tf":3.3166247903554},"52":{"tf":1.7320508075688772},"53":{"tf":1.7320508075688772},"54":{"tf":1.0},"73":{"tf":1.4142135623730951}}}}}}},"df":0,"docs":{},"e":{"a":{"df":0,"docs":{},"r":{"df":2,"docs":{"51":{"tf":1.0},"53":{"tf":1.0}}}},"df":0,"docs":{}}},"s":{"df":0,"docs":{},"t":{".":{"df":0,"docs":{},"l":{"df":0,"docs":{},"e":{"df":0,"docs":{},"n":{"df":0,"docs":{},"g":{"df":0,"docs":{},"t":{"df":0,"docs":{},"h":{"df":1,"docs":{"46":{"tf":1.7320508075688772}}}}}}}}},"df":1,"docs":{"46":{"tf":1.7320508075688772}}}}},"o":{"df":0,"docs":{},"s":{"df":0,"docs":{},"s":{"df":1,"docs":{"77":{"tf":1.0}}}}}},"m":{"a":{"df":0,"docs":{},"t":{"c":{"df":0,"docs":{},"h":{"df":1,"docs":{"47":{"tf":1.0}}}},"df":0,"docs":{},"h":{"df":0,"docs":{},"e":{"df":0,"docs":{},"m":{"a":{"df":0,"docs":{},"t":{"df":1,"docs":{"2":{"tf":1.0}}}},"df":0,"docs":{}}},"l":{"df":0,"docs":{},"i":{"b":{".":{"d":{"a":{"df":0,"docs":{},"t":{"a":{".":{"df":0,"docs":{},"n":{"a":{"df":0,"docs":{},"t":{".":{"b":{"a":{"df":0,"docs":{},"s":{"df":1,"docs":{"60":{"tf":1.0}}}},"df":0,"docs":{}},"df":0,"docs":{}},"df":0,"docs":{}}},"df":0,"docs":{}},"s":{"df":0,"docs":{},"e":{"df":0,"docs":{},"t":{"df":0,"docs":{},"l":{"df":0,"docs":{},"i":{"df":0,"docs":{},"k":{"df":0,"docs":{},"e":{".":{"b":{"a":{"df":0,"docs":{},"s":{"df":1,"docs":{"37":{"tf":1.0}}}},"df":0,"docs":{}},"df":0,"docs":{}},"df":0,"docs":{}}}}}}}}},"df":0,"docs":{}},"df":0,"docs":{}}},"df":0,"docs":{}},"df":0,"docs":{},"t":{"a":{"c":{"df":0,"docs":{},"t":{"df":0,"docs":{},"i":{"c":{".":{"b":{"df":0,"docs":{},"y":{"c":{"df":0,"docs":{},"o":{"df":0,"docs":{},"n":{"df":0,"docs":{},"t":{"df":0,"docs":{},"r":{"a":{"df":1,"docs":{"16":{"tf":1.0}}},"df":0,"docs":{}}}}}},"df":0,"docs":{}}},"c":{"a":{"df":0,"docs":{},"s":{"df":2,"docs":{"22":{"tf":1.0},"45":{"tf":1.0}}}},"df":0,"docs":{},"h":{"df":0,"docs":{},"o":{"df":0,"docs":{},"o":{"df":0,"docs":{},"s":{"df":1,"docs":{"24":{"tf":1.0}}}}}},"o":{"df":0,"docs":{},"n":{"df":0,"docs":{},"v":{"df":0,"docs":{},"e":{"df":0,"docs":{},"r":{"df":0,"docs":{},"t":{"df":1,"docs":{"31":{"tf":1.0}}}}}}}}},"df":0,"docs":{},"g":{"c":{"df":0,"docs":{},"o":{"df":0,"docs":{},"n":{"df":0,"docs":{},"g":{"df":0,"docs":{},"r":{"df":1,"docs":{"58":{"tf":1.0}}}}}}},"df":0,"docs":{}},"l":{"df":0,"docs":{},"e":{"df":0,"docs":{},"f":{"df":0,"docs":{},"t":{"df":0,"docs":{},"r":{"df":0,"docs":{},"i":{"df":0,"docs":{},"g":{"df":0,"docs":{},"h":{"df":0,"docs":{},"t":{"df":1,"docs":{"50":{"tf":1.0}}}}}}}}}},"i":{"b":{"df":0,"docs":{},"r":{"a":{"df":0,"docs":{},"r":{"df":0,"docs":{},"y":{"df":0,"docs":{},"s":{"df":0,"docs":{},"e":{"a":{"df":0,"docs":{},"r":{"c":{"df":0,"docs":{},"h":{"df":2,"docs":{"11":{"tf":1.0},"35":{"tf":1.0}}}},"df":0,"docs":{}}},"df":0,"docs":{}}}}}},"df":0,"docs":{}}},"df":0,"docs":{},"n":{"a":{"df":0,"docs":{},"r":{"df":0,"docs":{},"i":{"df":0,"docs":{},"t":{"df":0,"docs":{},"h":{"df":2,"docs":{"51":{"tf":1.0},"53":{"tf":1.0}}}}}}},"df":0,"docs":{}}}},"n":{"df":0,"docs":{},"t":{"df":0,"docs":{},"h":{"df":0,"docs":{},"r":{"df":0,"docs":{},"e":{"df":0,"docs":{},"w":{"df":0,"docs":{},"r":{"df":0,"docs":{},"i":{"df":0,"docs":{},"t":{"df":1,"docs":{"64":{"tf":1.0}}}}}}}}}}},"p":{"df":0,"docs":{},"u":{"df":0,"docs":{},"s":{"df":0,"docs":{},"h":{"df":0,"docs":{},"n":{"df":0,"docs":{},"e":{"df":0,"docs":{},"g":{"df":1,"docs":{"54":{"tf":1.0}}}}}}}}},"r":{"df":1,"docs":{"62":{"tf":1.0}},"e":{"df":0,"docs":{},"l":{"a":{"df":0,"docs":{},"t":{"df":0,"docs":{},"i":{"df":0,"docs":{},"o":{"df":0,"docs":{},"n":{".":{"df":0,"docs":{},"r":{"df":0,"docs":{},"f":{"df":0,"docs":{},"l":{"df":2,"docs":{"60":{"tf":1.0},"61":{"tf":1.4142135623730951}}}}}},"df":0,"docs":{}}}}}},"df":0,"docs":{}}}},"s":{"a":{"df":0,"docs":{},"y":{"df":1,"docs":{"65":{"tf":1.0}}}},"df":0,"docs":{},"o":{"df":0,"docs":{},"l":{"df":0,"docs":{},"v":{"df":0,"docs":{},"e":{"b":{"df":0,"docs":{},"y":{"df":0,"docs":{},"e":{"df":0,"docs":{},"l":{"df":0,"docs":{},"i":{"df":0,"docs":{},"m":{"df":1,"docs":{"5":{"tf":1.0}}}}}}}},"df":0,"docs":{}}}}}},"t":{"a":{"df":0,"docs":{},"u":{"df":0,"docs":{},"t":{"df":0,"docs":{},"o":{"df":1,"docs":{"75":{"tf":1.0}}}}}},"df":0,"docs":{}},"w":{"df":0,"docs":{},"l":{"df":0,"docs":{},"o":{"df":0,"docs":{},"g":{"df":1,"docs":{"77":{"tf":1.0}}}}}}},"df":0,"docs":{}},"df":0,"docs":{}}}},"df":0,"docs":{}},"df":0,"docs":{}}},"4":{"df":2,"docs":{"2":{"tf":1.0},"50":{"tf":1.0}}},"df":0,"docs":{}},"df":0,"docs":{}}}}}},"df":1,"docs":{"47":{"tf":1.7320508075688772}},"o":{"df":0,"docs":{},"n":{"df":0,"docs":{},"o":{"df":0,"docs":{},"i":{"d":{"df":0,"docs":{},"h":{"df":0,"docs":{},"o":{"df":0,"docs":{},"m":{".":{"df":0,"docs":{},"m":{"a":{"df":0,"docs":{},"p":{"_":{"df":0,"docs":{},"m":{"df":0,"docs":{},"u":{"df":0,"docs":{},"l":{"df":1,"docs":{"11":{"tf":1.0}}}}}},"df":0,"docs":{}}},"df":0,"docs":{}}},"df":0,"docs":{}}}}},"df":0,"docs":{}}}}},"u":{"df":0,"docs":{},"l":{"_":{"df":0,"docs":{},"i":{"df":0,"docs":{},"n":{"df":0,"docs":{},"v":{"_":{"df":0,"docs":{},"e":{"df":0,"docs":{},"q":{"_":{"df":0,"docs":{},"i":{"df":0,"docs":{},"f":{"df":0,"docs":{},"f":{"_":{"df":0,"docs":{},"e":{"df":0,"docs":{},"q":{"_":{"df":0,"docs":{},"m":{"df":0,"docs":{},"u":{"df":0,"docs":{},"l":{"df":1,"docs":{"64":{"tf":1.4142135623730951}}}}}},"df":0,"docs":{}}}},"df":0,"docs":{}}}}},"df":0,"docs":{}}}},"df":0,"docs":{}}}},"n":{"df":0,"docs":{},"e":{"df":0,"docs":{},"g":{"df":1,"docs":{"73":{"tf":1.0}}}}}},"df":0,"docs":{}}},"y":{"a":{"b":{"df":1,"docs":{"73":{"tf":2.23606797749979}}},"df":0,"docs":{}},"df":0,"docs":{},"e":{"df":0,"docs":{},"q":{".":{"df":0,"docs":{},"r":{"df":0,"docs":{},"e":{"df":0,"docs":{},"f":{"df":0,"docs":{},"l":{"df":1,"docs":{"60":{"tf":1.0}}}}}}},"df":1,"docs":{"60":{"tf":1.7320508075688772}}}}}},"n":{"a":{"df":0,"docs":{},"m":{"df":0,"docs":{},"e":{"df":11,"docs":{"23":{"tf":1.0},"26":{"tf":1.0},"37":{"tf":1.0},"48":{"tf":1.0},"51":{"tf":1.0},"53":{"tf":1.0},"54":{"tf":1.0},"58":{"tf":1.0},"60":{"tf":1.0},"75":{"tf":1.0},"77":{"tf":1.0}}}},"t":{".":{"d":{"df":0,"docs":{},"v":{"d":{"_":{"df":0,"docs":{},"i":{"df":0,"docs":{},"f":{"df":0,"docs":{},"f":{"_":{"d":{"df":0,"docs":{},"i":{"df":0,"docs":{},"v":{"_":{"df":0,"docs":{},"m":{"df":0,"docs":{},"u":{"df":0,"docs":{},"l":{"_":{"df":0,"docs":{},"e":{"df":0,"docs":{},"q":{"df":1,"docs":{"74":{"tf":1.0}}}}},"df":0,"docs":{}}}}},"df":0,"docs":{}}}},"df":0,"docs":{}},"df":0,"docs":{}}}}},"df":0,"docs":{}},"df":0,"docs":{}}},"df":0,"docs":{},"l":{"df":0,"docs":{},"t":{".":{"b":{"a":{"df":0,"docs":{},"s":{"df":1,"docs":{"35":{"tf":1.0}}}},"df":0,"docs":{}},"df":0,"docs":{}},"df":0,"docs":{}}},"m":{"df":0,"docs":{},"u":{"df":0,"docs":{},"l":{"_":{"a":{"df":0,"docs":{},"s":{"df":0,"docs":{},"s":{"df":0,"docs":{},"o":{"c":{"df":1,"docs":{"63":{"tf":1.4142135623730951}}},"df":0,"docs":{}}}}},"df":0,"docs":{}},"df":0,"docs":{}}}},"s":{"df":0,"docs":{},"t":{"df":0,"docs":{},"r":{"df":0,"docs":{},"o":{"df":0,"docs":{},"n":{"df":0,"docs":{},"g":{"_":{"df":0,"docs":{},"i":{"df":0,"docs":{},"n":{"d":{"df":0,"docs":{},"u":{"c":{"df":0,"docs":{},"t":{"df":0,"docs":{},"i":{"df":0,"docs":{},"o":{"df":0,"docs":{},"n":{"_":{"df":0,"docs":{},"o":{"df":0,"docs":{},"n":{"df":1,"docs":{"47":{"tf":1.0}}}}},"df":0,"docs":{}}}}}},"df":0,"docs":{}}},"df":0,"docs":{}}}},"df":0,"docs":{}}}}}}}},"df":15,"docs":{"12":{"tf":1.0},"28":{"tf":1.0},"29":{"tf":1.0},"31":{"tf":1.4142135623730951},"36":{"tf":1.0},"38":{"tf":1.4142135623730951},"44":{"tf":2.8284271247461903},"45":{"tf":1.0},"47":{"tf":1.4142135623730951},"48":{"tf":1.0},"53":{"tf":1.0},"60":{"tf":1.0},"63":{"tf":1.0},"72":{"tf":1.0},"77":{"tf":1.4142135623730951}}}},"df":8,"docs":{"44":{"tf":3.872983346207417},"45":{"tf":1.7320508075688772},"46":{"tf":2.0},"47":{"tf":3.3166247903554},"48":{"tf":1.7320508075688772},"59":{"tf":3.7416573867739413},"60":{"tf":2.449489742783178},"72":{"tf":2.23606797749979}},"e":{"df":0,"docs":{},"e":{"d":{"df":25,"docs":{"11":{"tf":1.0},"16":{"tf":1.0},"18":{"tf":1.0},"22":{"tf":1.0},"23":{"tf":1.0},"24":{"tf":1.0},"3":{"tf":1.0},"31":{"tf":1.0},"35":{"tf":1.0},"37":{"tf":1.0},"39":{"tf":1.0},"45":{"tf":1.0},"5":{"tf":1.0},"50":{"tf":1.0},"51":{"tf":1.0},"53":{"tf":1.0},"54":{"tf":1.0},"58":{"tf":1.0},"59":{"tf":1.0},"60":{"tf":1.0},"62":{"tf":1.0},"64":{"tf":1.0},"65":{"tf":1.0},"75":{"tf":1.0},"77":{"tf":1.0}}},"df":0,"docs":{}},"g":{"a":{"df":0,"docs":{},"t":{"df":1,"docs":{"54":{"tf":1.0}}}},"df":0,"docs":{}}},"l":{"df":0,"docs":{},"i":{"df":0,"docs":{},"n":{"a":{"df":0,"docs":{},"r":{"df":0,"docs":{},"i":{"df":0,"docs":{},"t":{"df":0,"docs":{},"h":{"df":1,"docs":{"53":{"tf":2.23606797749979}}}}}}},"df":0,"docs":{}}}},"o":{"df":0,"docs":{},"n":{"c":{"df":0,"docs":{},"o":{"df":0,"docs":{},"m":{"df":0,"docs":{},"p":{"df":0,"docs":{},"u":{"df":0,"docs":{},"t":{"df":1,"docs":{"25":{"tf":1.0}}}}}}}},"df":1,"docs":{"53":{"tf":1.0}},"e":{"df":0,"docs":{},"m":{"df":0,"docs":{},"p":{"df":0,"docs":{},"t":{"df":0,"docs":{},"i":{"df":1,"docs":{"25":{"tf":1.0}}}}}}}}},"t":{"df":0,"docs":{},"h":{"_":{"df":0,"docs":{},"r":{"df":0,"docs":{},"e":{"df":0,"docs":{},"w":{"df":0,"docs":{},"r":{"df":0,"docs":{},"i":{"df":0,"docs":{},"t":{"df":2,"docs":{"59":{"tf":1.0},"64":{"tf":1.7320508075688772}}}}}}}}},"df":0,"docs":{}}}},"o":{"b":{"df":0,"docs":{},"t":{"a":{"df":0,"docs":{},"i":{"df":0,"docs":{},"n":{"df":1,"docs":{"59":{"tf":1.0}}}}},"df":0,"docs":{}}},"df":0,"docs":{},"n":{"df":0,"docs":{},"e":{"_":{"df":0,"docs":{},"m":{"df":0,"docs":{},"u":{"df":0,"docs":{},"l":{"df":1,"docs":{"64":{"tf":1.4142135623730951}}}}}},"df":0,"docs":{}}},"p":{"df":0,"docs":{},"e":{"df":0,"docs":{},"n":{"df":1,"docs":{"68":{"tf":1.0}}}},"t":{"df":0,"docs":{},"i":{"df":0,"docs":{},"o":{"df":0,"docs":{},"n":{"df":1,"docs":{"1":{"tf":1.0}}}}}}},"r":{".":{"df":0,"docs":{},"i":{"df":0,"docs":{},"n":{"df":0,"docs":{},"l":{"df":1,"docs":{"50":{"tf":1.4142135623730951}}},"r":{"df":1,"docs":{"50":{"tf":1.0}}}}}},"df":0,"docs":{}}},"p":{"(":{"0":{"df":1,"docs":{"47":{"tf":1.0}}},"df":0,"docs":{},"x":{"df":2,"docs":{"24":{"tf":1.4142135623730951},"48":{"tf":1.0}}}},"df":43,"docs":{"13":{"tf":1.7320508075688772},"15":{"tf":3.3166247903554},"16":{"tf":2.6457513110645907},"17":{"tf":2.8284271247461903},"18":{"tf":1.4142135623730951},"20":{"tf":2.449489742783178},"21":{"tf":1.7320508075688772},"22":{"tf":1.4142135623730951},"23":{"tf":3.0},"25":{"tf":2.449489742783178},"27":{"tf":3.0},"28":{"tf":1.0},"29":{"tf":2.6457513110645907},"33":{"tf":2.449489742783178},"35":{"tf":1.4142135623730951},"36":{"tf":1.7320508075688772},"39":{"tf":1.7320508075688772},"40":{"tf":3.0},"42":{"tf":2.23606797749979},"43":{"tf":1.4142135623730951},"44":{"tf":2.0},"46":{"tf":2.23606797749979},"47":{"tf":2.449489742783178},"48":{"tf":4.242640687119285},"49":{"tf":3.3166247903554},"5":{"tf":2.23606797749979},"50":{"tf":2.449489742783178},"54":{"tf":3.4641016151377544},"55":{"tf":2.0},"56":{"tf":2.23606797749979},"57":{"tf":2.6457513110645907},"59":{"tf":1.0},"6":{"tf":3.7416573867739413},"63":{"tf":1.7320508075688772},"65":{"tf":1.4142135623730951},"67":{"tf":2.23606797749979},"68":{"tf":1.4142135623730951},"7":{"tf":2.6457513110645907},"73":{"tf":1.7320508075688772},"74":{"tf":1.0},"75":{"tf":3.0},"76":{"tf":1.0},"9":{"tf":2.0}},"h":{"df":0,"docs":{},"r":{"a":{"df":0,"docs":{},"s":{"df":0,"docs":{},"e":{"b":{"df":0,"docs":{},"o":{"df":0,"docs":{},"o":{"df":0,"docs":{},"k":{"df":1,"docs":{"2":{"tf":1.0}}}}}},"df":0,"docs":{}}}},"df":0,"docs":{}}},"o":{"df":0,"docs":{},"s":{"df":0,"docs":{},"i":{"df":0,"docs":{},"t":{"df":2,"docs":{"44":{"tf":1.0},"45":{"tf":1.0}}}}}},"r":{"df":0,"docs":{},"o":{"df":0,"docs":{},"p":{"df":7,"docs":{"15":{"tf":1.0},"23":{"tf":1.0},"25":{"tf":1.0},"46":{"tf":1.0},"47":{"tf":1.0},"48":{"tf":1.0},"60":{"tf":1.0}}},"v":{"df":0,"docs":{},"e":{"df":2,"docs":{"19":{"tf":1.0},"30":{"tf":1.0}}}}}},"u":{"df":0,"docs":{},"s":{"df":0,"docs":{},"h":{"_":{"df":0,"docs":{},"n":{"df":0,"docs":{},"e":{"df":0,"docs":{},"g":{"df":1,"docs":{"54":{"tf":2.449489742783178}}}}}},"df":1,"docs":{"54":{"tf":1.0}}}}},"y":{"df":1,"docs":{"25":{"tf":1.4142135623730951}}}},"q":{"(":{"df":0,"docs":{},"i":{"df":1,"docs":{"48":{"tf":1.0}}}},"df":32,"docs":{"13":{"tf":1.0},"16":{"tf":2.23606797749979},"17":{"tf":2.0},"18":{"tf":1.4142135623730951},"20":{"tf":2.449489742783178},"21":{"tf":1.7320508075688772},"22":{"tf":1.4142135623730951},"23":{"tf":3.0},"27":{"tf":2.8284271247461903},"28":{"tf":1.0},"29":{"tf":1.0},"33":{"tf":1.4142135623730951},"35":{"tf":1.4142135623730951},"40":{"tf":2.6457513110645907},"42":{"tf":2.23606797749979},"44":{"tf":2.0},"48":{"tf":3.872983346207417},"49":{"tf":3.0},"5":{"tf":2.23606797749979},"50":{"tf":2.0},"54":{"tf":3.1622776601683795},"55":{"tf":1.4142135623730951},"56":{"tf":2.0},"57":{"tf":2.8284271247461903},"6":{"tf":3.4641016151377544},"63":{"tf":1.4142135623730951},"65":{"tf":1.4142135623730951},"67":{"tf":1.7320508075688772},"73":{"tf":1.7320508075688772},"74":{"tf":2.6457513110645907},"75":{"tf":2.23606797749979},"9":{"tf":2.0}}},"r":{"c":{"a":{"df":0,"docs":{},"s":{"df":0,"docs":{},"e":{"df":1,"docs":{"23":{"tf":2.23606797749979}}}}},"df":0,"docs":{}},"df":13,"docs":{"17":{"tf":2.449489742783178},"18":{"tf":1.4142135623730951},"20":{"tf":1.7320508075688772},"21":{"tf":1.7320508075688772},"22":{"tf":1.7320508075688772},"23":{"tf":2.0},"35":{"tf":1.4142135623730951},"40":{"tf":2.23606797749979},"48":{"tf":2.6457513110645907},"5":{"tf":1.4142135623730951},"57":{"tf":2.8284271247461903},"65":{"tf":1.4142135623730951},"75":{"tf":1.4142135623730951}},"e":{"c":{"df":0,"docs":{},"u":{"df":0,"docs":{},"r":{"df":0,"docs":{},"s":{"df":1,"docs":{"23":{"tf":1.0}}}}}},"df":0,"docs":{},"f":{"df":0,"docs":{},"i":{"df":0,"docs":{},"n":{"df":3,"docs":{"55":{"tf":2.23606797749979},"56":{"tf":2.23606797749979},"57":{"tf":2.0}}}},"l":{"df":2,"docs":{"60":{"tf":2.0},"61":{"tf":1.0}},"e":{"df":0,"docs":{},"x":{"df":1,"docs":{"60":{"tf":1.0}}}}}},"l":{"a":{"df":0,"docs":{},"t":{"df":1,"docs":{"58":{"tf":1.0}}}},"df":1,"docs":{"58":{"tf":2.6457513110645907}}},"p":{"df":0,"docs":{},"e":{"a":{"df":0,"docs":{},"t":{"df":1,"docs":{"5":{"tf":1.4142135623730951}}}},"df":0,"docs":{}},"l":{"a":{"c":{"df":2,"docs":{"59":{"tf":2.449489742783178},"73":{"tf":1.0}}},"df":0,"docs":{}},"df":0,"docs":{}}}},"f":{"df":0,"docs":{},"l":{"df":5,"docs":{"51":{"tf":1.0},"60":{"tf":2.449489742783178},"61":{"tf":2.23606797749979},"74":{"tf":1.4142135623730951},"76":{"tf":1.0}}}},"i":{"df":0,"docs":{},"g":{"df":0,"docs":{},"h":{"df":0,"docs":{},"t":{"df":3,"docs":{"20":{"tf":1.0},"27":{"tf":1.0},"50":{"tf":2.23606797749979}}}}},"n":{"df":0,"docs":{},"g":{"df":4,"docs":{"38":{"tf":1.0},"43":{"tf":1.0},"59":{"tf":2.0},"62":{"tf":2.6457513110645907}}}}},"w":{"df":11,"docs":{"28":{"tf":1.0},"3":{"tf":1.0},"31":{"tf":1.0},"4":{"tf":1.0},"43":{"tf":1.0},"48":{"tf":1.0},"59":{"tf":1.4142135623730951},"63":{"tf":3.7416573867739413},"64":{"tf":1.4142135623730951},"65":{"tf":1.0},"69":{"tf":1.0}}}},"s":{"a":{"df":0,"docs":{},"y":{"df":0,"docs":{},"s":{".":{"df":0,"docs":{},"n":{"df":0,"docs":{},"o":{"_":{"df":0,"docs":{},"v":{"df":0,"docs":{},"e":{"df":0,"docs":{},"r":{"df":0,"docs":{},"i":{"df":0,"docs":{},"f":{"df":0,"docs":{},"y":{"_":{"df":0,"docs":{},"i":{"df":0,"docs":{},"n":{"_":{"c":{"df":0,"docs":{},"i":{"df":1,"docs":{"66":{"tf":1.0}}}},"df":0,"docs":{}},"df":0,"docs":{}}}},"df":0,"docs":{}}}}}}}},"df":0,"docs":{}}},"v":{"df":0,"docs":{},"e":{"df":0,"docs":{},"r":{"df":0,"docs":{},"i":{"df":0,"docs":{},"f":{"df":0,"docs":{},"i":{"df":1,"docs":{"66":{"tf":1.0}}}}}}}}},"df":0,"docs":{}}}},"df":2,"docs":{"37":{"tf":2.449489742783178},"65":{"tf":1.4142135623730951}},"e":{"df":0,"docs":{},"t":{"_":{"df":0,"docs":{},"o":{"df":0,"docs":{},"p":{"df":0,"docs":{},"t":{"df":1,"docs":{"1":{"tf":1.0}}}}}},"df":1,"docs":{"37":{"tf":1.0}}}},"h":{"df":0,"docs":{},"o":{"df":0,"docs":{},"w":{"_":{"df":0,"docs":{},"t":{"df":0,"docs":{},"e":{"df":0,"docs":{},"r":{"df":0,"docs":{},"m":{"df":1,"docs":{"62":{"tf":1.4142135623730951}}}}}}},"df":15,"docs":{"16":{"tf":1.0},"26":{"tf":1.4142135623730951},"31":{"tf":1.0},"46":{"tf":1.4142135623730951},"48":{"tf":1.4142135623730951},"49":{"tf":1.0},"5":{"tf":1.7320508075688772},"54":{"tf":1.4142135623730951},"55":{"tf":1.0},"56":{"tf":1.0},"57":{"tf":2.6457513110645907},"6":{"tf":1.0},"67":{"tf":2.449489742783178},"73":{"tf":1.7320508075688772},"77":{"tf":1.4142135623730951}}}}},"i":{"df":0,"docs":{},"m":{"df":0,"docs":{},"p":{"_":{"a":{"df":0,"docs":{},"l":{"df":4,"docs":{"28":{"tf":1.0},"4":{"tf":1.0},"65":{"tf":1.0},"70":{"tf":1.7320508075688772}}}},"df":0,"docs":{}},"df":11,"docs":{"26":{"tf":1.4142135623730951},"3":{"tf":1.0},"44":{"tf":1.4142135623730951},"45":{"tf":1.4142135623730951},"62":{"tf":1.0},"65":{"tf":1.0},"68":{"tf":3.1622776601683795},"69":{"tf":2.0},"70":{"tf":1.4142135623730951},"71":{"tf":1.4142135623730951},"73":{"tf":2.449489742783178}}}}},"o":{"df":0,"docs":{},"r":{"df":0,"docs":{},"r":{"df":0,"docs":{},"i":{"df":4,"docs":{"12":{"tf":2.0},"46":{"tf":1.4142135623730951},"47":{"tf":1.4142135623730951},"72":{"tf":2.449489742783178}}},"y":{"a":{"df":0,"docs":{},"x":{"df":1,"docs":{"12":{"tf":1.4142135623730951}}}},"df":0,"docs":{}}}}},"p":{"df":0,"docs":{},"l":{"df":0,"docs":{},"i":{"df":0,"docs":{},"t":{"df":1,"docs":{"73":{"tf":2.6457513110645907}}}}}},"t":{"d":{".":{"df":0,"docs":{},"t":{"a":{"c":{"df":0,"docs":{},"t":{"df":0,"docs":{},"i":{"c":{".":{"df":0,"docs":{},"e":{"df":0,"docs":{},"x":{"df":0,"docs":{},"t":{"df":1,"docs":{"37":{"tf":1.0}}}}},"g":{"df":0,"docs":{},"u":{"a":{"df":0,"docs":{},"r":{"d":{"df":0,"docs":{},"e":{"df":0,"docs":{},"x":{"df":0,"docs":{},"p":{"df":0,"docs":{},"r":{"df":1,"docs":{"39":{"tf":1.0}}}}}}},"df":0,"docs":{}}},"df":0,"docs":{}}},"r":{"c":{"a":{"df":0,"docs":{},"s":{"df":1,"docs":{"23":{"tf":1.0}}}},"df":0,"docs":{}},"df":0,"docs":{},"e":{"df":0,"docs":{},"p":{"df":0,"docs":{},"l":{"a":{"c":{"df":1,"docs":{"59":{"tf":1.0}}},"df":0,"docs":{}},"df":0,"docs":{}}}}},"s":{"df":0,"docs":{},"h":{"df":0,"docs":{},"o":{"df":0,"docs":{},"w":{"df":0,"docs":{},"t":{"df":0,"docs":{},"e":{"df":0,"docs":{},"r":{"df":0,"docs":{},"m":{"df":1,"docs":{"18":{"tf":1.0}}}}}}}}}}},"df":0,"docs":{}},"df":0,"docs":{}}}},"df":0,"docs":{}},"df":0,"docs":{}}},"df":0,"docs":{}},"df":0,"docs":{}},"u":{"c":{"c":{"df":2,"docs":{"44":{"tf":2.6457513110645907},"46":{"tf":1.0}}},"df":0,"docs":{}},"df":0,"docs":{},"f":{"df":0,"docs":{},"f":{"df":0,"docs":{},"i":{"c":{"df":1,"docs":{"74":{"tf":3.0}}},"df":0,"docs":{}}}}}},"t":{"a":{"c":{"df":0,"docs":{},"t":{"df":0,"docs":{},"i":{"c":{"df":1,"docs":{"2":{"tf":1.0}}},"df":0,"docs":{}}}},"df":0,"docs":{},"u":{"df":0,"docs":{},"t":{"df":0,"docs":{},"o":{"df":1,"docs":{"75":{"tf":2.8284271247461903}},"l":{"df":0,"docs":{},"o":{"df":0,"docs":{},"g":{"df":1,"docs":{"75":{"tf":1.0}}}}}}}}},"df":2,"docs":{"12":{"tf":1.7320508075688772},"37":{"tf":2.449489742783178}},"h":{"df":0,"docs":{},"e":{"df":0,"docs":{},"o":{"df":0,"docs":{},"r":{"df":0,"docs":{},"e":{"df":0,"docs":{},"m":{"df":4,"docs":{"12":{"tf":1.0},"19":{"tf":1.0},"30":{"tf":1.0},"72":{"tf":1.0}}}},"i":{"df":1,"docs":{"2":{"tf":1.0}}}}}}},"r":{"df":0,"docs":{},"i":{"df":7,"docs":{"18":{"tf":1.0},"31":{"tf":1.0},"35":{"tf":1.4142135623730951},"51":{"tf":1.0},"53":{"tf":1.0},"65":{"tf":1.7320508075688772},"75":{"tf":1.4142135623730951}},"v":{"df":0,"docs":{},"i":{"a":{"df":0,"docs":{},"l":{"df":1,"docs":{"76":{"tf":2.8284271247461903}}}},"df":0,"docs":{}}}},"u":{"df":0,"docs":{},"e":{"df":2,"docs":{"1":{"tf":1.0},"66":{"tf":1.4142135623730951}}}}},"y":{"df":0,"docs":{},"p":{"df":0,"docs":{},"e":{"df":5,"docs":{"2":{"tf":1.0},"37":{"tf":1.0},"60":{"tf":1.0},"61":{"tf":1.0},"68":{"tf":1.7320508075688772}}}}}},"u":{"df":2,"docs":{"60":{"tf":1.0},"68":{"tf":1.7320508075688772}},"n":{"df":0,"docs":{},"f":{"df":0,"docs":{},"o":{"df":0,"docs":{},"l":{"d":{"df":1,"docs":{"73":{"tf":1.0}}},"df":0,"docs":{}}}},"i":{"df":0,"docs":{},"v":{"df":0,"docs":{},"e":{"df":0,"docs":{},"r":{"df":0,"docs":{},"s":{"df":1,"docs":{"68":{"tf":1.0}}}}}}}},"s":{"df":2,"docs":{"24":{"tf":1.4142135623730951},"47":{"tf":1.0}}}},"v":{"a":{"df":0,"docs":{},"r":{"df":0,"docs":{},"i":{"a":{"b":{"df":0,"docs":{},"l":{"df":7,"docs":{"23":{"tf":1.0},"25":{"tf":1.0},"37":{"tf":1.4142135623730951},"47":{"tf":1.0},"61":{"tf":1.0},"64":{"tf":1.0},"68":{"tf":1.0}}}},"df":0,"docs":{}},"df":0,"docs":{}}}},"df":1,"docs":{"68":{"tf":1.7320508075688772}}},"w":{"a":{"df":0,"docs":{},"r":{"df":0,"docs":{},"n":{"df":1,"docs":{"1":{"tf":1.0}},"i":{"df":0,"docs":{},"n":{"df":0,"docs":{},"g":{"a":{"df":0,"docs":{},"s":{"df":0,"docs":{},"e":{"df":0,"docs":{},"r":{"df":0,"docs":{},"r":{"df":0,"docs":{},"o":{"df":0,"docs":{},"r":{"df":1,"docs":{"1":{"tf":1.0}}}}}}}}},"df":0,"docs":{}}}}}}},"df":0,"docs":{},"i":{"df":0,"docs":{},"t":{"df":0,"docs":{},"h":{"df":0,"docs":{},"o":{"df":0,"docs":{},"u":{"df":0,"docs":{},"t":{"df":1,"docs":{"77":{"tf":1.0}}}}}}}},"l":{"df":0,"docs":{},"o":{"df":0,"docs":{},"g":{"df":1,"docs":{"77":{"tf":2.23606797749979}}}}}},"x":{")":{".":{"df":0,"docs":{},"p":{"df":0,"docs":{},"r":{"df":0,"docs":{},"o":{"df":0,"docs":{},"p":{"df":0,"docs":{},"e":{"df":0,"docs":{},"r":{"df":0,"docs":{},"t":{"df":0,"docs":{},"i":{"df":1,"docs":{"25":{"tf":1.0}}}}}}}}}},"v":{"a":{"df":0,"docs":{},"l":{"df":1,"docs":{"25":{"tf":1.0}}}},"df":0,"docs":{}}},"df":0,"docs":{}},"`":{"df":0,"docs":{},"が":{"df":0,"docs":{},"偶":{"df":0,"docs":{},"数":{"df":0,"docs":{},"の":{"df":0,"docs":{},"と":{"df":0,"docs":{},"き":{"`":{"3":{"df":1,"docs":{"43":{"tf":1.0}}},"df":0,"docs":{}},"df":0,"docs":{}}}}}}}},"df":24,"docs":{"12":{"tf":3.4641016151377544},"24":{"tf":3.1622776601683795},"25":{"tf":4.358898943540674},"26":{"tf":3.4641016151377544},"28":{"tf":2.6457513110645907},"29":{"tf":1.7320508075688772},"3":{"tf":1.0},"35":{"tf":1.7320508075688772},"36":{"tf":3.3166247903554},"37":{"tf":2.6457513110645907},"38":{"tf":3.872983346207417},"4":{"tf":1.0},"43":{"tf":3.4641016151377544},"48":{"tf":2.449489742783178},"51":{"tf":2.8284271247461903},"52":{"tf":1.4142135623730951},"54":{"tf":3.1622776601683795},"58":{"tf":2.23606797749979},"61":{"tf":1.7320508075688772},"62":{"tf":2.449489742783178},"65":{"tf":2.8284271247461903},"66":{"tf":1.4142135623730951},"72":{"tf":1.7320508075688772},"73":{"tf":5.196152422706632}}},"y":{"df":14,"docs":{"12":{"tf":3.4641016151377544},"24":{"tf":4.0},"25":{"tf":3.3166247903554},"3":{"tf":1.4142135623730951},"4":{"tf":1.4142135623730951},"43":{"tf":2.449489742783178},"48":{"tf":3.3166247903554},"51":{"tf":1.4142135623730951},"52":{"tf":1.4142135623730951},"54":{"tf":2.0},"62":{"tf":2.449489742783178},"65":{"tf":2.6457513110645907},"66":{"tf":2.0},"72":{"tf":1.7320508075688772}}},"z":{"df":6,"docs":{"3":{"tf":1.0},"4":{"tf":1.0},"43":{"tf":1.4142135623730951},"51":{"tf":1.4142135623730951},"65":{"tf":1.0},"72":{"tf":1.7320508075688772}},"e":{"df":0,"docs":{},"r":{"df":0,"docs":{},"o":{"df":2,"docs":{"44":{"tf":1.7320508075688772},"46":{"tf":1.0}}}}}}}},"title":{"root":{"a":{"df":0,"docs":{},"e":{"df":0,"docs":{},"s":{"df":0,"docs":{},"o":{"df":0,"docs":{},"p":{"df":2,"docs":{"3":{"tf":1.0},"4":{"tf":1.0}}}}}},"p":{"df":0,"docs":{},"p":{"df":0,"docs":{},"l":{"df":0,"docs":{},"i":{"df":3,"docs":{"11":{"tf":1.0},"56":{"tf":1.0},"6":{"tf":1.0}}},"y":{"_":{"a":{"df":0,"docs":{},"s":{"df":0,"docs":{},"s":{"df":0,"docs":{},"u":{"df":0,"docs":{},"m":{"df":0,"docs":{},"p":{"df":0,"docs":{},"t":{"df":2,"docs":{"10":{"tf":1.0},"5":{"tf":1.0}}}}}}}}},"df":0,"docs":{}},"df":0,"docs":{}}}}},"s":{"df":0,"docs":{},"s":{"df":0,"docs":{},"u":{"df":0,"docs":{},"m":{"df":0,"docs":{},"p":{"df":0,"docs":{},"t":{"df":2,"docs":{"13":{"tf":1.0},"34":{"tf":1.0}}}}}}}}},"b":{"df":0,"docs":{},"y":{"_":{"c":{"a":{"df":0,"docs":{},"s":{"df":1,"docs":{"15":{"tf":1.0}}}},"df":0,"docs":{},"o":{"df":0,"docs":{},"n":{"df":0,"docs":{},"t":{"df":0,"docs":{},"r":{"a":{"df":1,"docs":{"16":{"tf":1.0}}},"df":0,"docs":{}}}}}},"df":0,"docs":{}},"df":0,"docs":{}}},"c":{"a":{"df":0,"docs":{},"l":{"c":{"df":1,"docs":{"19":{"tf":1.0}}},"df":0,"docs":{}},"s":{"df":0,"docs":{},"e":{"df":3,"docs":{"20":{"tf":1.0},"21":{"tf":1.0},"22":{"tf":1.0}}}}},"df":0,"docs":{},"h":{"df":0,"docs":{},"o":{"df":0,"docs":{},"o":{"df":0,"docs":{},"s":{"df":1,"docs":{"24":{"tf":1.0}}}}}},"o":{"df":0,"docs":{},"n":{"df":0,"docs":{},"g":{"df":0,"docs":{},"r":{"df":1,"docs":{"26":{"tf":1.0}}}},"s":{"df":0,"docs":{},"t":{"df":0,"docs":{},"r":{"df":0,"docs":{},"u":{"c":{"df":0,"docs":{},"t":{"df":0,"docs":{},"o":{"df":0,"docs":{},"r":{"df":2,"docs":{"27":{"tf":1.0},"57":{"tf":1.0}}}}}},"df":0,"docs":{}}}}},"t":{"df":0,"docs":{},"r":{"a":{"d":{"df":0,"docs":{},"i":{"c":{"df":0,"docs":{},"t":{"df":1,"docs":{"29":{"tf":1.0}}}},"df":0,"docs":{}}},"df":0,"docs":{}},"df":0,"docs":{}}},"v":{"df":1,"docs":{"30":{"tf":1.0}},"e":{"df":0,"docs":{},"r":{"df":0,"docs":{},"t":{"df":1,"docs":{"31":{"tf":1.0}}}}}}}}},"d":{"df":0,"docs":{},"o":{"df":0,"docs":{},"n":{"df":0,"docs":{},"e":{"df":1,"docs":{"32":{"tf":1.0}}}}},"s":{"df":0,"docs":{},"i":{"df":0,"docs":{},"m":{"df":0,"docs":{},"p":{"df":1,"docs":{"71":{"tf":1.0}}}}}}},"df":0,"docs":{},"e":{"df":0,"docs":{},"x":{"a":{"c":{"df":0,"docs":{},"t":{"df":4,"docs":{"14":{"tf":1.0},"33":{"tf":1.0},"35":{"tf":1.0},"9":{"tf":1.0}}}},"df":0,"docs":{}},"df":0,"docs":{},"i":{"df":0,"docs":{},"s":{"df":0,"docs":{},"t":{"df":1,"docs":{"36":{"tf":1.0}}}}},"t":{"df":1,"docs":{"37":{"tf":1.0}}}}},"f":{"df":0,"docs":{},"u":{"df":0,"docs":{},"n":{"df":0,"docs":{},"e":{"df":0,"docs":{},"x":{"df":0,"docs":{},"t":{"df":1,"docs":{"38":{"tf":1.0}}}}}}}},"g":{"df":0,"docs":{},"u":{"a":{"df":0,"docs":{},"r":{"d":{"_":{"df":0,"docs":{},"h":{"df":0,"docs":{},"y":{"df":0,"docs":{},"p":{"df":1,"docs":{"39":{"tf":1.0}}}}}},"df":0,"docs":{}},"df":0,"docs":{}}},"df":0,"docs":{}}},"i":{"df":0,"docs":{},"n":{"d":{"df":0,"docs":{},"u":{"c":{"df":0,"docs":{},"t":{"df":2,"docs":{"44":{"tf":1.0},"45":{"tf":1.0}}}},"df":0,"docs":{}}},"df":0,"docs":{},"t":{"df":0,"docs":{},"r":{"df":0,"docs":{},"o":{"df":1,"docs":{"48":{"tf":1.0}}}}}}},"l":{"df":0,"docs":{},"e":{"a":{"df":0,"docs":{},"n":{"4":{"df":1,"docs":{"0":{"tf":1.0}}},"df":0,"docs":{}}},"df":0,"docs":{},"f":{"df":0,"docs":{},"t":{"df":1,"docs":{"50":{"tf":1.0}}}}},"i":{"df":0,"docs":{},"n":{"a":{"df":0,"docs":{},"r":{"df":0,"docs":{},"i":{"df":0,"docs":{},"t":{"df":0,"docs":{},"h":{"df":1,"docs":{"51":{"tf":1.0}}}}}}},"df":0,"docs":{}}}},"n":{"df":0,"docs":{},"l":{"df":0,"docs":{},"i":{"df":0,"docs":{},"n":{"a":{"df":0,"docs":{},"r":{"df":0,"docs":{},"i":{"df":0,"docs":{},"t":{"df":0,"docs":{},"h":{"df":1,"docs":{"53":{"tf":1.0}}}}}}},"df":0,"docs":{}}}},"t":{"df":0,"docs":{},"h":{"_":{"df":0,"docs":{},"r":{"df":0,"docs":{},"e":{"df":0,"docs":{},"w":{"df":0,"docs":{},"r":{"df":0,"docs":{},"i":{"df":0,"docs":{},"t":{"df":1,"docs":{"64":{"tf":1.0}}}}}}}}},"df":0,"docs":{}}}},"p":{"df":0,"docs":{},"u":{"df":0,"docs":{},"s":{"df":0,"docs":{},"h":{"_":{"df":0,"docs":{},"n":{"df":0,"docs":{},"e":{"df":0,"docs":{},"g":{"df":1,"docs":{"54":{"tf":1.0}}}}}},"df":0,"docs":{}}}}},"r":{"c":{"a":{"df":0,"docs":{},"s":{"df":0,"docs":{},"e":{"df":1,"docs":{"23":{"tf":1.0}}}}},"df":0,"docs":{}},"df":0,"docs":{},"e":{"df":0,"docs":{},"f":{"df":0,"docs":{},"i":{"df":0,"docs":{},"n":{"df":1,"docs":{"55":{"tf":1.0}}}}},"l":{"df":1,"docs":{"58":{"tf":1.0}}},"p":{"df":0,"docs":{},"l":{"a":{"c":{"df":1,"docs":{"59":{"tf":1.0}}},"df":0,"docs":{}},"df":0,"docs":{}}}},"f":{"df":0,"docs":{},"l":{"df":1,"docs":{"60":{"tf":1.0}}}},"i":{"df":0,"docs":{},"g":{"df":0,"docs":{},"h":{"df":0,"docs":{},"t":{"df":1,"docs":{"50":{"tf":1.0}}}}},"n":{"df":0,"docs":{},"g":{"df":1,"docs":{"62":{"tf":1.0}}}}},"w":{"df":1,"docs":{"63":{"tf":1.0}}}},"s":{"df":0,"docs":{},"h":{"df":0,"docs":{},"o":{"df":0,"docs":{},"w":{"df":1,"docs":{"67":{"tf":1.0}}}}},"i":{"df":0,"docs":{},"m":{"df":0,"docs":{},"p":{"_":{"a":{"df":0,"docs":{},"l":{"df":1,"docs":{"70":{"tf":1.0}}}},"df":0,"docs":{}},"df":2,"docs":{"68":{"tf":1.0},"69":{"tf":1.0}}}}},"o":{"df":0,"docs":{},"r":{"df":0,"docs":{},"r":{"df":0,"docs":{},"i":{"df":1,"docs":{"72":{"tf":1.0}}}}}},"p":{"df":0,"docs":{},"l":{"df":0,"docs":{},"i":{"df":0,"docs":{},"t":{"df":1,"docs":{"73":{"tf":1.0}}}}}},"u":{"df":0,"docs":{},"f":{"df":0,"docs":{},"f":{"df":0,"docs":{},"i":{"c":{"df":1,"docs":{"74":{"tf":1.0}}},"df":0,"docs":{}}}}}},"t":{"a":{"df":0,"docs":{},"u":{"df":0,"docs":{},"t":{"df":0,"docs":{},"o":{"df":1,"docs":{"75":{"tf":1.0}}}}}},"df":0,"docs":{},"r":{"df":0,"docs":{},"i":{"df":0,"docs":{},"v":{"df":0,"docs":{},"i":{"a":{"df":0,"docs":{},"l":{"df":1,"docs":{"76":{"tf":1.0}}}},"df":0,"docs":{}}}}}},"w":{"df":0,"docs":{},"l":{"df":0,"docs":{},"o":{"df":0,"docs":{},"g":{"df":1,"docs":{"77":{"tf":1.0}}}}}}}}},"lang":"English","pipeline":["trimmer","stopWordFilter","stemmer"],"ref":"id","version":"0.9.5"},"results_options":{"limit_results":30,"teaser_word_count":30},"search_options":{"bool":"OR","expand":true,"fields":{"body":{"boost":1},"breadcrumbs":{"boost":1},"title":{"boost":2}}}});
\ No newline at end of file
+Object.assign(window.search, {"doc_urls":["index.html#lean4-タクティク逆引きリスト","index.html#オプションについて","index.html#リンク集","aesop.html#aesop","apply_assumption.html#apply_assumption","apply.html#apply","apply.html#否定--について","apply.html#よくあるエラー","apply.html#exact-との関連","apply.html#apply_assumption-との関連","apply_search.html#apply","assumption.html#assumption","assumption.html#exact-との関連","by_cases.html#by_cases","by_contra.html#by_contra","by.html#by","by.html#by-1","calc.html#calc","cases.html#cases","cases.html#case-を書かない","cases.html#cases-1","cases.html#rcases","choose.html#choose","choose.html#補足","congr.html#congr","constructor.html#constructor","constructor.html#同値を示す","contradiction.html#contradiction","conv.html#conv","convert.html#convert","done.html#done","exact.html#exact","exact.html#assumption-との関連","exact_search.html#exact","exists.html#exists","ext.html#ext","funext.html#funext","guard_hyp.html#guard_hyp","have.html#have","have.html#パターンマッチ","have.html#論理積-","have.html#存在-","induction.html#induction","induction.html#induction-1","induction.html#一般のについての帰納法","induction.html#強い帰納法","intro.html#intro","intro.html#否定--について","left_right.html#left-right","linarith.html#linarith","linarith.html#補足","nlinarith.html#nlinarith","push_neg.html#push_neg","refine.html#refine","refine.html#apply-との関連","refine.html#constructor-との関連","rel.html#rel","replace.html#replace","rfl.html#rfl","rfl.html#補足","ring.html#ring","rw.html#rw","rw.html#nth_rw","says.html#says","says.html#オプション","show.html#show","simp.html#simp","simp.html#simp-1","simp.html#simp_all","simp.html#dsimp","sorry.html#sorry","split.html#split","suffices.html#suffices","tauto.html#tauto","trivial.html#trivial","wlog.html#wlog"],"index":{"documentStore":{"docInfo":{"0":{"body":1,"breadcrumbs":2,"title":1},"1":{"body":6,"breadcrumbs":1,"title":0},"10":{"body":61,"breadcrumbs":3,"title":1},"11":{"body":9,"breadcrumbs":2,"title":1},"12":{"body":2,"breadcrumbs":2,"title":1},"13":{"body":30,"breadcrumbs":2,"title":1},"14":{"body":31,"breadcrumbs":2,"title":1},"15":{"body":37,"breadcrumbs":0,"title":0},"16":{"body":24,"breadcrumbs":0,"title":0},"17":{"body":4,"breadcrumbs":2,"title":1},"18":{"body":49,"breadcrumbs":2,"title":1},"19":{"body":33,"breadcrumbs":2,"title":1},"2":{"body":10,"breadcrumbs":1,"title":0},"20":{"body":26,"breadcrumbs":2,"title":1},"21":{"body":61,"breadcrumbs":2,"title":1},"22":{"body":64,"breadcrumbs":2,"title":1},"23":{"body":67,"breadcrumbs":1,"title":0},"24":{"body":75,"breadcrumbs":2,"title":1},"25":{"body":36,"breadcrumbs":2,"title":1},"26":{"body":27,"breadcrumbs":1,"title":0},"27":{"body":31,"breadcrumbs":2,"title":1},"28":{"body":4,"breadcrumbs":2,"title":1},"29":{"body":37,"breadcrumbs":2,"title":1},"3":{"body":75,"breadcrumbs":2,"title":1},"30":{"body":1,"breadcrumbs":2,"title":1},"31":{"body":25,"breadcrumbs":2,"title":1},"32":{"body":3,"breadcrumbs":2,"title":1},"33":{"body":37,"breadcrumbs":3,"title":1},"34":{"body":23,"breadcrumbs":2,"title":1},"35":{"body":48,"breadcrumbs":2,"title":1},"36":{"body":40,"breadcrumbs":2,"title":1},"37":{"body":13,"breadcrumbs":2,"title":1},"38":{"body":39,"breadcrumbs":0,"title":0},"39":{"body":0,"breadcrumbs":0,"title":0},"4":{"body":54,"breadcrumbs":2,"title":1},"40":{"body":17,"breadcrumbs":0,"title":0},"41":{"body":38,"breadcrumbs":0,"title":0},"42":{"body":67,"breadcrumbs":2,"title":1},"43":{"body":22,"breadcrumbs":2,"title":1},"44":{"body":51,"breadcrumbs":1,"title":0},"45":{"body":40,"breadcrumbs":1,"title":0},"46":{"body":101,"breadcrumbs":2,"title":1},"47":{"body":42,"breadcrumbs":1,"title":0},"48":{"body":29,"breadcrumbs":4,"title":2},"49":{"body":43,"breadcrumbs":2,"title":1},"5":{"body":49,"breadcrumbs":2,"title":1},"50":{"body":13,"breadcrumbs":1,"title":0},"51":{"body":21,"breadcrumbs":2,"title":1},"52":{"body":62,"breadcrumbs":2,"title":1},"53":{"body":17,"breadcrumbs":2,"title":1},"54":{"body":26,"breadcrumbs":2,"title":1},"55":{"body":62,"breadcrumbs":2,"title":1},"56":{"body":36,"breadcrumbs":2,"title":1},"57":{"body":81,"breadcrumbs":2,"title":1},"58":{"body":34,"breadcrumbs":2,"title":1},"59":{"body":27,"breadcrumbs":1,"title":0},"6":{"body":21,"breadcrumbs":1,"title":0},"60":{"body":33,"breadcrumbs":2,"title":1},"61":{"body":55,"breadcrumbs":2,"title":1},"62":{"body":34,"breadcrumbs":2,"title":1},"63":{"body":70,"breadcrumbs":0,"title":0},"64":{"body":13,"breadcrumbs":0,"title":0},"65":{"body":19,"breadcrumbs":2,"title":1},"66":{"body":142,"breadcrumbs":2,"title":1},"67":{"body":2,"breadcrumbs":2,"title":1},"68":{"body":2,"breadcrumbs":2,"title":1},"69":{"body":2,"breadcrumbs":2,"title":1},"7":{"body":1,"breadcrumbs":1,"title":0},"70":{"body":26,"breadcrumbs":2,"title":1},"71":{"body":115,"breadcrumbs":2,"title":1},"72":{"body":38,"breadcrumbs":2,"title":1},"73":{"body":39,"breadcrumbs":2,"title":1},"74":{"body":16,"breadcrumbs":2,"title":1},"75":{"body":42,"breadcrumbs":2,"title":1},"8":{"body":17,"breadcrumbs":2,"title":1},"9":{"body":3,"breadcrumbs":2,"title":1}},"docs":{"0":{"body":"「普段の数学を Lean でどうやって実現するんだろう」という疑問に答えるために，よく使うタクティクをユースケースから逆引きできるようにまとめたリストです． なお，タクティクの説明に付記している名前の由来についての説明は公式に説明があったものではなく，あくまで憶測であることをお断りしておきます．","breadcrumbs":"Lean4 タクティク逆引きリスト » Lean4 タクティク逆引きリスト","id":"0","title":"Lean4 タクティク逆引きリスト"},"1":{"body":"タクティクによっては，オプションを設定することで挙動を変更することができます．オプションの設定には，set_option を使用します．たとえば，set_option warningAsError true と書くと，warning(警告) がエラーとして扱われるようになります． 使用できるオプションの一覧は #help option または こちらのリスト で確認することができます．","breadcrumbs":"Lean4 タクティク逆引きリスト » オプションについて","id":"1","title":"オプションについて"},"10":{"body":"apply? は，カレントゴールを apply や refine で変形することができないか，ライブラリから検索して提案してくれるタクティクです． 複数の候補が提案されたときは，どれを選ぶとゴールが何に変わるのか表示されるので，その中から好ましいものを選ぶと良いでしょう． import Mathlib.Algebra.Group.Defs\nimport Mathlib.Algebra.Hom.Group.Defs\nimport Mathlib.Tactic.LibrarySearch -- apply? を使うのに必要 /-- 群準同型は積を保つ -/\nexample [Group G] [Group H] (f : G →* H) (a b : G) : f (a * b) = f a * f b := by -- `exact MonoidHom.map_mul f a b` を提案してくれる apply? /-! ## 補足 `apply?` はあくまで証明を書くときに補助として使うものです． `sorry` と同じように，清書した証明に残してはいけません． `sorry` と同じと言いましたが，実際 `apply?` は `sorryAx` を裏で使用します．\n-/ theorem T (x y : Nat) (_: x ≤ y) : 2 ^ x ≤ 2 ^ y := by apply? -- `apply?` しただけで `done` が通り，示せているように見える done -- 以下に示すように，裏で `sorryAx` が使われている /-- info: 'T' depends on axioms: [sorryAx] -/\n#guard_msgs in #print axioms T","breadcrumbs":"apply?: apply できるか検索 » apply?","id":"10","title":"apply?"},"11":{"body":"assumption は，現在のゴール ⊢ P がローカルコンテキストにあるとき，ゴールを閉じます． example (hP: P) (_: Q) : P := by assumption","breadcrumbs":"assumption: 仮定からゴールを閉じる » assumption","id":"11","title":"assumption"},"12":{"body":"assumption による証明は，どの仮定を使うか明示すれば exact で書き直すことができます．","breadcrumbs":"assumption: 仮定からゴールを閉じる » exact との関連","id":"12","title":"exact との関連"},"13":{"body":"by_cases は排中律を使って場合分けをするタクティクです． by_cases h: P とすると，P が成り立つときと成り立たないときのゴールがそれぞれ生成されます． example (P: Prop) : ¬¬P → P := by intro hnnP -- `P` が成り立つかどうかで場合分けする by_cases hP: P case inl => -- `P` が成り立つとき guard_hyp hP : P assumption case inr => -- `¬ P` が成り立つとき guard_hyp hP : ¬P contradiction","breadcrumbs":"by_cases: 排中律 » by_cases","id":"13","title":"by_cases"},"14":{"body":"needs: import Mathlib.Tactic.ByContra by_contra は，背理法を使いたいときに役立つタクティクです． ゴールが ⊢ P であるときに by_contra h を実行すると，h : ¬ P がローカルコンテキストに追加されて，同時にゴールが ⊢ False になります． example (h: ¬Q → ¬P) : P → Q := by -- `P` であると仮定する intro hP -- `¬Q` であると仮定して矛盾を導きたい by_contra hnQ show False -- `¬ Q → ¬ P` と `¬Q` から `¬P` が導かれる have := h hnQ -- これは仮定に矛盾 contradiction","breadcrumbs":"by_contra: 背理法 » by_contra","id":"14","title":"by_contra"},"15":{"body":"Lean においては，命題は型で，証明はその項です．命題 P の証明を構成するとは項 h : P を構成するということです．by は，証明の構成をタクティクで行いたいときに使います． -- `P → R` というのは `P` の証明を与えられたときに `R` の証明を返す関数の型\n-- したがって，その証明は関数となる\nexample (hPQ : P → Q) (hQR : Q → R) : P → R := fun hP ↦ hQR (hPQ hP) -- 同じ命題をタクティクで示した例\nexample (hPQ : P → Q) (hQR : Q → R) : P → R := by intro hP exact hQR (hPQ hP)","breadcrumbs":"by: タクティクモードに入る » by","id":"15","title":"by"},"16":{"body":"needs: import Std.Tactic.ShowTerm by? を使うとタクティクモードで構成した証明を直接構成した証明に変換してくれます． example (hPQ : P → Q) (hQR : Q → R) : P → R := by? -- `Try this: fun hP => hQR (hPQ hP)` と提案してくれる intro hP exact hQR (hPQ hP)","breadcrumbs":"by: タクティクモードに入る » by?","id":"16","title":"by?"},"17":{"body":"calc は計算モードに入るためのタクティクです．詳細については Theorem Proving in Lean4 をご参照ください．","breadcrumbs":"calc: 計算モードに入る » calc","id":"17","title":"calc"},"18":{"body":"cases は場合分けを行います．ローカルコンテキストに h: P ∨ Q があるときに cases h とすると，仮定に P を付け加えたゴール inl と，仮定に Q を付け加えたゴール inr を生成します．それぞれ，insert left と insert right の略ではないかと思います． example : P ∨ Q → (P → R) → (Q → R) → R := by -- `h: P ∨ Q` intro h hPR hQR -- `case inl` と `case inr` の２つのゴールを生成する cases h -- `P` が成り立つ場合 case inl hP => exact hPR hP -- `Q` が成り立つ場合 case inr hQ => exact hQR hQ","breadcrumbs":"cases: 論理和∨を使う » cases","id":"18","title":"cases"},"19":{"body":"上記の例では case を場合分けの枝ごとに書いていますが，下の例のように case を書かずに済ませることもできます． example : P ∨ Q → (P → R) → (Q → R) → R := by -- `h: P ∨ Q` intro h hPR hQR -- `case inl` と `case inr` の２つのゴールを生成する cases h with | inl hP => exact hPR hP | inr hQ => exact hQR hQ","breadcrumbs":"cases: 論理和∨を使う » case を書かない","id":"19","title":"case を書かない"},"2":{"body":"Mathematics in type Theory 日本語訳 このリストでは「命題は型，証明はその項」という型理論を基礎として数学を実装する際の事実は既知としています．こういった話に全く馴染みがない方は，まずこちらの記事を読まれると良いと思います． mathlib4-all-tactics 全タクティクの網羅的なリスト． 数学系のためのLean勉強会 Lean で数学をどのように実装するのか，実際に実装する過程を追うことで学べる教材です．いくつかコード例を拝借させていただきました． Lean phrasebook 英語ですが，数学でのよくある推論ステップが，Lean にどのように翻訳されるかがよくまとめられたリストです．","breadcrumbs":"Lean4 タクティク逆引きリスト » リンク集","id":"2","title":"リンク集"},"20":{"body":"needs: import Mathlib.Tactic.Cases cases' を使用すると分解した仮定に簡潔に名前をつけることができます． example : P ∨ Q → (P → R) → (Q → R) → R := by intro h hPR hQR -- 場合分けをする cases' h with hP hQ · apply hPR hP · apply hQR hQ","breadcrumbs":"cases: 論理和∨を使う » cases'","id":"20","title":"cases'"},"21":{"body":"needs: import Std.Tactic.RCases named after: 再帰的(recursive) cases rcases は cases をパターンに従って再帰的に適用します．論理和∨以外にも使うことができます． variable (P Q R : Prop) example : P ∨ Q → (P → R) → (Q → R) → R := by intro h hPR hQR -- 場合分けをする rcases h with hP | hQ · apply hPR hP · apply hQR hQ example : P ∧ Q → Q ∧ P := by -- `h: P ∧ Q` と仮定する intro h -- `h: P ∧ Q` を `hP: P` と `hQ: Q` に分解する rcases h with ⟨hP, hQ⟩ -- `Q ∧ P` を証明する exact ⟨hQ, hP⟩","breadcrumbs":"cases: 論理和∨を使う » rcases","id":"21","title":"rcases"},"22":{"body":"needs: import Mathlib.Tactic.Choose h : ∀ x, ∃ y, P(x, y) が成り立っているときに，choose f hf using h は写像 f: X → Y と f が満たす性質 hf : ∀ x, P(x, f x) のペアを作ります． example (f : X → Y) (hf : ∀ y, ∃ x, f x = y) : ∃ g : Y → X, ∀ y, f (g y) = y := by -- 写像 `g : Y → X` を構成する choose g hg using hf -- `g` が満たす条件がローカルコンテキストに追加される guard_hyp g: Y → X guard_hyp hg: ∀ (y : Y), f (g y) = y exact ⟨g, hg⟩","breadcrumbs":"choose: 選択関数を得る » choose","id":"22","title":"choose"},"23":{"body":"choose が自動で示してくれることは選択原理 Classical.choice を使って手動で示すことができます．たとえば次のようになります． variable (P : X → Y → Prop) noncomputable example (h : ∀ x, ∃ y, P x y) : ∃ f : X → Y, ∀ x, P x (f x) := by -- `f` を作る let f' : (x : X) → {y // P x y} := fun x ↦ have hne_st : Nonempty {y // P x y} := let ⟨y, py⟩ := h x; ⟨⟨y, py⟩⟩ Classical.choice hne_st let f : X → Y := fun x ↦ (f' x).val -- 上記で作った関数が条件を満たすことを示す have h₁ : ∀ x, P x (f x) := by intro x exact (f' x).property exists f","breadcrumbs":"choose: 選択関数を得る » 補足","id":"23","title":"補足"},"24":{"body":"named after: 合同(congruence) congr は，⊢ f as = f bs という形のゴールがあったときに，ゴールを ⊢ as = bs に変えます．再帰的に適用されるので，⊢ g (f as) = g (f bs) という形のゴールでも同じ結果になります． example (f : Int → X) (h : x = 0) : f (2 + x) = f 2 := by congr show 2 + x = 2 simp only [h, add_zero] congr が適用される再帰の深さを引数として渡すことができます．これは，主に単に congr とするだけだと「行き過ぎ」になるときに調整する目的で使用されます． example (f : Int → Int) (g : Int → X) (h : x = 0) (hf : ∀ x, f x = f (- x)) : g (f (2 + x)) = g (f (- 2)) := by -- 仮に `congr` とすると -- ゴールが `⊢ 2 + x = -2` になってしまう congr 1 show f (2 + x) = f (-2) simp only [h, add_zero] exact hf _","breadcrumbs":"congr: ゴールの差異に注目する » congr","id":"24","title":"congr"},"25":{"body":"ゴールが ⊢ P ∧ Q であるとき，constructor を実行すると，ゴールが２つのゴール ⊢ P と ⊢ Q に分割されます． example (hP: P) (hQ: Q) : P ∧ Q := by -- goal が `left` と `right` に分割される constructor · -- `P` を示す exact hP · -- `Q` を示す exact hQ なお h: P ∧ Q から P や Q の証明を得るのは，それぞれ h.left と h.right で可能です． example (h: P ∧ Q) : P := by exact h.left","breadcrumbs":"constructor: 論理積∧を示す » constructor","id":"25","title":"constructor"},"26":{"body":"constructor はゴールが ⊢ P ↔ Q であるときにも使用できます． example (x : Nat) : x = 0 ↔ x + 1 = 1 := by constructor · -- `x = 0 → x + 1 = 1` を示す intro hx rw [hx] · -- `x + 1 = 1 → x = 0` を示す simp_all","breadcrumbs":"constructor: 論理積∧を示す » 同値を示す","id":"26","title":"同値を示す"},"27":{"body":"矛盾からはどんな命題でも証明することができます．これを爆発律(principle of explosion)と呼びますが，contradiction は，この爆発律を使ってゴールを閉じるタクティクです． ローカルコンテキストに P と ¬ P が同時にあるなど，矛盾した状況にあるときにゴールを閉じます． -- `False`\nexample (h : False) : P := by contradiction -- 明らかに偽な等式\nexample (h : 2 + 2 = 3) : P := by contradiction -- 明らかに偽な等式\nexample (x : Nat) (h : x ≠ x) : P := by contradiction -- 矛盾する仮定\nexample (hP : P) (hnP : ¬ P) : Q := by contradiction","breadcrumbs":"contradiction: 爆発律 » contradiction","id":"27","title":"contradiction"},"28":{"body":"conv は変換モードに入るためのタクティクです．詳細については Theorem Proving in Lean4 をご参照ください．","breadcrumbs":"conv: 変換モードに入る » conv","id":"28","title":"conv"},"29":{"body":"needs: import Mathlib.Tactic.Convert ローカルコンテキストに現在のゴールに近いけれども等しくはない h があるとき，exact h としても失敗します．しかし convert h は成功する可能性があり，成功した場合は h とゴールの差分を新たなゴールとします． example (f : Nat → Nat) (h : f (a + b) = 0) (hc: a + b = c) : f (c) = 0 := by -- `h` はゴールと等しくないので失敗する try exact [h] -- `h` とゴールの差分を新たなゴールにする convert h -- ゴールが `⊢ c = a + b` に変わっている show c = a + b rw [hc]","breadcrumbs":"convert: 惜しい補題を使う » convert","id":"29","title":"convert"},"3":{"body":"aesop は，intro や simp を使用してルーチンな証明を自動で行う，強力なタクティクです． aesop? を使うことにより，中身を見ることも可能です． import Aesop -- `aesop` を使用するため\nimport Mathlib.Init.Function -- `Injective` を使用するため\nimport Mathlib.Tactic.Says -- `says` を使用するため -- CI 環境で `says` のチェックをしない\nset_option says.no_verify_in_CI true -- 以下 `X` `Y` `Z`を集合とする\nvariable {X Y Z : Type} open Function /-! ## aesop -/ -- 合成 `g ∘ f` が単射なら，`f` も単射\nexample {f : X → Y} {g : Y → Z} (hgfinj : Injective (g ∘ f)) : Injective f := by rw [Injective] show ∀ ⦃a₁ a₂ : X⦄, f a₁ = f a₂ → a₁ = a₂ -- 示すべきことがまだまだあるように見えるが，一発で証明が終わる aesop /-! ## aesop? aesop が成功するとき，aesop? に置き換えると， ゴールを達成するのにどんなタクティクを使用したか教えてくれる．\n-/ example {f : X → Y} {g : Y → Z} (hgfinj : Injective (g ∘ f)) : Injective f := by rw [Injective] -- `aesop?` は `says` 以下に続く一連のタクティクを示す aesop? says intro a₁ a₂ a apply hgfinj simp_all only [comp_apply]","breadcrumbs":"aesop: ルーチン自動化 » aesop","id":"3","title":"aesop"},"30":{"body":"done は，証明終了の合図です．証明すべきゴールが残っていない時に成功し，それ以外の時にはエラーになります．QED のようなものです．","breadcrumbs":"done: 証明終了を宣言 » done","id":"30","title":"done"},"31":{"body":"ゴールが P で，ローカルコンテキストに hP: P があるときに，exact hP はゴールを閉じます． example (hP: P) : P := by exact hP hP がゴールの証明になっていないときには，失敗してエラーになります． exact ⟨ hP, hQ ⟩ のようにすると，論理積∧の形をした命題を証明することができます． example (hP: P) (hQ: Q) : P ∧ Q := by exact ⟨ hP, hQ ⟩","breadcrumbs":"exact: 証明を直接構成 » exact","id":"31","title":"exact"},"32":{"body":"exact は常にどの命題を使うか明示する必要がありますが，「ゴールを exact で閉じることができるような命題をローカルコンテキストから自動で探す」 assumption というタクティクもあります．","breadcrumbs":"exact: 証明を直接構成 » assumption との関連","id":"32","title":"assumption との関連"},"33":{"body":"exact? は，カレントゴールを exact で閉じることができないか，ライブラリから検索して提案してくれるタクティクです．閉じることができなければ，エラーになります． import Mathlib.Tactic.LibrarySearch -- `exact?` を使うのに必要 variable (P Q : Prop) -- `exact?` はライブラリ検索を行う\nexample : x < x + 1 := by -- `Try this: exact Nat.lt.base x` と出力される exact? -- ローカルコンテキストにある仮定を自動で使ってゴールを導いてくれる\nexample (hPQ : P → Q) (hQR : Q → R) (hQ : P) : R := by -- `Try this: exact hQR (hPQ hQ)` と出力される exact? -- 証明は `exact?` だけで終わっている done","breadcrumbs":"exact?: exact できるか検索 » exact?","id":"33","title":"exact?"},"34":{"body":"exists は，「～という x が存在する」という命題を示すために，「この x を使え」と指示するコマンドです． ゴールが ⊢ ∃ x, P x のとき，x: X がローカルコンテキストにあれば，exists x によりゴールが P x に変わります．同時に，P x が自明な場合は証明が終了します． example : ∃ x : Nat, 3 * x + 1 = 7 := by exists 2","breadcrumbs":"exists: 存在∃を示す » exists","id":"34","title":"exists"},"35":{"body":"needs: import Std.Tactic.Ext named after: 外延性(extensionality) ext は，外延性を使うタクティクです．外延性とは，「同じものから作られているものは同じである」という主張のことです．たとえば 集合 A, B ⊂ α について A = B は x ∈ A ↔ x ∈ B と同じ 2つの写像 f g : A → B があるとき f = g は ∀ a ∈ A, f a = g a と同じ といったことを指します． @[ext] で登録されたルールを使用するため，集合の等式 A = B を示すときは Mathlib.Data.SetLike.Basic も必要です． variable {α : Type} -- `s` と `t` は `α` の部分集合\nvariable (s t : Set α) example : s ∩ t = t ∩ s := by -- `x ∈ α` を取る．` x ∈ s ∩ t ↔ x ∈ t ∩ s` を証明すればよい ext x aesop なお A ⊂ B を示すために元を取るのは intro x で可能です．","breadcrumbs":"ext: 外延性を使う » ext","id":"35","title":"ext"},"36":{"body":"関数 f と g が等しいことを示す際に，引数 x をとって f x = g x を示そうとすることがありますが，funext はそれを行うタクティクです. def f := fun (x : Nat) ↦ x + x def g := fun (x : Nat) ↦ 2 * x example : f = g := by -- 引数 `x` を取る funext x -- `f x` と `g x` を展開する dsimp [f, g] -- `x + x` と `2 * x` が等しいことを証明する ring","breadcrumbs":"funext: 関数等式を示す » funext","id":"36","title":"funext"},"37":{"body":"needs: import Std.Tactic.GuardExpr guard_hyp は，ローカルコンテキストにある命題を確認するタクティクです．指定した仮定が存在すれば成功し，そうでなければ失敗します． example (hP : P) : P := by -- 現在ローカルコンテキストにある命題を確認できる guard_hyp hP : P exact hP 通常の証明で使うことはあまりないかもしれません．このタクティクリストでは，ローカルコンテキストの変化を説明するために使用することがあります．","breadcrumbs":"guard_hyp: 仮定や補題を確認 » guard_hyp","id":"37","title":"guard_hyp"},"38":{"body":"have は，証明の途中でわかることをローカルコンテキストに追加するコマンドです． have h: P := ... で P という命題の証明を構成し，その証明に h という名前を付けることができます． example (hPQ: P → Q) (hQR: Q → R) : P → R := by -- 示したいことが `P → R` なので，`P` だと仮定する intro hP -- 仮定 `hPQ : P → Q` と `hP : P` から `Q` が導かれる have hQ : Q := by exact hPQ hP -- 仮定 `hQR : Q → R` と `hQ : Q` から `R` が導かれる exact hQR hQ 名前を省略して have : P := ... とすると，自動的に this という名前になります．","breadcrumbs":"have: 補題を用意する » have","id":"38","title":"have"},"39":{"body":"補題を示すだけでなく，ある特定の形をした主張を分解するのにも have は使うことができます．","breadcrumbs":"have: 補題を用意する » パターンマッチ","id":"39","title":"パターンマッチ"},"4":{"body":"needs: import Mathlib.Tactic.SolveByElim apply_assumption は，ゴールが ⊢ head であるときに，... → ∀ _, ... → head という形の命題をローカルコンテキストから探し，それを用いてゴールを書き換えます． import Mathlib.Tactic.SolveByElim variable (P Q R : Prop) /-! ## apply_assumption -/ example (hPQ : P → Q) : ¬ Q → ¬ P := by intro hQn hP -- 矛盾を示したい show False -- 自動で `hQn` を適用 apply_assumption show Q -- 自動で `hPQ` を適用 apply_assumption show P -- 自動で `hP` を適用 apply_assumption -- 証明終わり done /-! ## repeat apply_assumption タクティクを繰り返すことを指示するタクティク `repeat` と組み合わせると， 「ローカルコンテキストにある仮定を適切に選んで apply, exact することを繰り返し， ゴールを閉じる」ことができます．\n-/ example (hPQ : P → Q) (hQR : Q → R) (hQ : P) : R := by repeat apply_assumption","breadcrumbs":"apply_assumption: 仮定から後方推論 » apply_assumption","id":"4","title":"apply_assumption"},"40":{"body":"次のように，P ∧ Q という命題から P と Q を取り出すことができます． example (hPQ: P ∧ Q) : P := by -- `P ∧ Q` という仮定を分解する -- `hQ: Q` は不要なのでアンダースコアに置き換える have ⟨ hP, _ ⟩ := hPQ assumption","breadcrumbs":"have: 補題を用意する » 論理積 ∧","id":"40","title":"論理積 ∧"},"41":{"body":"次のように，∃ x: X, P x という命題から，条件を満たす x を取り出すことができます．x: X と hx: P x がローカルコンテキストに追加されます． -- `x`が偶数のとき`3 * x`も偶数\nexample (x : ℕ) (hx : ∃ y, x = 2 * y) : ∃ z, 3 * x = 2 * z := by -- `hx` で存在が主張されている `y` と， -- `x = 2 * y` という命題を得る have ⟨y, hy⟩ := hx exists 3 * y rw [hy] ring","breadcrumbs":"have: 補題を用意する » 存在 ∃","id":"41","title":"存在 ∃"},"42":{"body":"induction は，帰納法のためのタクティクです． 自然数を例に説明します．Lean では自然数は次のように帰納的に定義されています. inductive Nat | zero : Nat | succ (n : Nat) : Nat succ は後者関数と呼ばれる関数で，n + 1 := succ n です． n : Nat についてゴール P n ⊢ Q n があったとします．このとき induction n を行うと，コンストラクタ zero と succ のそれぞれに対して，対応するゴールを生成します．つまり P 0 ⊢ Q 0 (P (succ a)) (P a → Q a) ⊢ Q (succ a) の２つのゴールです． -- 階乗関数\ndef fac : Nat → Nat | 0 => 1 | n + 1 => (n + 1) * fac n example (n : Nat) : 0 < fac n := by -- `n` についての帰納法で示す induction n with | zero => -- `fac` の定義から従う simp [fac] | succ n ih => -- `fac` の定義から従う simp [fac] positivity","breadcrumbs":"induction: 帰納法 » induction","id":"42","title":"induction"},"43":{"body":"needs: import Mathlib.Tactic.Cases induction' というタクティクもあります．こちらは箇条書きによる，より簡潔な書き方が可能です． example (n : Nat) : 0 < fac n := by -- `ih` は帰納法の仮定 -- `k` は `ih` に登場する変数 induction' n with k ih · simp [fac] · simp [fac] positivity","breadcrumbs":"induction: 帰納法 » induction'","id":"43","title":"induction'"},"44":{"body":"また，induction' では「リストの長さに対する帰納法」のようなより複雑な帰納法を行うことができます． example (l : List α) (P : List α → Prop) : P l := by -- リストの長さに対する帰納法 induction' h : l.length generalizing l case zero => -- リストの長さが 0 のとき guard_hyp h: List.length l = 0 show P l sorry case succ n IH => -- リストの長さが `n + 1` のとき guard_hyp h: List.length l = n + 1 -- 帰納法の仮定が使える guard_hyp IH: ∀ (l : List α), List.length l = n → P l show P l sorry","breadcrumbs":"induction: 帰納法 » 一般の～についての帰納法","id":"44","title":"一般の～についての帰納法"},"45":{"body":"時には，より強い帰納法が必要なこともあります．強い帰納法とは，たとえば P(0) を示す (∀ k < n, P (k)) → P (n) を示す したがって ∀ n, P (n) である という形式で表されるような帰納法のことです．これは超限帰納法の特別な場合です．これを使用するには，Nat.strong_induction_on を使って次のようにします． variable (P : Nat → Prop) example (n : Nat) : P n := by -- `n` についての強い帰納法で示す induction' n using Nat.strong_induction_on with n ih -- 仮定が追加される guard_hyp ih : ∀ (m : ℕ), m < n → P m match n with | 0 => sorry | k + 1 => sorry","breadcrumbs":"induction: 帰納法 » 強い帰納法","id":"45","title":"強い帰納法"},"46":{"body":"named after: 導入(introduce) intro は数学で慣習的に行われる P → Q を示すときに最初に P を仮定する ∀ x ∈ A, P(x) を示すときに最初に x ∈ A が与えられたと仮定する といった導入を実行します． 具体的には，intro は ゴールが ⊢ P → Q という形であるときに P をローカルコンテキストに追加して，ゴールを ⊢ Q に変える ゴールが ⊢ ∀ x, P x という形であるときに x をローカルコンテキストに追加してゴールを ⊢ P x に変える といった挙動をします． example (hPQ: P → Q) (hQR: Q → R) : P → R := by -- 示したいことが `P → R` なので，`P` だと仮定する intro hP -- `R` を示したい show R -- 仮定 `hPQ : P → Q` と `hP : P` から `Q` が導かれる have hQ : Q := hPQ hP -- 仮定 `hQR : Q → R` と `hQ : Q` から `R` が導かれる exact hQR hQ もう一つ使用例を挙げておきます： example (P Q : Nat → Prop) (h : ∀ n, P n ↔ Q n) : ∀ y, P (y + 1) → Q (y + 1) := by -- 任意の `y` について示すので，`intro` で `y` を導入する -- そして `P (y + 1) → Q(y + 1)` を示したいので，`P (y + 1)` を仮定する intro y hyP -- `Q (y + 1)` を示せば良い show Q (y + 1) -- 同値を使ってゴールを書き換える rw [← h] -- 仮定 `P (y + 1)` より従う assumption","breadcrumbs":"intro: 含意→や全称∀を示す » intro","id":"46","title":"intro"},"47":{"body":"Lean では否定 ¬ P は P → False として定義されているので，ゴールが ¬ P のときに intro すると P が仮定に追加されて，ゴールが False に変わります． False は矛盾を導けば証明できます． example (h: P → Q) : ¬Q → ¬P := by -- 示したいことが `¬Q → ¬P` なので，`¬Q` だと仮定する -- そうするとゴールが `¬P` になるので， -- さらに `intro` を行って仮定 `hP : P` を導入する intro hnQ hP -- 矛盾を示したい show False -- `hP : P` と `h : P → Q` から `Q` が導かれる have hQ : Q := h hP -- `hQ : Q` と `hnQ : ¬Q` から矛盾が導かれる contradiction","breadcrumbs":"intro: 含意→や全称∀を示す » 否定 ¬ について","id":"47","title":"否定 ¬ について"},"48":{"body":"needs: import Mathlib.Tactic.LeftRight ゴールが ⊢ P ∨ Q であるとき，left はゴールを ⊢ P に，right はゴールを ⊢ Q に変えます． example (hP: P) : P ∨ Q := by left assumption left, right を使わずに Mathlib4 なしで同じことをするには，Or.inl または Or.inr を使用します． example (hP: P) : P ∨ Q := by apply Or.inl assumption","breadcrumbs":"left, right: 論理和∨を示す » left, right","id":"48","title":"left, right"},"49":{"body":"needs: import Mathlib.Tactic.Linarith named after: 線形算術(linear arithmetic) linarith は線形な(不)等式を導くことができます． example (h1 : 2 * x < 3 * y) (h2 : -4 * x + 2 * z < 0): 12 * y - 4 * z ≥ 0 := by linarith linarith はローカルコンテキストを読み取ってくれるので，linarith が通らないとき補題を追加してあげると通るようになることがあります． example : id x ≤ x := by -- `linarith` で示すことはできない try linarith have : id x = x := rfl -- `id x = x` だと教えてあげると `linarith` で示せる linarith","breadcrumbs":"linarith: 線形(不)等式を示す » linarith","id":"49","title":"linarith"},"5":{"body":"apply は含意 → をゴールに適用するタクティクです． ゴールが ⊢ Q で，ローカルコンテキストに h: P → Q があるときに，apply h を実行するとゴールが ⊢ P に書き換わります． -- `P → Q` かつ `P` ならば `Q`\nexample (h: P → Q) (hP: P) : Q := by apply h -- ゴールが `P` に変わっている show P exact hP 注意点として，h: P → Q は P の証明を受け取って Q の証明を返す関数でもあるので，上記の例は apply を使わずに exact h hP で閉じることもできます． -- `P → Q` かつ `P` ならば `Q`\nexample (h: P → Q) (hP: P) : Q := by exact h hP","breadcrumbs":"apply: 含意→を使う » apply","id":"5","title":"apply"},"50":{"body":"もう少し詳細に書くと，linarith は「ロールコンテキストにある線形な(不)等式系に矛盾があるか調べる」タクティクなので，次のような使い方もできます． example (h1: x = 2 * y) (h2 : - x + 2 * y = 1) : False := by linarith","breadcrumbs":"linarith: 線形(不)等式を示す » 補足","id":"50","title":"補足"},"51":{"body":"needs: import Mathlib.Tactic.Linarith named after: non-linear(非線形) arithmetic(算術) nlinarith は非線形な式も扱えるように linarith にいくつか前処理を追加したものです． example (a b: Nat) (h : a ≤ b) : a ^ 2 ≤ b ^ 2 := by -- `linarith` では示すことができない try linarith nlinarith","breadcrumbs":"nlinarith: 非線形な(不)等式を示す » nlinarith","id":"51","title":"nlinarith"},"52":{"body":"needs: import Mathlib.Tactic.PushNeg named after: 押し込む(push) 否定(negation) push_neg はドモルガン則を使って，否定を式の中に押し込みます．たとえば ¬ (P ∧ Q) は P → ¬ Q に， ¬ ∀ x, P x は ∃ x, ¬ P x に という調子で変形します． [1] example (h: P → Q) : ¬ (P ∧ ¬ Q) := by -- ドモルガン則を適用して，`¬` を内側に押し込む push_neg -- `¬` を内側に押し込んだ結果，`¬ P ∨ Q` が得られる -- これは `P → Q` と同値 show P → Q exact h example : ¬ ∃ x : Int , ∀ y : Int, (x + y = 0) := by -- ドモルガン則を適用して，`¬` を内側に押し込む push_neg -- `¬` を内側に押し込んだ結果，ゴールが変わる show ∀ x, ∃ y, ¬ (x + y = 0) intro x exists (- x + 1) linarith [1] モードによって ¬ (P ∧ Q) を P → ¬ Q としたり，¬ P ∨ ¬ Q としたりします．","breadcrumbs":"push_neg: ドモルガン » push_neg","id":"52","title":"push_neg"},"53":{"body":"refine は exact と同様に機能しますが，プレースホルダを受け入れて新しいゴールを生成するという違いがあります． example (hP: P) (hQ: Q) : P ∧ Q := by -- 穴埋め形式で証明を作ることができる refine ⟨?_, hQ⟩ -- ゴールが `⊢ P` になる show P exact hP","breadcrumbs":"refine: 一般の後方推論 » refine","id":"53","title":"refine"},"54":{"body":"h : P → Q という命題があって，ゴールが ⊢ Q であるとき refine h ?_ は apply h と同様に機能するので，refine で apply を代用することができます． example (hPQ : P → Q) (hP : P) : Q := by refine hPQ ?_ -- ゴールが `⊢ P` になる show P refine hP","breadcrumbs":"refine: 一般の後方推論 » apply との関連","id":"54","title":"apply との関連"},"55":{"body":"refine は constructor の代わりに使うこともできます．実際 refine は constructor よりも柔軟で，⊢ P ∧ Q ∧ R のような形のゴールは constructor よりも簡潔に分割できます． example (hP: P) (hQ: Q) (hR : R) : P ∧ Q ∧ R := by -- ゴールを３つに分割する refine ⟨?_, ?_, ?_⟩ · show P exact hP · show Q exact hQ · show R exact hR -- `constructor` を使った場合\n-- 一度に２つのゴールに分割することしかできない\nexample (hP: P) (hQ: Q) (hR : R) : P ∧ Q ∧ R := by constructor · show P exact hP · show Q ∧ R constructor · show Q exact hQ · show R exact hR","breadcrumbs":"refine: 一般の後方推論 » constructor との関連","id":"55","title":"constructor との関連"},"56":{"body":"needs: import Mathlib.Tactic.GCongr named after: 関係(relation) rel は，不等式を代入して適用し，不等式を示します． example (h1 : a ≤ b) (h2 : c ≤ d) : a + c ≤ b + d := by rel [h1, h2] rel は，たとえば整数 x: Int に対して 0 ≤ x ^ 2 であることを自動的に適用するなど, 多少の推論を行います． example (x: Int) (h1 : a ≤ b) : x ^ 2 * a ≤ x ^ 2 * b := by rel [h1]","breadcrumbs":"rel: 不等式を使う » rel","id":"56","title":"rel"},"57":{"body":"needs: import Std.Tactic.Replace replace は have と同じく補題を入手するためのタクティクですが，have とは異なりローカルコンテキストにすでにある命題を置き換えることができます． have を使った場合，ローカルコンテキストにすでに h : P がある状態で，再び h という名前で別の命題を示すと，古い方の h はアクセス不能になって † が付いた状態になってしまいます． replace であれば，古い方が新しい方に置き換えられ，† の付いた命題は出現しません． example : ∀ (n : Int), Even (5 * n) → Even n := by intro n hn -- `Even (5 * n)` という仮定を分解 obtain ⟨ k, hk ⟩ := hn -- 以下がローカルコンテキストに追加される guard_hyp hk: 5 * n = k + k -- `k + k` という形が使いづらいので，`2 * k` に置き換える replace hk : 5 * n = 2 * k := by rw [hk] ring -- `hk` の内容が変化している guard_hyp hk: 5 * n = 2 * k -- 計算をする have := by calc n _ = 5 * n - 4 * n := by ring _ = 2 * k - 4 * n := by rw [hk] _ = 2 * (k - 2 * n) := by ring exists k - 2 * n nth_rw 1 [this] ring","breadcrumbs":"replace: 補題の入れ替え » replace","id":"57","title":"replace"},"58":{"body":"needs: import Mathlib.Tactic.Relation.Rfl named after: 反射律(reflexivity) rfl は，refl attribute の付けられた定理を用いて関係の反射性を示すタクティクです． inductive MyEq {α : Type u} : α → α → Prop | refl (a : α) : MyEq a a attribute [refl] MyEq.refl example (n : ℕ) : MyEq n n := by rfl @[refl] で登録された定理を用いるので，追加でライブラリを import することにより示すことができる命題が増えます． -- `import Mathlib.Data.Nat.Basic` が必要\nexample (n : Nat) : n ≤ n := by rfl","breadcrumbs":"rfl: 関係の反射性を示す » rfl","id":"58","title":"rfl"},"59":{"body":"実は Mathlib.Tactic.Relation.Rfl を import するかどうかにより，内部で呼び出されるタクティクが変わります． Mathlib.Tactic.Relation.Rfl ありなら Lean.MVarId.rfl が， なしなら Lean.MVarId.refl が それぞれ参照されます．後者は @[refl] が付けられた一般の関係の反射性にアクセスできず，等号 = の反射性しか使うことができません． 後者の場合 rfl は，単に定義から等しいものが等しいことを示すタクティクになります． variable (α : Type) example : 1 + 1 = 2 := by rfl example (x : α) : x = x := by rfl example : (2 ^ 70 + 3 ^ 70) % 13 = 0 := by rfl","breadcrumbs":"rfl: 関係の反射性を示す » 補足","id":"59","title":"補足"},"6":{"body":"また，Lean では否定 ¬ P は P → False として実装されているため，ゴールが ⊢ False であるときに hn: ¬P に対して apply hn とするとゴールが ⊢ P に書き換わります． -- 矛盾\nexample (hn: ¬ P) (hP: P) : False := by -- ゴールが `P` に変わる apply hn exact hP","breadcrumbs":"apply: 含意→を使う » 否定 ¬ について","id":"6","title":"否定 ¬ について"},"60":{"body":"needs: import Mathlib.Tactic.Ring ring は，可換環の等式を示します． example : (x + y) ^ 2 = x ^ 2 + 2 * x * y + y ^ 2 := by ring simp 等と異なり，ring? タクティクは用意されていませんが，show_term で具体的にどんなルールが適用されたのかを知ることができます．ただし，その出力結果は非常に長く読みづらいものであることがしばしばです．例えば， example : (x + y) ^ 2 = x ^ 2 + 2 * x * y + y ^ 2 := by show_term ring の出力をここに掲載すると100行を超えてしまいます．","breadcrumbs":"ring: 環の等式を示す » ring","id":"60","title":"ring"},"61":{"body":"rw は rewrite（書き換え）を行うタクティクです．等式や同値をもとに書き換えを行います． hab: a = b や hPQ : P ↔ Q がローカルコンテキストにあるとき， rw [hab] はゴールの中の a をすべて b に置き換え， rw [hPQ] はゴールの中の P をすべて Q に置き換えます． 順番は重要で，b を a に置き換えたいときなどは rw [← hab] のように ← をつけます． h1, h2, ... について続けて置き換えを行いたいときは，rw [h1, h2, ...] のようにします． ゴールではなく，ローカルコンテキストにある h: P を書き換えたいときには at をつけて rw [hPQ] at h とします．すべての箇所で置き換えたいときは rw [hPQ] at * とします． example (a b c d e f : Nat) (h : a * b = c * d) (h' : e = f) : a * (b * e) = c * (d * f) := by rw [h'] -- 結合法則を使う rw [← Nat.mul_assoc] rw [h] -- 結合法則を使う rw [Nat.mul_assoc]","breadcrumbs":"rw: 同値変形 » rw","id":"61","title":"rw"},"62":{"body":"needs: import Mathlib.Tactic.NthRewrite rw はマッチした項をすべて置き換えてしまいます．特定の項だけを書き換えたいとき，nth_rw が使用できます．対象の式中に現れる順番を1始まりで指定することで，項を指定します．指定された順番が式中の対象の項の数よりも多い場合はエラーになります． -- `G` は群\nvariable [Group G] example (a b : G) : a * b⁻¹ = 1 ↔ a = b := by -- `one_mul: 1 * b = b` を使って `b` を `1 * b` に書き換える -- `b` は2回出現するが，2番目だけ置き換える nth_rw 2 [← one_mul b] -- `mul_inv_eq_iff_eq_mul: a * b⁻¹ = c ↔ a = c * b` を使う exact mul_inv_eq_iff_eq_mul","breadcrumbs":"rw: 同値変形 » nth_rw","id":"62","title":"nth_rw"},"63":{"body":"needs: import Mathlib.Tactic.Says exact? や apply? は証明を書いている過程で使用することを想定したタクティクです．Try this: という提案をクリックして採用したら，exact? や apply? は提案内容で上書きされて，最終的な証明には残りません． では，証明のある部分が apply? などにより提案された内容であることを明示したい場合はどうしたら良いでしょうか？says タクティクはまさにその問題を解決するタクティクです． example (hPQ : P → Q) (hQR : Q → R) (hRS : R → S) (hP : P) : S := by -- `exact?` は実行されない exact? says exact hRS (hQR (hPQ hP)) また，simp? や aesop? などに対しても使用することができ，やはりドキュメントとして役に立ちます． -- 合成 `g ∘ f` が単射なら，`f` も単射\nexample {f : X → Y} {g : Y → Z} (hgfinj : Injective (g ∘ f)) : Injective f := by rw [Injective] aesop? says intro a₁ a₂ a apply hgfinj simp_all only [comp_apply] より詳細には，検索タクティク X があり，その提案内容が Try this: Y だったとき，X says とすると says は Try this: Y の代わりに Try this: X says Y という提案を infoview 上で出します．それをクリックすると，X says の内容が X says Y で置換されます．そして，X says Y が実行されるときには X は飛ばされます．","breadcrumbs":"says: タクティク提案の痕跡を残す » says","id":"63","title":"says"},"64":{"body":"says.verify : Bool : true にすると，X says Y の Y のところに，実際には提案されていないタクティクを入れたときにエラーになります． says.no_verify_in_CI : Bool : true にすると，CI 環境で X says Y の Y の部分が実際に提案されている内容と一致するかのチェックが走らなくなります．","breadcrumbs":"says: タクティク提案の痕跡を残す » オプション","id":"64","title":"オプション"},"65":{"body":"show P は, ゴールの中に ⊢ P があるときにそれをメインのゴールにします． たとえば，証明中にこれから示すべきことを明示し，コードを読みやすくする目的で使うことができます． example (hP: P) (hQ: Q) : P ∧ Q := by constructor · show P exact hP · show Q exact hQ","breadcrumbs":"show: 示すべきことを宣言 » show","id":"65","title":"show"},"66":{"body":"simp は，ターゲットを決められた規則に基づいて自動で簡約（simplify）するタクティクです．カスタマイズすることが可能で，簡約に使ってほしい命題を登録することができます． universe u v -- 圏の公理\nclass Category (C : Type u) where -- 射 Hom : C → C → Type v -- 射の合成 comp : ∀ {a b c : C}, Hom a b → Hom b c → Hom a c -- 恒等射. `id a` が `a` 上の恒等射を意味する id : ∀ (a : C), Hom a a -- 恒等射の性質 id_comp : ∀ {a b : C} (f : Hom a b), comp (id a) f = f comp_id : ∀ {a b : C} (f : Hom a b), comp f (id b) = f -- 射の結合律 assoc : ∀ {a b c d : C} (f : Hom a b) (g : Hom b c) (h : Hom c d), comp (comp f g) h = comp f (comp g h) -- `f : Hom a b`と`g : Hom b c`の合成を`f ≫ g`と書く\ninfixr:80 \" ≫ \" => Category.comp -- `Category.hoge` ではなく `hoge` で呼び出せるようにする\nopen Category -- 公理の等式が `simp` で使えるようにする\nattribute [simp] id_comp comp_id assoc -- 変数の定義\nvariable {C : Type u} [Category.{u, v} C] {a b c d e : C} example (f : Hom a b) (g : Hom b c) (h : Hom c d) (i : Hom d e) : (f ≫ (id b ≫ g)) ≫ (h ≫ i) = f ≫ (g ≫ ((id c ≫ h) ≫ i)) := by -- 上で `simp` で使えるようにした等式を使って自動で簡約する simp 既知の h: P という証明を使って簡約させたいときは，明示的に simp [h] と指定することで可能です． 何も指定しなければゴールを簡約しますが，ローカルコンテキストにある h: P を簡約させたければ simp at h と指定することで可能です．","breadcrumbs":"simp: 簡約 » simp","id":"66","title":"simp"},"67":{"body":"simp は自動的に証明を行ってくれますが，何が使われたのか知りたいときもあります．simp? は簡約に何が使われたのかを示してくれるので，rw などを用いて明示的に書き直すことができます．","breadcrumbs":"simp: 簡約 » simp?","id":"67","title":"simp?"},"68":{"body":"simp_all は simp [*] at * の強化版で，ローカルコンテキストとゴールをこれ以上簡約できなくなるまですべて簡約します．","breadcrumbs":"simp: 簡約 » simp_all","id":"68","title":"simp_all"},"69":{"body":"dsimp は，定義上(definitionally)等しいもの同士しか簡約しないという制約付きの simp です．","breadcrumbs":"simp: 簡約 » dsimp","id":"69","title":"dsimp"},"7":{"body":"apply には引数が必須なのですが，省略しても近くにエラーが出ません．一般に，構文的に間違った証明を書いた場合には，エラーがわかりやすい場所に出てくれる保証はありません．","breadcrumbs":"apply: 含意→を使う » よくあるエラー","id":"7","title":"よくあるエラー"},"70":{"body":"証明の細部を埋める前にコンパイルが通るようにしたいとき，証明で埋めるべき箇所に sorry と書くとコンパイルが通るようになります．ただし，sorry を使用しているという旨の警告が出ます． -- Fermat の最終定理\ndef FermatLastTheorem := ∀ x y z n : Nat, n > 2 ∧ x * y * z ≠ 0 → x ^ n + y ^ n ≠ z ^ n theorem flt : FermatLastTheorem := sorry","breadcrumbs":"sorry: 証明したことにする » sorry","id":"70","title":"sorry"},"71":{"body":"ゴールにある if ... then ... else 式を扱うのに有用なタクティクです． if 式を扱う必要が生じるのは，典型的には Lean で定義したアルゴリズムや関数に関して，何か性質を証明しようとしたときです． ゴールが ⊢ Q (if P then a else b) であったときに，split を使用すると2つのサブゴールが生成されます．具体的には 1つはローカルコンテキストに † : P が追加され，ゴールが ⊢ Q (a) 1つはローカルコンテキストに † : ¬ P が追加され，ゴールが ⊢ Q (b) というサブゴールです．split によって追加される仮定は名前がついているとは限りません．名前がついていなかった場合，case などで名前を付けることができます． -- if 式を使って関数を定義する\ndef myabs (x : Int) : Int := if x ≥ 0 then x else - x example (x : Int) : myabs (2 * x) = 2 * myabs x := by -- `myabs` の定義を展開する unfold myabs -- ゴールの中に if 式があって複雑 show (if 2 * x ≥ 0 then 2 * x else -(2 * x)) = 2 * if x ≥ 0 then x else -x -- `split` タクティクでケース分割する split case inl h => -- `2 * x ≥ 0` の場合 guard_hyp h: 2 * x ≥ 0 -- 左辺にあった if 式が消えた show 2 * x = 2 * if x ≥ 0 then x else -x replace h : x ≥ 0 := by linarith [h] -- `simp` で if を消すことができる simp? [h] says simp only [ge_iff_le, h, ite_true] case inr h => -- `2 * x < 0` の場合 guard_hyp h: ¬2 * x ≥ 0 -- 左辺にあった if 式が消えた show -(2 * x) = 2 * if x ≥ 0 then x else -x -- if 式を消すための補題を準備する have hx : ¬ x ≥ 0 := by linarith [h] -- `simp` で簡約 simp? [h, hx] says simp only [ge_iff_le, hx, ite_false, mul_neg]","breadcrumbs":"split: if 式を含む命題を示す » split","id":"71","title":"split"},"72":{"body":"suffices は，数学でよくある「～を示せば十分である」という推論を行うタクティクです． ゴールが ⊢ P であるときに suffices Q from を実行すると， suffices Q from のブロック内では，仮定に this: Q が追加され， suffices Q from 以降では，ゴールが ⊢ Q に書き換えられます． apply と似ていますが，apply と違って「十分条件になっていること」の証明が明らかでないときにも使うことができます． example : 13 ∣ (2 ^ 70 + 3 ^ 70) := by -- 余りがゼロであることを示せば十分 suffices (2 ^ 70 + 3 ^ 70) % 13 = 0 from by exact Iff.mpr (Nat.dvd_iff_div_mul_eq (2 ^ 70 + 3 ^ 70) 13) rfl rfl suffices Q from ... という形式の場合は，証明を直接構成することが必要です．suffices Q from by ... とすると，タクティクによって証明を構成するモードになります．","breadcrumbs":"suffices: 十分条件に帰着 » suffices","id":"72","title":"suffices"},"73":{"body":"needs: import Mathlib.Tactic.Tauto named after: トートロジー(tautology) tauto は， トートロジー(恒真式)であることに基づいてゴールを閉じるタクティクです． ゴールを閉じることができなければエラーになります． -- 含意の導入\nexample (h : P) : Q → P := by tauto -- フレーゲの3段論法\nexample : (P → (Q → R)) → ((P → Q) → (P → R)) := by tauto -- 排中律\nexample : P ∨ ¬ P := by -- `aesop` では示すことができない try aesop tauto -- 対偶\nexample (h : P → Q) : ¬ Q → ¬ P := by -- `exact?` では示すことができない try exact? tauto","breadcrumbs":"tauto: トートロジーを示す » tauto","id":"73","title":"tauto"},"74":{"body":"trivial は明らかなことを示します． trivial は，rfl や contradiction などのタクティクを実行して，現在のゴールを閉じようとします． -- 定義から明らかな等式\nexample : 1 + 1 = 2 := by trivial -- 矛盾があるので, どんな命題でも証明できる\nexample (h: False) : P := by trivial 普段の数学でいう「自明」な命題は trivial では示せないことがほとんどだと思います． aesop を試してみてください．","breadcrumbs":"trivial: 自明 » trivial","id":"74","title":"trivial"},"75":{"body":"needs: import Mathlib.Tactic.WLOG named after: 一般性を失わずに(without loss of generarity) wlog は，数学でよく使われる「一般性を失うことなく～と仮定してよい」というフレーズの Lean での対応物です． example (a b : Nat) : a + b = b + a := by -- `a ≤ b` だと仮定しても一般性を失わない wlog h : a ≤ b with H -- `a ≤ b` なら成り立つと仮定して，そうでないときにも成り立つことを示す · show a + b = b + a guard_hyp H : ∀ (a b : Nat), a ≤ b → a + b = b + a guard_hyp h : ¬a ≤ b abel -- `a ≤ b` であるときに成り立つことを示す · show a + b = b + a guard_hyp h: a ≤ b abel","breadcrumbs":"wlog: 一般性を失わずに特殊化 » wlog","id":"75","title":"wlog"},"8":{"body":"exact の代わりに apply を使うことができます． -- `P → Q` かつ `P` ならば `Q`\nexample (h: P → Q) (hP: P) : Q := by apply h apply hP","breadcrumbs":"apply: 含意→を使う » exact との関連","id":"8","title":"exact との関連"},"9":{"body":"apply は常にどの命題を使うか明示する必要がありますが，「ゴールに apply が適用できるような命題をローカルコンテキストから自動で探す」 apply_assumption というタクティクもあります．","breadcrumbs":"apply: 含意→を使う » apply_assumption との関連","id":"9","title":"apply_assumption との関連"}},"length":76,"save":true},"fields":["title","body","breadcrumbs"],"index":{"body":{"root":{"0":{"df":14,"docs":{"24":{"tf":1.4142135623730951},"26":{"tf":1.7320508075688772},"29":{"tf":1.4142135623730951},"42":{"tf":2.0},"43":{"tf":1.0},"44":{"tf":1.4142135623730951},"45":{"tf":1.0},"49":{"tf":1.4142135623730951},"52":{"tf":1.4142135623730951},"56":{"tf":1.0},"59":{"tf":1.0},"70":{"tf":1.0},"71":{"tf":3.3166247903554},"72":{"tf":1.0}}},"1":{"0":{"0":{"df":1,"docs":{"60":{"tf":1.0}}},"df":0,"docs":{}},"2":{"df":1,"docs":{"49":{"tf":1.0}}},"3":{"df":2,"docs":{"59":{"tf":1.0},"72":{"tf":1.7320508075688772}}},"df":15,"docs":{"24":{"tf":1.0},"26":{"tf":2.449489742783178},"33":{"tf":1.0},"34":{"tf":1.0},"42":{"tf":2.0},"44":{"tf":1.4142135623730951},"45":{"tf":1.0},"46":{"tf":2.8284271247461903},"50":{"tf":1.0},"52":{"tf":1.7320508075688772},"57":{"tf":1.0},"59":{"tf":1.4142135623730951},"62":{"tf":1.7320508075688772},"71":{"tf":1.4142135623730951},"74":{"tf":1.4142135623730951}}},"2":{"df":19,"docs":{"10":{"tf":1.4142135623730951},"24":{"tf":3.1622776601683795},"27":{"tf":1.4142135623730951},"34":{"tf":1.0},"35":{"tf":1.0},"36":{"tf":1.4142135623730951},"41":{"tf":1.7320508075688772},"49":{"tf":1.4142135623730951},"50":{"tf":1.4142135623730951},"51":{"tf":1.4142135623730951},"56":{"tf":1.7320508075688772},"57":{"tf":2.6457513110645907},"59":{"tf":1.4142135623730951},"60":{"tf":2.8284271247461903},"62":{"tf":1.0},"70":{"tf":1.0},"71":{"tf":3.872983346207417},"72":{"tf":1.7320508075688772},"74":{"tf":1.0}},"回":{"df":0,"docs":{},"出":{"df":0,"docs":{},"現":{"df":0,"docs":{},"す":{"df":0,"docs":{},"る":{"df":0,"docs":{},"が":{"df":0,"docs":{},"，":{"2":{"df":1,"docs":{"62":{"tf":1.0}}},"df":0,"docs":{}}}}}}}}},"3":{"df":7,"docs":{"27":{"tf":1.0},"34":{"tf":1.0},"41":{"tf":1.4142135623730951},"49":{"tf":1.0},"59":{"tf":1.0},"72":{"tf":1.7320508075688772},"73":{"tf":1.0}}},"4":{"df":2,"docs":{"49":{"tf":1.4142135623730951},"57":{"tf":1.4142135623730951}}},"5":{"df":1,"docs":{"57":{"tf":2.449489742783178}}},"7":{"0":{"df":2,"docs":{"59":{"tf":1.4142135623730951},"72":{"tf":2.449489742783178}}},"df":1,"docs":{"34":{"tf":1.0}}},"_":{"df":9,"docs":{"10":{"tf":1.0},"11":{"tf":1.0},"24":{"tf":1.0},"4":{"tf":1.0},"40":{"tf":1.0},"53":{"tf":1.0},"54":{"tf":1.4142135623730951},"55":{"tf":1.7320508075688772},"57":{"tf":1.7320508075688772}}},"a":{"b":{"df":0,"docs":{},"e":{"df":0,"docs":{},"l":{"df":1,"docs":{"75":{"tf":1.4142135623730951}}}}},"d":{"d":{"_":{"df":0,"docs":{},"z":{"df":0,"docs":{},"e":{"df":0,"docs":{},"r":{"df":0,"docs":{},"o":{"df":1,"docs":{"24":{"tf":1.4142135623730951}}}}}}},"df":0,"docs":{}},"df":0,"docs":{}},"df":0,"docs":{},"e":{"df":0,"docs":{},"s":{"df":0,"docs":{},"o":{"df":0,"docs":{},"p":{"df":5,"docs":{"3":{"tf":3.4641016151377544},"35":{"tf":1.0},"63":{"tf":1.4142135623730951},"73":{"tf":1.4142135623730951},"74":{"tf":1.0}}}}}},"p":{"df":0,"docs":{},"p":{"df":0,"docs":{},"l":{"df":0,"docs":{},"i":{"df":14,"docs":{"10":{"tf":3.0},"20":{"tf":1.4142135623730951},"21":{"tf":1.4142135623730951},"3":{"tf":1.0},"4":{"tf":1.0},"48":{"tf":1.0},"5":{"tf":2.23606797749979},"54":{"tf":1.7320508075688772},"6":{"tf":1.4142135623730951},"63":{"tf":2.0},"7":{"tf":1.0},"72":{"tf":1.4142135623730951},"8":{"tf":1.7320508075688772},"9":{"tf":1.4142135623730951}}},"y":{"_":{"a":{"df":0,"docs":{},"s":{"df":0,"docs":{},"s":{"df":0,"docs":{},"u":{"df":0,"docs":{},"m":{"df":0,"docs":{},"p":{"df":0,"docs":{},"t":{"df":2,"docs":{"4":{"tf":2.8284271247461903},"9":{"tf":1.4142135623730951}}}}}}}}},"df":0,"docs":{}},"df":0,"docs":{}}}}},"r":{"df":0,"docs":{},"i":{"df":0,"docs":{},"t":{"df":0,"docs":{},"h":{"df":0,"docs":{},"m":{"df":0,"docs":{},"e":{"df":0,"docs":{},"t":{"df":2,"docs":{"49":{"tf":1.0},"51":{"tf":1.0}}}}}}}}},"s":{"df":0,"docs":{},"s":{"df":0,"docs":{},"o":{"c":{"df":1,"docs":{"66":{"tf":1.4142135623730951}}},"df":0,"docs":{}},"u":{"df":0,"docs":{},"m":{"df":0,"docs":{},"p":{"df":0,"docs":{},"t":{"df":7,"docs":{"11":{"tf":1.7320508075688772},"12":{"tf":1.0},"13":{"tf":1.0},"32":{"tf":1.4142135623730951},"40":{"tf":1.0},"46":{"tf":1.0},"48":{"tf":1.4142135623730951}}}}}}}},"t":{"df":0,"docs":{},"t":{"df":0,"docs":{},"r":{"df":0,"docs":{},"i":{"b":{"df":0,"docs":{},"u":{"df":0,"docs":{},"t":{"df":2,"docs":{"58":{"tf":1.4142135623730951},"66":{"tf":1.0}}}}},"df":0,"docs":{}}}}},"x":{"df":0,"docs":{},"i":{"df":0,"docs":{},"o":{"df":0,"docs":{},"m":{"df":1,"docs":{"10":{"tf":1.4142135623730951}}}}}}},"b":{"`":{"df":0,"docs":{},"と":{"`":{"df":0,"docs":{},"g":{"df":1,"docs":{"66":{"tf":1.0}}}},"df":0,"docs":{}}},"df":10,"docs":{"10":{"tf":2.0},"29":{"tf":2.0},"35":{"tf":2.449489742783178},"51":{"tf":1.7320508075688772},"56":{"tf":2.0},"61":{"tf":2.449489742783178},"62":{"tf":3.3166247903554},"66":{"tf":4.0},"71":{"tf":1.4142135623730951},"75":{"tf":4.123105625617661}},"o":{"df":0,"docs":{},"o":{"df":0,"docs":{},"l":{"df":1,"docs":{"64":{"tf":1.4142135623730951}}}}},"s":{"df":1,"docs":{"24":{"tf":1.7320508075688772}}},"y":{"_":{"c":{"a":{"df":0,"docs":{},"s":{"df":1,"docs":{"13":{"tf":2.0}}}},"df":0,"docs":{},"o":{"df":0,"docs":{},"n":{"df":0,"docs":{},"t":{"df":0,"docs":{},"r":{"a":{"df":1,"docs":{"14":{"tf":2.0}}},"df":0,"docs":{}}}}}},"df":0,"docs":{}},"df":0,"docs":{}}},"c":{"`":{"df":0,"docs":{},"の":{"df":0,"docs":{},"合":{"df":0,"docs":{},"成":{"df":0,"docs":{},"を":{"`":{"df":0,"docs":{},"f":{"df":1,"docs":{"66":{"tf":1.0}}}},"df":0,"docs":{}}}}}},"a":{"df":0,"docs":{},"l":{"c":{"df":2,"docs":{"17":{"tf":1.4142135623730951},"57":{"tf":1.0}}},"df":0,"docs":{}},"s":{"df":0,"docs":{},"e":{"df":7,"docs":{"13":{"tf":1.4142135623730951},"18":{"tf":2.8284271247461903},"19":{"tf":2.449489742783178},"20":{"tf":1.7320508075688772},"21":{"tf":1.4142135623730951},"44":{"tf":1.4142135623730951},"71":{"tf":1.4142135623730951}}}},"t":{"df":0,"docs":{},"e":{"df":0,"docs":{},"g":{"df":0,"docs":{},"o":{"df":0,"docs":{},"r":{"df":0,"docs":{},"i":{"df":1,"docs":{"66":{"tf":1.4142135623730951}}},"y":{".":{"c":{"df":0,"docs":{},"o":{"df":0,"docs":{},"m":{"df":0,"docs":{},"p":{"df":1,"docs":{"66":{"tf":1.0}}}}}},"df":0,"docs":{},"h":{"df":0,"docs":{},"o":{"df":0,"docs":{},"g":{"df":1,"docs":{"66":{"tf":1.0}}}}},"{":{"df":0,"docs":{},"u":{"df":1,"docs":{"66":{"tf":1.0}}}}},"df":0,"docs":{}}}}}}}},"df":5,"docs":{"29":{"tf":2.0},"56":{"tf":1.4142135623730951},"61":{"tf":1.7320508075688772},"62":{"tf":1.4142135623730951},"66":{"tf":4.58257569495584}},"h":{"df":0,"docs":{},"o":{"df":0,"docs":{},"o":{"df":0,"docs":{},"s":{"df":2,"docs":{"22":{"tf":1.7320508075688772},"23":{"tf":1.0}}}}}},"i":{"df":2,"docs":{"3":{"tf":1.0},"64":{"tf":1.0}}},"l":{"a":{"df":0,"docs":{},"s":{"df":0,"docs":{},"s":{"df":1,"docs":{"66":{"tf":1.0}},"i":{"c":{"a":{"df":0,"docs":{},"l":{".":{"c":{"df":0,"docs":{},"h":{"df":0,"docs":{},"o":{"df":0,"docs":{},"i":{"c":{"df":1,"docs":{"23":{"tf":1.4142135623730951}}},"df":0,"docs":{}}}}},"df":0,"docs":{}},"df":0,"docs":{}}},"df":0,"docs":{}},"df":0,"docs":{}}}}},"df":0,"docs":{}},"o":{"df":0,"docs":{},"m":{"df":0,"docs":{},"p":{"_":{"a":{"df":0,"docs":{},"p":{"df":0,"docs":{},"p":{"df":0,"docs":{},"l":{"df":0,"docs":{},"i":{"df":2,"docs":{"3":{"tf":1.0},"63":{"tf":1.0}}}}}}},"df":0,"docs":{},"i":{"d":{"df":1,"docs":{"66":{"tf":1.4142135623730951}}},"df":0,"docs":{}}},"df":1,"docs":{"66":{"tf":2.6457513110645907}}}},"n":{"df":0,"docs":{},"g":{"df":0,"docs":{},"r":{"df":1,"docs":{"24":{"tf":2.6457513110645907}},"u":{"df":0,"docs":{},"e":{"df":0,"docs":{},"n":{"c":{"df":1,"docs":{"24":{"tf":1.0}}},"df":0,"docs":{}}}}}},"s":{"df":0,"docs":{},"t":{"df":0,"docs":{},"r":{"df":0,"docs":{},"u":{"c":{"df":0,"docs":{},"t":{"df":0,"docs":{},"o":{"df":0,"docs":{},"r":{"df":4,"docs":{"25":{"tf":1.7320508075688772},"26":{"tf":1.4142135623730951},"55":{"tf":2.6457513110645907},"65":{"tf":1.0}}}}}},"df":0,"docs":{}}}}},"t":{"df":0,"docs":{},"r":{"a":{"d":{"df":0,"docs":{},"i":{"c":{"df":0,"docs":{},"t":{"df":5,"docs":{"13":{"tf":1.0},"14":{"tf":1.0},"27":{"tf":2.23606797749979},"47":{"tf":1.0},"74":{"tf":1.0}}}},"df":0,"docs":{}}},"df":0,"docs":{}},"df":0,"docs":{}}},"v":{"df":1,"docs":{"28":{"tf":1.4142135623730951}},"e":{"df":0,"docs":{},"r":{"df":0,"docs":{},"t":{"df":1,"docs":{"29":{"tf":1.7320508075688772}}}}}}}}},"d":{"df":3,"docs":{"56":{"tf":1.4142135623730951},"61":{"tf":1.7320508075688772},"66":{"tf":2.23606797749979}},"e":{"df":0,"docs":{},"f":{"df":4,"docs":{"36":{"tf":1.4142135623730951},"42":{"tf":1.0},"70":{"tf":1.0},"71":{"tf":1.0}}},"p":{"df":0,"docs":{},"e":{"df":0,"docs":{},"n":{"d":{"df":1,"docs":{"10":{"tf":1.0}}},"df":0,"docs":{}}}}},"o":{"df":0,"docs":{},"n":{"df":0,"docs":{},"e":{"df":4,"docs":{"10":{"tf":1.4142135623730951},"30":{"tf":1.4142135623730951},"33":{"tf":1.0},"4":{"tf":1.0}}}}},"s":{"df":0,"docs":{},"i":{"df":0,"docs":{},"m":{"df":0,"docs":{},"p":{"df":2,"docs":{"36":{"tf":1.0},"69":{"tf":1.4142135623730951}}}}}}},"df":0,"docs":{},"e":{"df":2,"docs":{"61":{"tf":1.7320508075688772},"66":{"tf":1.4142135623730951}},"v":{"df":0,"docs":{},"e":{"df":0,"docs":{},"n":{"df":1,"docs":{"57":{"tf":1.7320508075688772}}}}},"x":{"a":{"c":{"df":0,"docs":{},"t":{"df":30,"docs":{"10":{"tf":1.0},"12":{"tf":1.4142135623730951},"15":{"tf":1.0},"16":{"tf":1.0},"18":{"tf":1.4142135623730951},"19":{"tf":1.4142135623730951},"21":{"tf":1.0},"22":{"tf":1.0},"23":{"tf":1.0},"24":{"tf":1.0},"25":{"tf":1.7320508075688772},"29":{"tf":1.4142135623730951},"31":{"tf":2.23606797749979},"32":{"tf":1.4142135623730951},"33":{"tf":3.1622776601683795},"37":{"tf":1.0},"38":{"tf":1.4142135623730951},"4":{"tf":1.0},"46":{"tf":1.0},"5":{"tf":1.7320508075688772},"52":{"tf":1.0},"53":{"tf":1.4142135623730951},"55":{"tf":2.449489742783178},"6":{"tf":1.0},"62":{"tf":1.0},"63":{"tf":2.23606797749979},"65":{"tf":1.4142135623730951},"72":{"tf":1.0},"73":{"tf":1.4142135623730951},"8":{"tf":1.4142135623730951}}}},"df":0,"docs":{},"m":{"df":0,"docs":{},"p":{"df":0,"docs":{},"l":{"df":60,"docs":{"10":{"tf":1.0},"11":{"tf":1.0},"13":{"tf":1.0},"14":{"tf":1.0},"15":{"tf":1.4142135623730951},"16":{"tf":1.0},"18":{"tf":1.0},"19":{"tf":1.0},"20":{"tf":1.0},"21":{"tf":1.4142135623730951},"22":{"tf":1.0},"23":{"tf":1.0},"24":{"tf":1.4142135623730951},"25":{"tf":1.4142135623730951},"26":{"tf":1.0},"27":{"tf":2.0},"29":{"tf":1.0},"3":{"tf":1.4142135623730951},"31":{"tf":1.4142135623730951},"33":{"tf":1.4142135623730951},"34":{"tf":1.0},"35":{"tf":1.0},"36":{"tf":1.0},"37":{"tf":1.0},"38":{"tf":1.0},"4":{"tf":1.4142135623730951},"40":{"tf":1.0},"41":{"tf":1.0},"42":{"tf":1.0},"43":{"tf":1.0},"44":{"tf":1.0},"45":{"tf":1.0},"46":{"tf":1.4142135623730951},"47":{"tf":1.0},"48":{"tf":1.4142135623730951},"49":{"tf":1.4142135623730951},"5":{"tf":1.4142135623730951},"50":{"tf":1.0},"51":{"tf":1.0},"52":{"tf":1.4142135623730951},"53":{"tf":1.0},"54":{"tf":1.0},"55":{"tf":1.4142135623730951},"56":{"tf":1.4142135623730951},"57":{"tf":1.0},"58":{"tf":1.4142135623730951},"59":{"tf":1.7320508075688772},"6":{"tf":1.0},"60":{"tf":1.4142135623730951},"61":{"tf":1.0},"62":{"tf":1.0},"63":{"tf":1.4142135623730951},"65":{"tf":1.0},"66":{"tf":1.0},"71":{"tf":1.0},"72":{"tf":1.0},"73":{"tf":2.0},"74":{"tf":1.4142135623730951},"75":{"tf":1.0},"8":{"tf":1.0}}}}}},"df":0,"docs":{},"i":{"df":0,"docs":{},"s":{"df":0,"docs":{},"t":{"df":5,"docs":{"23":{"tf":1.0},"34":{"tf":2.0},"41":{"tf":1.0},"52":{"tf":1.0},"57":{"tf":1.0}}}}},"p":{"df":0,"docs":{},"l":{"df":0,"docs":{},"o":{"df":0,"docs":{},"s":{"df":0,"docs":{},"i":{"df":0,"docs":{},"o":{"df":0,"docs":{},"n":{")":{"df":0,"docs":{},"と":{"df":0,"docs":{},"呼":{"df":0,"docs":{},"び":{"df":0,"docs":{},"ま":{"df":0,"docs":{},"す":{"df":0,"docs":{},"が":{"df":0,"docs":{},"，":{"c":{"df":0,"docs":{},"o":{"df":0,"docs":{},"n":{"df":0,"docs":{},"t":{"df":0,"docs":{},"r":{"a":{"d":{"df":0,"docs":{},"i":{"c":{"df":0,"docs":{},"t":{"df":1,"docs":{"27":{"tf":1.0}}}},"df":0,"docs":{}}},"df":0,"docs":{}},"df":0,"docs":{}}}}}},"df":0,"docs":{}}}}}}}}},"df":0,"docs":{}}}}}}}},"t":{"df":1,"docs":{"35":{"tf":2.0}},"e":{"df":0,"docs":{},"n":{"df":0,"docs":{},"s":{"df":0,"docs":{},"i":{"df":0,"docs":{},"o":{"df":0,"docs":{},"n":{"df":1,"docs":{"35":{"tf":1.0}}}}}}}}}}},"f":{"a":{"c":{"df":2,"docs":{"42":{"tf":2.6457513110645907},"43":{"tf":1.7320508075688772}}},"df":0,"docs":{},"l":{"df":0,"docs":{},"s":{"df":7,"docs":{"14":{"tf":1.4142135623730951},"27":{"tf":1.4142135623730951},"4":{"tf":1.0},"47":{"tf":2.0},"50":{"tf":1.0},"6":{"tf":1.7320508075688772},"74":{"tf":1.0}}}}},"df":11,"docs":{"10":{"tf":2.23606797749979},"22":{"tf":2.8284271247461903},"23":{"tf":3.0},"24":{"tf":3.7416573867739413},"29":{"tf":1.7320508075688772},"3":{"tf":3.1622776601683795},"35":{"tf":1.7320508075688772},"36":{"tf":2.449489742783178},"61":{"tf":1.7320508075688772},"63":{"tf":2.23606797749979},"66":{"tf":3.605551275463989}},"e":{"df":0,"docs":{},"r":{"df":0,"docs":{},"m":{"a":{"df":0,"docs":{},"t":{"df":1,"docs":{"70":{"tf":1.0}},"l":{"a":{"df":0,"docs":{},"s":{"df":0,"docs":{},"t":{"df":0,"docs":{},"t":{"df":0,"docs":{},"h":{"df":0,"docs":{},"e":{"df":0,"docs":{},"o":{"df":0,"docs":{},"r":{"df":0,"docs":{},"e":{"df":0,"docs":{},"m":{"df":1,"docs":{"70":{"tf":1.4142135623730951}}}}}}}}}}}},"df":0,"docs":{}}}},"df":0,"docs":{}}}},"l":{"df":0,"docs":{},"t":{"df":1,"docs":{"70":{"tf":1.0}}}},"u":{"df":0,"docs":{},"n":{"c":{"df":0,"docs":{},"t":{"df":0,"docs":{},"i":{"df":0,"docs":{},"o":{"df":0,"docs":{},"n":{"df":1,"docs":{"3":{"tf":1.0}}}}}}},"df":4,"docs":{"15":{"tf":1.0},"16":{"tf":1.0},"23":{"tf":1.4142135623730951},"36":{"tf":1.4142135623730951}},"e":{"df":0,"docs":{},"x":{"df":0,"docs":{},"t":{"df":1,"docs":{"36":{"tf":1.7320508075688772}}}}}}}},"g":{"df":9,"docs":{"10":{"tf":1.7320508075688772},"22":{"tf":2.8284271247461903},"24":{"tf":2.23606797749979},"3":{"tf":2.23606797749979},"35":{"tf":1.7320508075688772},"36":{"tf":2.449489742783178},"62":{"tf":1.7320508075688772},"63":{"tf":1.7320508075688772},"66":{"tf":2.6457513110645907}},"e":{"_":{"df":0,"docs":{},"i":{"df":0,"docs":{},"f":{"df":0,"docs":{},"f":{"_":{"df":0,"docs":{},"l":{"df":1,"docs":{"71":{"tf":1.4142135623730951}}}},"df":0,"docs":{}}}}},"df":0,"docs":{},"n":{"df":0,"docs":{},"e":{"df":0,"docs":{},"r":{"a":{"df":0,"docs":{},"r":{"df":1,"docs":{"75":{"tf":1.0}}}},"df":1,"docs":{"44":{"tf":1.0}}}}}},"o":{"a":{"df":0,"docs":{},"l":{"df":1,"docs":{"25":{"tf":1.0}}}},"df":0,"docs":{}},"r":{"df":0,"docs":{},"o":{"df":0,"docs":{},"u":{"df":0,"docs":{},"p":{"df":2,"docs":{"10":{"tf":1.4142135623730951},"62":{"tf":1.0}}}}}},"u":{"a":{"df":0,"docs":{},"r":{"d":{"_":{"df":0,"docs":{},"h":{"df":0,"docs":{},"y":{"df":0,"docs":{},"p":{"df":8,"docs":{"13":{"tf":1.4142135623730951},"22":{"tf":1.4142135623730951},"37":{"tf":1.7320508075688772},"44":{"tf":1.7320508075688772},"45":{"tf":1.0},"57":{"tf":1.4142135623730951},"71":{"tf":1.4142135623730951},"75":{"tf":1.7320508075688772}}}}},"m":{"df":0,"docs":{},"s":{"df":0,"docs":{},"g":{"df":1,"docs":{"10":{"tf":1.0}}}}}},"df":0,"docs":{}},"df":0,"docs":{}}},"df":0,"docs":{}}},"h":{".":{"df":0,"docs":{},"l":{"df":0,"docs":{},"e":{"df":0,"docs":{},"f":{"df":0,"docs":{},"t":{"df":1,"docs":{"25":{"tf":1.4142135623730951}}}}}},"r":{"df":0,"docs":{},"i":{"df":0,"docs":{},"g":{"df":0,"docs":{},"h":{"df":0,"docs":{},"t":{"df":1,"docs":{"25":{"tf":1.0}}}}}}}},"1":{"df":4,"docs":{"49":{"tf":1.0},"50":{"tf":1.0},"56":{"tf":2.0},"61":{"tf":1.4142135623730951}}},"2":{"df":4,"docs":{"49":{"tf":1.0},"50":{"tf":1.0},"56":{"tf":1.4142135623730951},"61":{"tf":1.4142135623730951}}},"a":{"b":{"df":1,"docs":{"61":{"tf":1.7320508075688772}}},"df":0,"docs":{}},"c":{"df":1,"docs":{"29":{"tf":1.4142135623730951}}},"df":30,"docs":{"10":{"tf":1.4142135623730951},"13":{"tf":1.0},"14":{"tf":2.0},"15":{"tf":1.0},"18":{"tf":2.23606797749979},"19":{"tf":1.7320508075688772},"20":{"tf":1.4142135623730951},"21":{"tf":2.449489742783178},"22":{"tf":1.4142135623730951},"23":{"tf":1.7320508075688772},"24":{"tf":2.0},"25":{"tf":1.4142135623730951},"27":{"tf":1.7320508075688772},"29":{"tf":3.0},"38":{"tf":1.4142135623730951},"44":{"tf":1.7320508075688772},"46":{"tf":1.4142135623730951},"47":{"tf":1.7320508075688772},"5":{"tf":2.8284271247461903},"51":{"tf":1.0},"52":{"tf":1.4142135623730951},"54":{"tf":1.7320508075688772},"57":{"tf":1.7320508075688772},"61":{"tf":2.449489742783178},"66":{"tf":3.1622776601683795},"71":{"tf":3.1622776601683795},"73":{"tf":1.4142135623730951},"74":{"tf":1.0},"75":{"tf":2.23606797749979},"8":{"tf":1.4142135623730951}},"e":{"a":{"d":{"df":1,"docs":{"4":{"tf":1.4142135623730951}}},"df":0,"docs":{}},"df":0,"docs":{},"l":{"df":0,"docs":{},"p":{"df":1,"docs":{"1":{"tf":1.0}}}}},"f":{"df":2,"docs":{"22":{"tf":2.0},"24":{"tf":1.4142135623730951}}},"g":{"df":1,"docs":{"22":{"tf":1.7320508075688772}},"f":{"df":0,"docs":{},"i":{"df":0,"docs":{},"n":{"df":0,"docs":{},"j":{"df":2,"docs":{"3":{"tf":1.7320508075688772},"63":{"tf":1.4142135623730951}}}}}}},"k":{"df":1,"docs":{"57":{"tf":2.6457513110645907}}},"n":{"df":2,"docs":{"57":{"tf":1.4142135623730951},"6":{"tf":2.0}},"e":{"_":{"df":0,"docs":{},"s":{"df":0,"docs":{},"t":{"df":1,"docs":{"23":{"tf":1.4142135623730951}}}}},"df":0,"docs":{}},"n":{"df":0,"docs":{},"p":{"df":1,"docs":{"13":{"tf":1.0}}}},"p":{"df":1,"docs":{"27":{"tf":1.0}}},"q":{"df":2,"docs":{"14":{"tf":1.4142135623730951},"47":{"tf":1.4142135623730951}}}},"o":{"df":0,"docs":{},"g":{"df":0,"docs":{},"e":{"df":1,"docs":{"66":{"tf":1.0}}}},"m":{"df":1,"docs":{"66":{"tf":4.0}}}},"p":{"df":27,"docs":{"11":{"tf":1.0},"13":{"tf":1.7320508075688772},"14":{"tf":1.0},"15":{"tf":2.0},"16":{"tf":2.0},"18":{"tf":1.4142135623730951},"19":{"tf":1.4142135623730951},"20":{"tf":1.4142135623730951},"21":{"tf":2.23606797749979},"25":{"tf":1.4142135623730951},"27":{"tf":1.0},"31":{"tf":2.8284271247461903},"37":{"tf":1.7320508075688772},"38":{"tf":1.7320508075688772},"4":{"tf":1.4142135623730951},"40":{"tf":1.0},"46":{"tf":1.7320508075688772},"47":{"tf":2.0},"48":{"tf":1.4142135623730951},"5":{"tf":2.23606797749979},"53":{"tf":1.4142135623730951},"54":{"tf":1.4142135623730951},"55":{"tf":2.0},"6":{"tf":1.4142135623730951},"63":{"tf":1.4142135623730951},"65":{"tf":1.4142135623730951},"8":{"tf":1.4142135623730951}},"q":{"df":10,"docs":{"15":{"tf":2.0},"16":{"tf":1.7320508075688772},"33":{"tf":1.4142135623730951},"38":{"tf":1.7320508075688772},"4":{"tf":1.7320508075688772},"40":{"tf":1.4142135623730951},"46":{"tf":1.7320508075688772},"54":{"tf":1.4142135623730951},"61":{"tf":2.0},"63":{"tf":1.4142135623730951}}},"r":{"df":4,"docs":{"18":{"tf":1.4142135623730951},"19":{"tf":1.4142135623730951},"20":{"tf":1.4142135623730951},"21":{"tf":1.4142135623730951}}}},"q":{"df":15,"docs":{"18":{"tf":1.4142135623730951},"19":{"tf":1.4142135623730951},"20":{"tf":1.4142135623730951},"21":{"tf":2.23606797749979},"25":{"tf":1.4142135623730951},"31":{"tf":1.7320508075688772},"33":{"tf":1.4142135623730951},"38":{"tf":1.7320508075688772},"4":{"tf":1.0},"40":{"tf":1.0},"46":{"tf":1.7320508075688772},"47":{"tf":1.4142135623730951},"53":{"tf":1.4142135623730951},"55":{"tf":2.0},"65":{"tf":1.4142135623730951}},"n":{"df":1,"docs":{"4":{"tf":1.4142135623730951}}},"r":{"df":11,"docs":{"15":{"tf":2.0},"16":{"tf":1.7320508075688772},"18":{"tf":1.4142135623730951},"19":{"tf":1.4142135623730951},"20":{"tf":1.4142135623730951},"21":{"tf":1.4142135623730951},"33":{"tf":1.4142135623730951},"38":{"tf":1.7320508075688772},"4":{"tf":1.0},"46":{"tf":1.7320508075688772},"63":{"tf":1.4142135623730951}}}},"r":{"df":2,"docs":{"55":{"tf":2.0},"63":{"tf":1.4142135623730951}}},"x":{"df":3,"docs":{"26":{"tf":1.4142135623730951},"41":{"tf":2.0},"71":{"tf":1.7320508075688772}}},"y":{"df":1,"docs":{"41":{"tf":1.4142135623730951}},"p":{"df":1,"docs":{"46":{"tf":1.0}}}}},"i":{"d":{"_":{"c":{"df":0,"docs":{},"o":{"df":0,"docs":{},"m":{"df":0,"docs":{},"p":{"df":1,"docs":{"66":{"tf":1.4142135623730951}}}}}},"df":0,"docs":{}},"df":2,"docs":{"49":{"tf":1.7320508075688772},"66":{"tf":2.449489742783178}}},"df":0,"docs":{},"f":{"df":0,"docs":{},"f":{".":{"df":0,"docs":{},"m":{"df":0,"docs":{},"p":{"df":0,"docs":{},"r":{"df":1,"docs":{"72":{"tf":1.0}}}}}},"df":0,"docs":{}}},"h":{"df":4,"docs":{"42":{"tf":1.0},"43":{"tf":1.7320508075688772},"44":{"tf":1.4142135623730951},"45":{"tf":1.4142135623730951}}},"m":{"df":0,"docs":{},"p":{"df":0,"docs":{},"o":{"df":0,"docs":{},"r":{"df":0,"docs":{},"t":{"df":26,"docs":{"10":{"tf":1.7320508075688772},"14":{"tf":1.0},"16":{"tf":1.0},"20":{"tf":1.0},"21":{"tf":1.0},"22":{"tf":1.0},"29":{"tf":1.0},"3":{"tf":1.7320508075688772},"33":{"tf":1.0},"35":{"tf":1.0},"37":{"tf":1.0},"4":{"tf":1.4142135623730951},"43":{"tf":1.0},"48":{"tf":1.0},"49":{"tf":1.0},"51":{"tf":1.0},"52":{"tf":1.0},"56":{"tf":1.0},"57":{"tf":1.0},"58":{"tf":1.7320508075688772},"59":{"tf":1.0},"60":{"tf":1.0},"62":{"tf":1.0},"63":{"tf":1.0},"73":{"tf":1.0},"75":{"tf":1.0}}}}}}},"n":{"d":{"df":0,"docs":{},"u":{"c":{"df":0,"docs":{},"t":{"df":5,"docs":{"42":{"tf":2.23606797749979},"43":{"tf":1.7320508075688772},"44":{"tf":1.4142135623730951},"45":{"tf":1.0},"58":{"tf":1.0}}}},"df":0,"docs":{}}},"df":0,"docs":{},"f":{"df":0,"docs":{},"i":{"df":0,"docs":{},"x":{"df":0,"docs":{},"r":{":":{"8":{"0":{"df":1,"docs":{"66":{"tf":1.0}}},"df":0,"docs":{}},"df":0,"docs":{}},"df":0,"docs":{}}}},"o":{"df":1,"docs":{"10":{"tf":1.0}},"v":{"df":0,"docs":{},"i":{"df":0,"docs":{},"e":{"df":0,"docs":{},"w":{"df":1,"docs":{"63":{"tf":1.0}}}}}}}},"j":{"df":0,"docs":{},"e":{"c":{"df":0,"docs":{},"t":{"df":2,"docs":{"3":{"tf":2.6457513110645907},"63":{"tf":1.7320508075688772}}}},"df":0,"docs":{}}},"l":{"df":4,"docs":{"13":{"tf":1.0},"18":{"tf":1.7320508075688772},"19":{"tf":1.4142135623730951},"71":{"tf":1.0}}},"r":{"df":4,"docs":{"13":{"tf":1.0},"18":{"tf":1.7320508075688772},"19":{"tf":1.4142135623730951},"71":{"tf":1.0}}},"s":{"df":0,"docs":{},"e":{"df":0,"docs":{},"r":{"df":0,"docs":{},"t":{"df":1,"docs":{"18":{"tf":1.4142135623730951}}}}}},"t":{"df":5,"docs":{"24":{"tf":2.0},"52":{"tf":1.4142135623730951},"56":{"tf":1.4142135623730951},"57":{"tf":1.0},"71":{"tf":1.7320508075688772}},"r":{"df":0,"docs":{},"o":{"d":{"df":0,"docs":{},"u":{"c":{"df":1,"docs":{"46":{"tf":1.0}}},"df":0,"docs":{}}},"df":19,"docs":{"13":{"tf":1.0},"14":{"tf":1.0},"15":{"tf":1.0},"16":{"tf":1.0},"18":{"tf":1.0},"19":{"tf":1.0},"20":{"tf":1.0},"21":{"tf":1.4142135623730951},"23":{"tf":1.0},"26":{"tf":1.0},"3":{"tf":1.4142135623730951},"35":{"tf":1.0},"38":{"tf":1.0},"4":{"tf":1.0},"46":{"tf":2.449489742783178},"47":{"tf":1.7320508075688772},"52":{"tf":1.0},"57":{"tf":1.0},"63":{"tf":1.0}}}}}},"t":{"df":0,"docs":{},"e":{"_":{"df":0,"docs":{},"f":{"a":{"df":0,"docs":{},"l":{"df":0,"docs":{},"s":{"df":1,"docs":{"71":{"tf":1.0}}}}},"df":0,"docs":{}},"t":{"df":0,"docs":{},"r":{"df":0,"docs":{},"u":{"df":1,"docs":{"71":{"tf":1.0}}}}}},"df":0,"docs":{}}}},"k":{"df":3,"docs":{"43":{"tf":1.4142135623730951},"45":{"tf":1.7320508075688772},"57":{"tf":3.3166247903554}}},"l":{".":{"df":0,"docs":{},"l":{"df":0,"docs":{},"e":{"df":0,"docs":{},"n":{"df":0,"docs":{},"g":{"df":0,"docs":{},"t":{"df":0,"docs":{},"h":{"df":1,"docs":{"44":{"tf":1.0}}}}}}}}},"df":1,"docs":{"44":{"tf":3.1622776601683795}},"e":{"a":{"df":0,"docs":{},"n":{".":{"df":0,"docs":{},"m":{"df":0,"docs":{},"v":{"a":{"df":0,"docs":{},"r":{"df":0,"docs":{},"i":{"d":{".":{"df":0,"docs":{},"r":{"df":0,"docs":{},"e":{"df":0,"docs":{},"f":{"df":0,"docs":{},"l":{"df":1,"docs":{"59":{"tf":1.0}}}}},"f":{"df":0,"docs":{},"l":{"df":1,"docs":{"59":{"tf":1.0}}}}}},"df":0,"docs":{}},"df":0,"docs":{}}}},"df":0,"docs":{}}}},"4":{"df":3,"docs":{"0":{"tf":1.0},"17":{"tf":1.0},"28":{"tf":1.0}}},"df":8,"docs":{"0":{"tf":1.0},"15":{"tf":1.0},"2":{"tf":2.0},"42":{"tf":1.0},"47":{"tf":1.0},"6":{"tf":1.0},"71":{"tf":1.0},"75":{"tf":1.0}}}},"df":0,"docs":{},"f":{"df":0,"docs":{},"t":{"df":3,"docs":{"18":{"tf":1.0},"25":{"tf":1.0},"48":{"tf":2.0}}}}},"i":{"df":0,"docs":{},"n":{"a":{"df":0,"docs":{},"r":{"df":0,"docs":{},"i":{"df":0,"docs":{},"t":{"df":0,"docs":{},"h":{"df":5,"docs":{"49":{"tf":3.0},"50":{"tf":1.4142135623730951},"51":{"tf":1.7320508075688772},"52":{"tf":1.0},"71":{"tf":1.4142135623730951}}}}}}},"df":0,"docs":{},"e":{"a":{"df":0,"docs":{},"r":{"df":2,"docs":{"49":{"tf":1.0},"51":{"tf":1.0}}}},"df":0,"docs":{}}},"s":{"df":0,"docs":{},"t":{".":{"df":0,"docs":{},"l":{"df":0,"docs":{},"e":{"df":0,"docs":{},"n":{"df":0,"docs":{},"g":{"df":0,"docs":{},"t":{"df":0,"docs":{},"h":{"df":1,"docs":{"44":{"tf":1.7320508075688772}}}}}}}}},"df":1,"docs":{"44":{"tf":1.7320508075688772}}}}},"o":{"df":0,"docs":{},"s":{"df":0,"docs":{},"s":{"df":1,"docs":{"75":{"tf":1.0}}}}}},"m":{"a":{"df":0,"docs":{},"t":{"c":{"df":0,"docs":{},"h":{"df":1,"docs":{"45":{"tf":1.0}}}},"df":0,"docs":{},"h":{"df":0,"docs":{},"e":{"df":0,"docs":{},"m":{"a":{"df":0,"docs":{},"t":{"df":1,"docs":{"2":{"tf":1.0}}}},"df":0,"docs":{}}},"l":{"df":0,"docs":{},"i":{"b":{".":{"a":{"df":0,"docs":{},"l":{"df":0,"docs":{},"g":{"df":0,"docs":{},"e":{"b":{"df":0,"docs":{},"r":{"a":{".":{"df":0,"docs":{},"g":{"df":0,"docs":{},"r":{"df":0,"docs":{},"o":{"df":0,"docs":{},"u":{"df":0,"docs":{},"p":{".":{"d":{"df":0,"docs":{},"e":{"df":0,"docs":{},"f":{"df":1,"docs":{"10":{"tf":1.0}}}}},"df":0,"docs":{}},"df":0,"docs":{}}}}}},"h":{"df":0,"docs":{},"o":{"df":0,"docs":{},"m":{".":{"df":0,"docs":{},"g":{"df":0,"docs":{},"r":{"df":0,"docs":{},"o":{"df":0,"docs":{},"u":{"df":0,"docs":{},"p":{".":{"d":{"df":0,"docs":{},"e":{"df":0,"docs":{},"f":{"df":1,"docs":{"10":{"tf":1.0}}}}},"df":0,"docs":{}},"df":0,"docs":{}}}}}}},"df":0,"docs":{}}}}},"df":0,"docs":{}},"df":0,"docs":{}}},"df":0,"docs":{}}}}},"d":{"a":{"df":0,"docs":{},"t":{"a":{".":{"df":0,"docs":{},"n":{"a":{"df":0,"docs":{},"t":{".":{"b":{"a":{"df":0,"docs":{},"s":{"df":1,"docs":{"58":{"tf":1.0}}}},"df":0,"docs":{}},"df":0,"docs":{}},"df":0,"docs":{}}},"df":0,"docs":{}},"s":{"df":0,"docs":{},"e":{"df":0,"docs":{},"t":{"df":0,"docs":{},"l":{"df":0,"docs":{},"i":{"df":0,"docs":{},"k":{"df":0,"docs":{},"e":{".":{"b":{"a":{"df":0,"docs":{},"s":{"df":1,"docs":{"35":{"tf":1.0}}}},"df":0,"docs":{}},"df":0,"docs":{}},"df":0,"docs":{}}}}}}}}},"df":0,"docs":{}},"df":0,"docs":{}}},"df":0,"docs":{}},"df":0,"docs":{},"i":{"df":0,"docs":{},"n":{"df":0,"docs":{},"i":{"df":0,"docs":{},"t":{".":{"df":0,"docs":{},"f":{"df":0,"docs":{},"u":{"df":0,"docs":{},"n":{"c":{"df":0,"docs":{},"t":{"df":1,"docs":{"3":{"tf":1.0}}}},"df":0,"docs":{}}}}},"df":0,"docs":{}}}}},"t":{"a":{"c":{"df":0,"docs":{},"t":{"df":0,"docs":{},"i":{"c":{".":{"b":{"df":0,"docs":{},"y":{"c":{"df":0,"docs":{},"o":{"df":0,"docs":{},"n":{"df":0,"docs":{},"t":{"df":0,"docs":{},"r":{"a":{"df":1,"docs":{"14":{"tf":1.0}}},"df":0,"docs":{}}}}}},"df":0,"docs":{}}},"c":{"a":{"df":0,"docs":{},"s":{"df":2,"docs":{"20":{"tf":1.0},"43":{"tf":1.0}}}},"df":0,"docs":{},"h":{"df":0,"docs":{},"o":{"df":0,"docs":{},"o":{"df":0,"docs":{},"s":{"df":1,"docs":{"22":{"tf":1.0}}}}}},"o":{"df":0,"docs":{},"n":{"df":0,"docs":{},"v":{"df":0,"docs":{},"e":{"df":0,"docs":{},"r":{"df":0,"docs":{},"t":{"df":1,"docs":{"29":{"tf":1.0}}}}}}}}},"df":0,"docs":{},"g":{"c":{"df":0,"docs":{},"o":{"df":0,"docs":{},"n":{"df":0,"docs":{},"g":{"df":0,"docs":{},"r":{"df":1,"docs":{"56":{"tf":1.0}}}}}}},"df":0,"docs":{}},"l":{"df":0,"docs":{},"e":{"df":0,"docs":{},"f":{"df":0,"docs":{},"t":{"df":0,"docs":{},"r":{"df":0,"docs":{},"i":{"df":0,"docs":{},"g":{"df":0,"docs":{},"h":{"df":0,"docs":{},"t":{"df":1,"docs":{"48":{"tf":1.0}}}}}}}}}},"i":{"b":{"df":0,"docs":{},"r":{"a":{"df":0,"docs":{},"r":{"df":0,"docs":{},"y":{"df":0,"docs":{},"s":{"df":0,"docs":{},"e":{"a":{"df":0,"docs":{},"r":{"c":{"df":0,"docs":{},"h":{"df":2,"docs":{"10":{"tf":1.0},"33":{"tf":1.0}}}},"df":0,"docs":{}}},"df":0,"docs":{}}}}}},"df":0,"docs":{}}},"df":0,"docs":{},"n":{"a":{"df":0,"docs":{},"r":{"df":0,"docs":{},"i":{"df":0,"docs":{},"t":{"df":0,"docs":{},"h":{"df":2,"docs":{"49":{"tf":1.0},"51":{"tf":1.0}}}}}}},"df":0,"docs":{}}}},"n":{"df":0,"docs":{},"t":{"df":0,"docs":{},"h":{"df":0,"docs":{},"r":{"df":0,"docs":{},"e":{"df":0,"docs":{},"w":{"df":0,"docs":{},"r":{"df":0,"docs":{},"i":{"df":0,"docs":{},"t":{"df":1,"docs":{"62":{"tf":1.0}}}}}}}}}}},"p":{"df":0,"docs":{},"u":{"df":0,"docs":{},"s":{"df":0,"docs":{},"h":{"df":0,"docs":{},"n":{"df":0,"docs":{},"e":{"df":0,"docs":{},"g":{"df":1,"docs":{"52":{"tf":1.0}}}}}}}}},"r":{"df":1,"docs":{"60":{"tf":1.0}},"e":{"df":0,"docs":{},"l":{"a":{"df":0,"docs":{},"t":{"df":0,"docs":{},"i":{"df":0,"docs":{},"o":{"df":0,"docs":{},"n":{".":{"df":0,"docs":{},"r":{"df":0,"docs":{},"f":{"df":0,"docs":{},"l":{"df":2,"docs":{"58":{"tf":1.0},"59":{"tf":1.4142135623730951}}}}}},"df":0,"docs":{}}}}}},"df":0,"docs":{}}}},"s":{"a":{"df":0,"docs":{},"y":{"df":2,"docs":{"3":{"tf":1.0},"63":{"tf":1.0}}}},"df":0,"docs":{},"o":{"df":0,"docs":{},"l":{"df":0,"docs":{},"v":{"df":0,"docs":{},"e":{"b":{"df":0,"docs":{},"y":{"df":0,"docs":{},"e":{"df":0,"docs":{},"l":{"df":0,"docs":{},"i":{"df":0,"docs":{},"m":{"df":1,"docs":{"4":{"tf":1.4142135623730951}}}}}}}},"df":0,"docs":{}}}}}},"t":{"a":{"df":0,"docs":{},"u":{"df":0,"docs":{},"t":{"df":0,"docs":{},"o":{"df":1,"docs":{"73":{"tf":1.0}}}}}},"df":0,"docs":{}},"w":{"df":0,"docs":{},"l":{"df":0,"docs":{},"o":{"df":0,"docs":{},"g":{"df":1,"docs":{"75":{"tf":1.0}}}}}}},"df":0,"docs":{}},"df":0,"docs":{}}}},"df":0,"docs":{}},"df":0,"docs":{}}},"4":{"df":2,"docs":{"2":{"tf":1.0},"48":{"tf":1.0}}},"df":0,"docs":{}},"df":0,"docs":{}}}}}},"df":1,"docs":{"45":{"tf":1.7320508075688772}},"o":{"df":0,"docs":{},"n":{"df":0,"docs":{},"o":{"df":0,"docs":{},"i":{"d":{"df":0,"docs":{},"h":{"df":0,"docs":{},"o":{"df":0,"docs":{},"m":{".":{"df":0,"docs":{},"m":{"a":{"df":0,"docs":{},"p":{"_":{"df":0,"docs":{},"m":{"df":0,"docs":{},"u":{"df":0,"docs":{},"l":{"df":1,"docs":{"10":{"tf":1.0}}}}}},"df":0,"docs":{}}},"df":0,"docs":{}}},"df":0,"docs":{}}}}},"df":0,"docs":{}}}}},"u":{"df":0,"docs":{},"l":{"_":{"df":0,"docs":{},"i":{"df":0,"docs":{},"n":{"df":0,"docs":{},"v":{"_":{"df":0,"docs":{},"e":{"df":0,"docs":{},"q":{"_":{"df":0,"docs":{},"i":{"df":0,"docs":{},"f":{"df":0,"docs":{},"f":{"_":{"df":0,"docs":{},"e":{"df":0,"docs":{},"q":{"_":{"df":0,"docs":{},"m":{"df":0,"docs":{},"u":{"df":0,"docs":{},"l":{"df":1,"docs":{"62":{"tf":1.4142135623730951}}}}}},"df":0,"docs":{}}}},"df":0,"docs":{}}}}},"df":0,"docs":{}}}},"df":0,"docs":{}}}},"n":{"df":0,"docs":{},"e":{"df":0,"docs":{},"g":{"df":1,"docs":{"71":{"tf":1.0}}}}}},"df":0,"docs":{}}},"y":{"a":{"b":{"df":1,"docs":{"71":{"tf":2.23606797749979}}},"df":0,"docs":{}},"df":0,"docs":{},"e":{"df":0,"docs":{},"q":{".":{"df":0,"docs":{},"r":{"df":0,"docs":{},"e":{"df":0,"docs":{},"f":{"df":0,"docs":{},"l":{"df":1,"docs":{"58":{"tf":1.0}}}}}}},"df":1,"docs":{"58":{"tf":1.7320508075688772}}}}}},"n":{"a":{"df":0,"docs":{},"m":{"df":0,"docs":{},"e":{"df":11,"docs":{"21":{"tf":1.0},"24":{"tf":1.0},"35":{"tf":1.0},"46":{"tf":1.0},"49":{"tf":1.0},"51":{"tf":1.0},"52":{"tf":1.0},"56":{"tf":1.0},"58":{"tf":1.0},"73":{"tf":1.0},"75":{"tf":1.0}}}},"t":{".":{"d":{"df":0,"docs":{},"v":{"d":{"_":{"df":0,"docs":{},"i":{"df":0,"docs":{},"f":{"df":0,"docs":{},"f":{"_":{"d":{"df":0,"docs":{},"i":{"df":0,"docs":{},"v":{"_":{"df":0,"docs":{},"m":{"df":0,"docs":{},"u":{"df":0,"docs":{},"l":{"_":{"df":0,"docs":{},"e":{"df":0,"docs":{},"q":{"df":1,"docs":{"72":{"tf":1.0}}}}},"df":0,"docs":{}}}}},"df":0,"docs":{}}}},"df":0,"docs":{}},"df":0,"docs":{}}}}},"df":0,"docs":{}},"df":0,"docs":{}}},"df":0,"docs":{},"l":{"df":0,"docs":{},"t":{".":{"b":{"a":{"df":0,"docs":{},"s":{"df":1,"docs":{"33":{"tf":1.0}}}},"df":0,"docs":{}},"df":0,"docs":{}},"df":0,"docs":{}}},"m":{"df":0,"docs":{},"u":{"df":0,"docs":{},"l":{"_":{"a":{"df":0,"docs":{},"s":{"df":0,"docs":{},"s":{"df":0,"docs":{},"o":{"c":{"df":1,"docs":{"61":{"tf":1.4142135623730951}}},"df":0,"docs":{}}}}},"df":0,"docs":{}},"df":0,"docs":{}}}},"s":{"df":0,"docs":{},"t":{"df":0,"docs":{},"r":{"df":0,"docs":{},"o":{"df":0,"docs":{},"n":{"df":0,"docs":{},"g":{"_":{"df":0,"docs":{},"i":{"df":0,"docs":{},"n":{"d":{"df":0,"docs":{},"u":{"c":{"df":0,"docs":{},"t":{"df":0,"docs":{},"i":{"df":0,"docs":{},"o":{"df":0,"docs":{},"n":{"_":{"df":0,"docs":{},"o":{"df":0,"docs":{},"n":{"df":1,"docs":{"45":{"tf":1.0}}}}},"df":0,"docs":{}}}}}},"df":0,"docs":{}}},"df":0,"docs":{}}}},"df":0,"docs":{}}}}}}}},"df":15,"docs":{"10":{"tf":1.0},"26":{"tf":1.0},"27":{"tf":1.0},"29":{"tf":1.4142135623730951},"34":{"tf":1.0},"36":{"tf":1.4142135623730951},"42":{"tf":2.8284271247461903},"43":{"tf":1.0},"45":{"tf":1.4142135623730951},"46":{"tf":1.0},"51":{"tf":1.0},"58":{"tf":1.0},"61":{"tf":1.0},"70":{"tf":1.0},"75":{"tf":1.4142135623730951}}}},"df":8,"docs":{"42":{"tf":3.872983346207417},"43":{"tf":1.7320508075688772},"44":{"tf":2.0},"45":{"tf":3.3166247903554},"46":{"tf":1.7320508075688772},"57":{"tf":3.7416573867739413},"58":{"tf":2.449489742783178},"70":{"tf":2.23606797749979}},"e":{"df":0,"docs":{},"e":{"d":{"df":22,"docs":{"14":{"tf":1.0},"16":{"tf":1.0},"20":{"tf":1.0},"21":{"tf":1.0},"22":{"tf":1.0},"29":{"tf":1.0},"35":{"tf":1.0},"37":{"tf":1.0},"4":{"tf":1.0},"43":{"tf":1.0},"48":{"tf":1.0},"49":{"tf":1.0},"51":{"tf":1.0},"52":{"tf":1.0},"56":{"tf":1.0},"57":{"tf":1.0},"58":{"tf":1.0},"60":{"tf":1.0},"62":{"tf":1.0},"63":{"tf":1.0},"73":{"tf":1.0},"75":{"tf":1.0}}},"df":0,"docs":{}},"g":{"a":{"df":0,"docs":{},"t":{"df":1,"docs":{"52":{"tf":1.0}}}},"df":0,"docs":{}}},"l":{"df":0,"docs":{},"i":{"df":0,"docs":{},"n":{"a":{"df":0,"docs":{},"r":{"df":0,"docs":{},"i":{"df":0,"docs":{},"t":{"df":0,"docs":{},"h":{"df":1,"docs":{"51":{"tf":1.7320508075688772}}}}}}},"df":0,"docs":{}}}},"o":{"df":0,"docs":{},"n":{"c":{"df":0,"docs":{},"o":{"df":0,"docs":{},"m":{"df":0,"docs":{},"p":{"df":0,"docs":{},"u":{"df":0,"docs":{},"t":{"df":1,"docs":{"23":{"tf":1.0}}}}}}}},"df":1,"docs":{"51":{"tf":1.0}},"e":{"df":0,"docs":{},"m":{"df":0,"docs":{},"p":{"df":0,"docs":{},"t":{"df":0,"docs":{},"i":{"df":1,"docs":{"23":{"tf":1.0}}}}}}}}},"t":{"df":0,"docs":{},"h":{"_":{"df":0,"docs":{},"r":{"df":0,"docs":{},"w":{"df":2,"docs":{"57":{"tf":1.0},"62":{"tf":1.4142135623730951}}}}},"df":0,"docs":{}}}},"o":{"b":{"df":0,"docs":{},"t":{"a":{"df":0,"docs":{},"i":{"df":0,"docs":{},"n":{"df":1,"docs":{"57":{"tf":1.0}}}}},"df":0,"docs":{}}},"df":0,"docs":{},"n":{"df":0,"docs":{},"e":{"_":{"df":0,"docs":{},"m":{"df":0,"docs":{},"u":{"df":0,"docs":{},"l":{"df":1,"docs":{"62":{"tf":1.4142135623730951}}}}}},"df":0,"docs":{}}},"p":{"df":0,"docs":{},"e":{"df":0,"docs":{},"n":{"df":2,"docs":{"3":{"tf":1.0},"66":{"tf":1.0}}}},"t":{"df":0,"docs":{},"i":{"df":0,"docs":{},"o":{"df":0,"docs":{},"n":{"df":1,"docs":{"1":{"tf":1.0}}}}}}},"r":{".":{"df":0,"docs":{},"i":{"df":0,"docs":{},"n":{"df":0,"docs":{},"l":{"df":1,"docs":{"48":{"tf":1.4142135623730951}}},"r":{"df":1,"docs":{"48":{"tf":1.0}}}}}},"df":0,"docs":{}}},"p":{"(":{"0":{"df":1,"docs":{"45":{"tf":1.0}}},"df":0,"docs":{},"x":{"df":2,"docs":{"22":{"tf":1.4142135623730951},"46":{"tf":1.0}}}},"df":43,"docs":{"11":{"tf":1.7320508075688772},"13":{"tf":3.3166247903554},"14":{"tf":2.6457513110645907},"15":{"tf":2.8284271247461903},"16":{"tf":1.4142135623730951},"18":{"tf":2.449489742783178},"19":{"tf":1.7320508075688772},"20":{"tf":1.4142135623730951},"21":{"tf":3.0},"23":{"tf":2.449489742783178},"25":{"tf":3.0},"26":{"tf":1.0},"27":{"tf":2.6457513110645907},"31":{"tf":2.449489742783178},"33":{"tf":1.7320508075688772},"34":{"tf":1.7320508075688772},"37":{"tf":1.7320508075688772},"38":{"tf":3.0},"4":{"tf":2.449489742783178},"40":{"tf":2.23606797749979},"41":{"tf":1.4142135623730951},"42":{"tf":2.0},"44":{"tf":2.23606797749979},"45":{"tf":2.449489742783178},"46":{"tf":4.242640687119285},"47":{"tf":3.3166247903554},"48":{"tf":2.449489742783178},"5":{"tf":3.7416573867739413},"52":{"tf":3.4641016151377544},"53":{"tf":2.0},"54":{"tf":2.23606797749979},"55":{"tf":2.6457513110645907},"57":{"tf":1.0},"6":{"tf":2.6457513110645907},"61":{"tf":1.7320508075688772},"63":{"tf":1.4142135623730951},"65":{"tf":2.23606797749979},"66":{"tf":1.4142135623730951},"71":{"tf":1.7320508075688772},"72":{"tf":1.0},"73":{"tf":3.0},"74":{"tf":1.0},"8":{"tf":2.0}},"h":{"df":0,"docs":{},"r":{"a":{"df":0,"docs":{},"s":{"df":0,"docs":{},"e":{"b":{"df":0,"docs":{},"o":{"df":0,"docs":{},"o":{"df":0,"docs":{},"k":{"df":1,"docs":{"2":{"tf":1.0}}}}}},"df":0,"docs":{}}}},"df":0,"docs":{}}},"o":{"df":0,"docs":{},"s":{"df":0,"docs":{},"i":{"df":0,"docs":{},"t":{"df":2,"docs":{"42":{"tf":1.0},"43":{"tf":1.0}}}}}},"r":{"df":0,"docs":{},"i":{"df":0,"docs":{},"n":{"df":0,"docs":{},"t":{"df":1,"docs":{"10":{"tf":1.0}}}}},"o":{"df":0,"docs":{},"p":{"df":9,"docs":{"13":{"tf":1.0},"21":{"tf":1.0},"23":{"tf":1.0},"33":{"tf":1.0},"4":{"tf":1.0},"44":{"tf":1.0},"45":{"tf":1.0},"46":{"tf":1.0},"58":{"tf":1.0}}},"v":{"df":0,"docs":{},"e":{"df":2,"docs":{"17":{"tf":1.0},"28":{"tf":1.0}}}}}},"u":{"df":0,"docs":{},"s":{"df":0,"docs":{},"h":{"_":{"df":0,"docs":{},"n":{"df":0,"docs":{},"e":{"df":0,"docs":{},"g":{"df":1,"docs":{"52":{"tf":2.0}}}}}},"df":1,"docs":{"52":{"tf":1.0}}}}},"y":{"df":1,"docs":{"23":{"tf":1.4142135623730951}}}},"q":{"(":{"df":0,"docs":{},"i":{"df":1,"docs":{"46":{"tf":1.0}}}},"df":32,"docs":{"11":{"tf":1.0},"14":{"tf":2.23606797749979},"15":{"tf":2.0},"16":{"tf":1.4142135623730951},"18":{"tf":2.449489742783178},"19":{"tf":1.7320508075688772},"20":{"tf":1.4142135623730951},"21":{"tf":3.0},"25":{"tf":2.8284271247461903},"26":{"tf":1.0},"27":{"tf":1.0},"31":{"tf":1.4142135623730951},"33":{"tf":1.7320508075688772},"38":{"tf":2.6457513110645907},"4":{"tf":2.449489742783178},"40":{"tf":2.23606797749979},"42":{"tf":2.0},"46":{"tf":3.872983346207417},"47":{"tf":3.0},"48":{"tf":2.0},"5":{"tf":3.4641016151377544},"52":{"tf":3.1622776601683795},"53":{"tf":1.4142135623730951},"54":{"tf":2.0},"55":{"tf":2.8284271247461903},"61":{"tf":1.4142135623730951},"63":{"tf":1.4142135623730951},"65":{"tf":1.7320508075688772},"71":{"tf":1.7320508075688772},"72":{"tf":2.6457513110645907},"73":{"tf":2.23606797749979},"8":{"tf":2.0}}},"r":{"c":{"a":{"df":0,"docs":{},"s":{"df":0,"docs":{},"e":{"df":1,"docs":{"21":{"tf":2.0}}}}},"df":0,"docs":{}},"df":13,"docs":{"15":{"tf":2.449489742783178},"16":{"tf":1.4142135623730951},"18":{"tf":1.7320508075688772},"19":{"tf":1.7320508075688772},"20":{"tf":1.7320508075688772},"21":{"tf":2.0},"33":{"tf":1.4142135623730951},"38":{"tf":2.23606797749979},"4":{"tf":1.7320508075688772},"46":{"tf":2.6457513110645907},"55":{"tf":2.8284271247461903},"63":{"tf":1.4142135623730951},"73":{"tf":1.4142135623730951}},"e":{"c":{"df":0,"docs":{},"u":{"df":0,"docs":{},"r":{"df":0,"docs":{},"s":{"df":1,"docs":{"21":{"tf":1.0}}}}}},"df":0,"docs":{},"f":{"df":0,"docs":{},"i":{"df":0,"docs":{},"n":{"df":4,"docs":{"10":{"tf":1.0},"53":{"tf":1.7320508075688772},"54":{"tf":2.0},"55":{"tf":1.7320508075688772}}}},"l":{"df":2,"docs":{"58":{"tf":2.0},"59":{"tf":1.0}},"e":{"df":0,"docs":{},"x":{"df":1,"docs":{"58":{"tf":1.0}}}}}},"l":{"a":{"df":0,"docs":{},"t":{"df":1,"docs":{"56":{"tf":1.0}}}},"df":1,"docs":{"56":{"tf":2.23606797749979}}},"p":{"df":0,"docs":{},"e":{"a":{"df":0,"docs":{},"t":{"df":1,"docs":{"4":{"tf":1.7320508075688772}}}},"df":0,"docs":{}},"l":{"a":{"c":{"df":2,"docs":{"57":{"tf":2.0},"71":{"tf":1.0}}},"df":0,"docs":{}},"df":0,"docs":{}}}},"f":{"df":0,"docs":{},"l":{"df":5,"docs":{"49":{"tf":1.0},"58":{"tf":2.0},"59":{"tf":2.0},"72":{"tf":1.4142135623730951},"74":{"tf":1.0}}}},"i":{"df":0,"docs":{},"g":{"df":0,"docs":{},"h":{"df":0,"docs":{},"t":{"df":3,"docs":{"18":{"tf":1.0},"25":{"tf":1.0},"48":{"tf":1.7320508075688772}}}}},"n":{"df":0,"docs":{},"g":{"df":4,"docs":{"36":{"tf":1.0},"41":{"tf":1.0},"57":{"tf":2.0},"60":{"tf":2.23606797749979}}}}},"w":{"df":10,"docs":{"26":{"tf":1.0},"29":{"tf":1.0},"3":{"tf":1.4142135623730951},"41":{"tf":1.0},"46":{"tf":1.0},"57":{"tf":1.4142135623730951},"61":{"tf":3.4641016151377544},"62":{"tf":1.0},"63":{"tf":1.0},"67":{"tf":1.0}}}},"s":{"a":{"df":0,"docs":{},"y":{"df":0,"docs":{},"s":{".":{"df":0,"docs":{},"n":{"df":0,"docs":{},"o":{"_":{"df":0,"docs":{},"v":{"df":0,"docs":{},"e":{"df":0,"docs":{},"r":{"df":0,"docs":{},"i":{"df":0,"docs":{},"f":{"df":0,"docs":{},"y":{"_":{"df":0,"docs":{},"i":{"df":0,"docs":{},"n":{"_":{"c":{"df":0,"docs":{},"i":{"df":2,"docs":{"3":{"tf":1.0},"64":{"tf":1.0}}}},"df":0,"docs":{}},"df":0,"docs":{}}}},"df":0,"docs":{}}}}}}}},"df":0,"docs":{}}},"v":{"df":0,"docs":{},"e":{"df":0,"docs":{},"r":{"df":0,"docs":{},"i":{"df":0,"docs":{},"f":{"df":0,"docs":{},"i":{"df":1,"docs":{"64":{"tf":1.0}}}}}}}}},"df":0,"docs":{}}}},"df":2,"docs":{"35":{"tf":2.449489742783178},"63":{"tf":1.4142135623730951}},"e":{"df":0,"docs":{},"t":{"_":{"df":0,"docs":{},"o":{"df":0,"docs":{},"p":{"df":0,"docs":{},"t":{"df":2,"docs":{"1":{"tf":1.0},"3":{"tf":1.0}}}}}},"df":1,"docs":{"35":{"tf":1.0}}}},"h":{"df":0,"docs":{},"o":{"df":0,"docs":{},"w":{"_":{"df":0,"docs":{},"t":{"df":0,"docs":{},"e":{"df":0,"docs":{},"r":{"df":0,"docs":{},"m":{"df":1,"docs":{"60":{"tf":1.4142135623730951}}}}}}},"df":16,"docs":{"14":{"tf":1.0},"24":{"tf":1.4142135623730951},"29":{"tf":1.0},"3":{"tf":1.0},"4":{"tf":1.7320508075688772},"44":{"tf":1.4142135623730951},"46":{"tf":1.4142135623730951},"47":{"tf":1.0},"5":{"tf":1.0},"52":{"tf":1.4142135623730951},"53":{"tf":1.0},"54":{"tf":1.0},"55":{"tf":2.6457513110645907},"65":{"tf":2.0},"71":{"tf":1.7320508075688772},"75":{"tf":1.4142135623730951}}}}},"i":{"df":0,"docs":{},"m":{"df":0,"docs":{},"p":{"_":{"a":{"df":0,"docs":{},"l":{"df":4,"docs":{"26":{"tf":1.0},"3":{"tf":1.0},"63":{"tf":1.0},"68":{"tf":1.4142135623730951}}}},"df":0,"docs":{}},"df":11,"docs":{"24":{"tf":1.4142135623730951},"3":{"tf":1.0},"42":{"tf":1.4142135623730951},"43":{"tf":1.4142135623730951},"60":{"tf":1.0},"63":{"tf":1.0},"66":{"tf":2.8284271247461903},"67":{"tf":1.4142135623730951},"68":{"tf":1.0},"69":{"tf":1.0},"71":{"tf":2.449489742783178}}}}},"o":{"df":0,"docs":{},"r":{"df":0,"docs":{},"r":{"df":0,"docs":{},"i":{"df":4,"docs":{"10":{"tf":1.4142135623730951},"44":{"tf":1.4142135623730951},"45":{"tf":1.4142135623730951},"70":{"tf":2.0}}},"y":{"a":{"df":0,"docs":{},"x":{"df":1,"docs":{"10":{"tf":1.7320508075688772}}}},"df":0,"docs":{}}}}},"p":{"df":0,"docs":{},"l":{"df":0,"docs":{},"i":{"df":0,"docs":{},"t":{"df":1,"docs":{"71":{"tf":2.23606797749979}}}}}},"t":{"d":{".":{"df":0,"docs":{},"t":{"a":{"c":{"df":0,"docs":{},"t":{"df":0,"docs":{},"i":{"c":{".":{"df":0,"docs":{},"e":{"df":0,"docs":{},"x":{"df":0,"docs":{},"t":{"df":1,"docs":{"35":{"tf":1.0}}}}},"g":{"df":0,"docs":{},"u":{"a":{"df":0,"docs":{},"r":{"d":{"df":0,"docs":{},"e":{"df":0,"docs":{},"x":{"df":0,"docs":{},"p":{"df":0,"docs":{},"r":{"df":1,"docs":{"37":{"tf":1.0}}}}}}},"df":0,"docs":{}}},"df":0,"docs":{}}},"r":{"c":{"a":{"df":0,"docs":{},"s":{"df":1,"docs":{"21":{"tf":1.0}}}},"df":0,"docs":{}},"df":0,"docs":{},"e":{"df":0,"docs":{},"p":{"df":0,"docs":{},"l":{"a":{"c":{"df":1,"docs":{"57":{"tf":1.0}}},"df":0,"docs":{}},"df":0,"docs":{}}}}},"s":{"df":0,"docs":{},"h":{"df":0,"docs":{},"o":{"df":0,"docs":{},"w":{"df":0,"docs":{},"t":{"df":0,"docs":{},"e":{"df":0,"docs":{},"r":{"df":0,"docs":{},"m":{"df":1,"docs":{"16":{"tf":1.0}}}}}}}}}}},"df":0,"docs":{}},"df":0,"docs":{}}}},"df":0,"docs":{}},"df":0,"docs":{}}},"df":0,"docs":{}},"df":0,"docs":{}},"u":{"c":{"c":{"df":2,"docs":{"42":{"tf":2.6457513110645907},"44":{"tf":1.0}}},"df":0,"docs":{}},"df":0,"docs":{},"f":{"df":0,"docs":{},"f":{"df":0,"docs":{},"i":{"c":{"df":1,"docs":{"72":{"tf":2.6457513110645907}}},"df":0,"docs":{}}}}}},"t":{"a":{"c":{"df":0,"docs":{},"t":{"df":0,"docs":{},"i":{"c":{"df":1,"docs":{"2":{"tf":1.0}}},"df":0,"docs":{}}}},"df":0,"docs":{},"u":{"df":0,"docs":{},"t":{"df":0,"docs":{},"o":{"df":1,"docs":{"73":{"tf":2.449489742783178}},"l":{"df":0,"docs":{},"o":{"df":0,"docs":{},"g":{"df":1,"docs":{"73":{"tf":1.0}}}}}}}}},"df":2,"docs":{"10":{"tf":1.7320508075688772},"35":{"tf":2.449489742783178}},"h":{"df":0,"docs":{},"e":{"df":0,"docs":{},"o":{"df":0,"docs":{},"r":{"df":0,"docs":{},"e":{"df":0,"docs":{},"m":{"df":4,"docs":{"10":{"tf":1.0},"17":{"tf":1.0},"28":{"tf":1.0},"70":{"tf":1.0}}}},"i":{"df":1,"docs":{"2":{"tf":1.0}}}}}}},"r":{"df":0,"docs":{},"i":{"df":7,"docs":{"16":{"tf":1.0},"29":{"tf":1.0},"33":{"tf":1.4142135623730951},"49":{"tf":1.0},"51":{"tf":1.0},"63":{"tf":1.7320508075688772},"73":{"tf":1.4142135623730951}},"v":{"df":0,"docs":{},"i":{"a":{"df":0,"docs":{},"l":{"df":1,"docs":{"74":{"tf":2.449489742783178}}}},"df":0,"docs":{}}}},"u":{"df":0,"docs":{},"e":{"df":3,"docs":{"1":{"tf":1.0},"3":{"tf":1.0},"64":{"tf":1.4142135623730951}}}}},"y":{"df":0,"docs":{},"p":{"df":0,"docs":{},"e":{"df":6,"docs":{"2":{"tf":1.0},"3":{"tf":1.0},"35":{"tf":1.0},"58":{"tf":1.0},"59":{"tf":1.0},"66":{"tf":1.7320508075688772}}}}}},"u":{"df":2,"docs":{"58":{"tf":1.0},"66":{"tf":1.7320508075688772}},"n":{"df":0,"docs":{},"f":{"df":0,"docs":{},"o":{"df":0,"docs":{},"l":{"d":{"df":1,"docs":{"71":{"tf":1.0}}},"df":0,"docs":{}}}},"i":{"df":0,"docs":{},"v":{"df":0,"docs":{},"e":{"df":0,"docs":{},"r":{"df":0,"docs":{},"s":{"df":1,"docs":{"66":{"tf":1.0}}}}}}}},"s":{"df":2,"docs":{"22":{"tf":1.4142135623730951},"45":{"tf":1.0}}}},"v":{"a":{"df":0,"docs":{},"r":{"df":0,"docs":{},"i":{"a":{"b":{"df":0,"docs":{},"l":{"df":10,"docs":{"21":{"tf":1.0},"23":{"tf":1.0},"3":{"tf":1.0},"33":{"tf":1.0},"35":{"tf":1.4142135623730951},"4":{"tf":1.0},"45":{"tf":1.0},"59":{"tf":1.0},"62":{"tf":1.0},"66":{"tf":1.0}}}},"df":0,"docs":{}},"df":0,"docs":{}}}},"df":1,"docs":{"66":{"tf":1.7320508075688772}}},"w":{"a":{"df":0,"docs":{},"r":{"df":0,"docs":{},"n":{"df":1,"docs":{"1":{"tf":1.0}},"i":{"df":0,"docs":{},"n":{"df":0,"docs":{},"g":{"a":{"df":0,"docs":{},"s":{"df":0,"docs":{},"e":{"df":0,"docs":{},"r":{"df":0,"docs":{},"r":{"df":0,"docs":{},"o":{"df":0,"docs":{},"r":{"df":1,"docs":{"1":{"tf":1.0}}}}}}}}},"df":0,"docs":{}}}}}}},"df":0,"docs":{},"i":{"df":0,"docs":{},"t":{"df":0,"docs":{},"h":{"df":0,"docs":{},"o":{"df":0,"docs":{},"u":{"df":0,"docs":{},"t":{"df":1,"docs":{"75":{"tf":1.0}}}}}}}},"l":{"df":0,"docs":{},"o":{"df":0,"docs":{},"g":{"df":1,"docs":{"75":{"tf":1.7320508075688772}}}}}},"x":{")":{".":{"df":0,"docs":{},"p":{"df":0,"docs":{},"r":{"df":0,"docs":{},"o":{"df":0,"docs":{},"p":{"df":0,"docs":{},"e":{"df":0,"docs":{},"r":{"df":0,"docs":{},"t":{"df":0,"docs":{},"i":{"df":1,"docs":{"23":{"tf":1.0}}}}}}}}}},"v":{"a":{"df":0,"docs":{},"l":{"df":1,"docs":{"23":{"tf":1.0}}}},"df":0,"docs":{}}},"df":0,"docs":{}},"`":{"df":0,"docs":{},"が":{"df":0,"docs":{},"偶":{"df":0,"docs":{},"数":{"df":0,"docs":{},"の":{"df":0,"docs":{},"と":{"df":0,"docs":{},"き":{"`":{"3":{"df":1,"docs":{"41":{"tf":1.0}}},"df":0,"docs":{}},"df":0,"docs":{}}}}}}}},"df":23,"docs":{"10":{"tf":1.7320508075688772},"22":{"tf":3.1622776601683795},"23":{"tf":4.358898943540674},"24":{"tf":3.4641016151377544},"26":{"tf":2.6457513110645907},"27":{"tf":1.7320508075688772},"3":{"tf":2.23606797749979},"33":{"tf":1.7320508075688772},"34":{"tf":3.3166247903554},"35":{"tf":2.6457513110645907},"36":{"tf":3.872983346207417},"41":{"tf":3.4641016151377544},"46":{"tf":2.449489742783178},"49":{"tf":2.8284271247461903},"50":{"tf":1.4142135623730951},"52":{"tf":3.1622776601683795},"56":{"tf":2.23606797749979},"59":{"tf":1.7320508075688772},"60":{"tf":2.449489742783178},"63":{"tf":2.8284271247461903},"64":{"tf":1.4142135623730951},"70":{"tf":1.7320508075688772},"71":{"tf":5.196152422706632}}},"y":{"df":13,"docs":{"10":{"tf":1.7320508075688772},"22":{"tf":4.0},"23":{"tf":3.3166247903554},"3":{"tf":2.449489742783178},"41":{"tf":2.449489742783178},"46":{"tf":3.3166247903554},"49":{"tf":1.4142135623730951},"50":{"tf":1.4142135623730951},"52":{"tf":2.0},"60":{"tf":2.449489742783178},"63":{"tf":2.6457513110645907},"64":{"tf":2.0},"70":{"tf":1.7320508075688772}}},"z":{"df":5,"docs":{"3":{"tf":2.0},"41":{"tf":1.4142135623730951},"49":{"tf":1.4142135623730951},"63":{"tf":1.0},"70":{"tf":1.7320508075688772}},"e":{"df":0,"docs":{},"r":{"df":0,"docs":{},"o":{"df":2,"docs":{"42":{"tf":1.7320508075688772},"44":{"tf":1.0}}}}}}}},"breadcrumbs":{"root":{"0":{"df":14,"docs":{"24":{"tf":1.4142135623730951},"26":{"tf":1.7320508075688772},"29":{"tf":1.4142135623730951},"42":{"tf":2.0},"43":{"tf":1.0},"44":{"tf":1.4142135623730951},"45":{"tf":1.0},"49":{"tf":1.4142135623730951},"52":{"tf":1.4142135623730951},"56":{"tf":1.0},"59":{"tf":1.0},"70":{"tf":1.0},"71":{"tf":3.3166247903554},"72":{"tf":1.0}}},"1":{"0":{"0":{"df":1,"docs":{"60":{"tf":1.0}}},"df":0,"docs":{}},"2":{"df":1,"docs":{"49":{"tf":1.0}}},"3":{"df":2,"docs":{"59":{"tf":1.0},"72":{"tf":1.7320508075688772}}},"df":15,"docs":{"24":{"tf":1.0},"26":{"tf":2.449489742783178},"33":{"tf":1.0},"34":{"tf":1.0},"42":{"tf":2.0},"44":{"tf":1.4142135623730951},"45":{"tf":1.0},"46":{"tf":2.8284271247461903},"50":{"tf":1.0},"52":{"tf":1.7320508075688772},"57":{"tf":1.0},"59":{"tf":1.4142135623730951},"62":{"tf":1.7320508075688772},"71":{"tf":1.4142135623730951},"74":{"tf":1.4142135623730951}}},"2":{"df":19,"docs":{"10":{"tf":1.4142135623730951},"24":{"tf":3.1622776601683795},"27":{"tf":1.4142135623730951},"34":{"tf":1.0},"35":{"tf":1.0},"36":{"tf":1.4142135623730951},"41":{"tf":1.7320508075688772},"49":{"tf":1.4142135623730951},"50":{"tf":1.4142135623730951},"51":{"tf":1.4142135623730951},"56":{"tf":1.7320508075688772},"57":{"tf":2.6457513110645907},"59":{"tf":1.4142135623730951},"60":{"tf":2.8284271247461903},"62":{"tf":1.0},"70":{"tf":1.0},"71":{"tf":3.872983346207417},"72":{"tf":1.7320508075688772},"74":{"tf":1.0}},"回":{"df":0,"docs":{},"出":{"df":0,"docs":{},"現":{"df":0,"docs":{},"す":{"df":0,"docs":{},"る":{"df":0,"docs":{},"が":{"df":0,"docs":{},"，":{"2":{"df":1,"docs":{"62":{"tf":1.0}}},"df":0,"docs":{}}}}}}}}},"3":{"df":7,"docs":{"27":{"tf":1.0},"34":{"tf":1.0},"41":{"tf":1.4142135623730951},"49":{"tf":1.0},"59":{"tf":1.0},"72":{"tf":1.7320508075688772},"73":{"tf":1.0}}},"4":{"df":2,"docs":{"49":{"tf":1.4142135623730951},"57":{"tf":1.4142135623730951}}},"5":{"df":1,"docs":{"57":{"tf":2.449489742783178}}},"7":{"0":{"df":2,"docs":{"59":{"tf":1.4142135623730951},"72":{"tf":2.449489742783178}}},"df":1,"docs":{"34":{"tf":1.0}}},"_":{"df":9,"docs":{"10":{"tf":1.0},"11":{"tf":1.0},"24":{"tf":1.0},"4":{"tf":1.0},"40":{"tf":1.0},"53":{"tf":1.0},"54":{"tf":1.4142135623730951},"55":{"tf":1.7320508075688772},"57":{"tf":1.7320508075688772}}},"a":{"b":{"df":0,"docs":{},"e":{"df":0,"docs":{},"l":{"df":1,"docs":{"75":{"tf":1.4142135623730951}}}}},"d":{"d":{"_":{"df":0,"docs":{},"z":{"df":0,"docs":{},"e":{"df":0,"docs":{},"r":{"df":0,"docs":{},"o":{"df":1,"docs":{"24":{"tf":1.4142135623730951}}}}}}},"df":0,"docs":{}},"df":0,"docs":{}},"df":0,"docs":{},"e":{"df":0,"docs":{},"s":{"df":0,"docs":{},"o":{"df":0,"docs":{},"p":{"df":5,"docs":{"3":{"tf":3.7416573867739413},"35":{"tf":1.0},"63":{"tf":1.4142135623730951},"73":{"tf":1.4142135623730951},"74":{"tf":1.0}}}}}},"p":{"df":0,"docs":{},"p":{"df":0,"docs":{},"l":{"df":0,"docs":{},"i":{"df":14,"docs":{"10":{"tf":3.4641016151377544},"20":{"tf":1.4142135623730951},"21":{"tf":1.4142135623730951},"3":{"tf":1.0},"4":{"tf":1.0},"48":{"tf":1.0},"5":{"tf":2.6457513110645907},"54":{"tf":2.0},"6":{"tf":1.7320508075688772},"63":{"tf":2.0},"7":{"tf":1.4142135623730951},"72":{"tf":1.4142135623730951},"8":{"tf":2.0},"9":{"tf":1.7320508075688772}}},"y":{"_":{"a":{"df":0,"docs":{},"s":{"df":0,"docs":{},"s":{"df":0,"docs":{},"u":{"df":0,"docs":{},"m":{"df":0,"docs":{},"p":{"df":0,"docs":{},"t":{"df":2,"docs":{"4":{"tf":3.1622776601683795},"9":{"tf":1.7320508075688772}}}}}}}}},"df":0,"docs":{}},"df":0,"docs":{}}}}},"r":{"df":0,"docs":{},"i":{"df":0,"docs":{},"t":{"df":0,"docs":{},"h":{"df":0,"docs":{},"m":{"df":0,"docs":{},"e":{"df":0,"docs":{},"t":{"df":2,"docs":{"49":{"tf":1.0},"51":{"tf":1.0}}}}}}}}},"s":{"df":0,"docs":{},"s":{"df":0,"docs":{},"o":{"c":{"df":1,"docs":{"66":{"tf":1.4142135623730951}}},"df":0,"docs":{}},"u":{"df":0,"docs":{},"m":{"df":0,"docs":{},"p":{"df":0,"docs":{},"t":{"df":7,"docs":{"11":{"tf":2.23606797749979},"12":{"tf":1.4142135623730951},"13":{"tf":1.0},"32":{"tf":1.7320508075688772},"40":{"tf":1.0},"46":{"tf":1.0},"48":{"tf":1.4142135623730951}}}}}}}},"t":{"df":0,"docs":{},"t":{"df":0,"docs":{},"r":{"df":0,"docs":{},"i":{"b":{"df":0,"docs":{},"u":{"df":0,"docs":{},"t":{"df":2,"docs":{"58":{"tf":1.4142135623730951},"66":{"tf":1.0}}}}},"df":0,"docs":{}}}}},"x":{"df":0,"docs":{},"i":{"df":0,"docs":{},"o":{"df":0,"docs":{},"m":{"df":1,"docs":{"10":{"tf":1.4142135623730951}}}}}}},"b":{"`":{"df":0,"docs":{},"と":{"`":{"df":0,"docs":{},"g":{"df":1,"docs":{"66":{"tf":1.0}}}},"df":0,"docs":{}}},"df":10,"docs":{"10":{"tf":2.0},"29":{"tf":2.0},"35":{"tf":2.449489742783178},"51":{"tf":1.7320508075688772},"56":{"tf":2.0},"61":{"tf":2.449489742783178},"62":{"tf":3.3166247903554},"66":{"tf":4.0},"71":{"tf":1.4142135623730951},"75":{"tf":4.123105625617661}},"o":{"df":0,"docs":{},"o":{"df":0,"docs":{},"l":{"df":1,"docs":{"64":{"tf":1.4142135623730951}}}}},"s":{"df":1,"docs":{"24":{"tf":1.7320508075688772}}},"y":{"_":{"c":{"a":{"df":0,"docs":{},"s":{"df":1,"docs":{"13":{"tf":2.449489742783178}}}},"df":0,"docs":{},"o":{"df":0,"docs":{},"n":{"df":0,"docs":{},"t":{"df":0,"docs":{},"r":{"a":{"df":1,"docs":{"14":{"tf":2.449489742783178}}},"df":0,"docs":{}}}}}},"df":0,"docs":{}},"df":0,"docs":{}}},"c":{"`":{"df":0,"docs":{},"の":{"df":0,"docs":{},"合":{"df":0,"docs":{},"成":{"df":0,"docs":{},"を":{"`":{"df":0,"docs":{},"f":{"df":1,"docs":{"66":{"tf":1.0}}}},"df":0,"docs":{}}}}}},"a":{"df":0,"docs":{},"l":{"c":{"df":2,"docs":{"17":{"tf":2.0},"57":{"tf":1.0}}},"df":0,"docs":{}},"s":{"df":0,"docs":{},"e":{"df":7,"docs":{"13":{"tf":1.4142135623730951},"18":{"tf":3.1622776601683795},"19":{"tf":2.8284271247461903},"20":{"tf":2.23606797749979},"21":{"tf":1.7320508075688772},"44":{"tf":1.4142135623730951},"71":{"tf":1.4142135623730951}}}},"t":{"df":0,"docs":{},"e":{"df":0,"docs":{},"g":{"df":0,"docs":{},"o":{"df":0,"docs":{},"r":{"df":0,"docs":{},"i":{"df":1,"docs":{"66":{"tf":1.4142135623730951}}},"y":{".":{"c":{"df":0,"docs":{},"o":{"df":0,"docs":{},"m":{"df":0,"docs":{},"p":{"df":1,"docs":{"66":{"tf":1.0}}}}}},"df":0,"docs":{},"h":{"df":0,"docs":{},"o":{"df":0,"docs":{},"g":{"df":1,"docs":{"66":{"tf":1.0}}}}},"{":{"df":0,"docs":{},"u":{"df":1,"docs":{"66":{"tf":1.0}}}}},"df":0,"docs":{}}}}}}}},"df":5,"docs":{"29":{"tf":2.0},"56":{"tf":1.4142135623730951},"61":{"tf":1.7320508075688772},"62":{"tf":1.4142135623730951},"66":{"tf":4.58257569495584}},"h":{"df":0,"docs":{},"o":{"df":0,"docs":{},"o":{"df":0,"docs":{},"s":{"df":2,"docs":{"22":{"tf":2.23606797749979},"23":{"tf":1.4142135623730951}}}}}},"i":{"df":2,"docs":{"3":{"tf":1.0},"64":{"tf":1.0}}},"l":{"a":{"df":0,"docs":{},"s":{"df":0,"docs":{},"s":{"df":1,"docs":{"66":{"tf":1.0}},"i":{"c":{"a":{"df":0,"docs":{},"l":{".":{"c":{"df":0,"docs":{},"h":{"df":0,"docs":{},"o":{"df":0,"docs":{},"i":{"c":{"df":1,"docs":{"23":{"tf":1.4142135623730951}}},"df":0,"docs":{}}}}},"df":0,"docs":{}},"df":0,"docs":{}}},"df":0,"docs":{}},"df":0,"docs":{}}}}},"df":0,"docs":{}},"o":{"df":0,"docs":{},"m":{"df":0,"docs":{},"p":{"_":{"a":{"df":0,"docs":{},"p":{"df":0,"docs":{},"p":{"df":0,"docs":{},"l":{"df":0,"docs":{},"i":{"df":2,"docs":{"3":{"tf":1.0},"63":{"tf":1.0}}}}}}},"df":0,"docs":{},"i":{"d":{"df":1,"docs":{"66":{"tf":1.4142135623730951}}},"df":0,"docs":{}}},"df":1,"docs":{"66":{"tf":2.6457513110645907}}}},"n":{"df":0,"docs":{},"g":{"df":0,"docs":{},"r":{"df":1,"docs":{"24":{"tf":3.0}},"u":{"df":0,"docs":{},"e":{"df":0,"docs":{},"n":{"c":{"df":1,"docs":{"24":{"tf":1.0}}},"df":0,"docs":{}}}}}},"s":{"df":0,"docs":{},"t":{"df":0,"docs":{},"r":{"df":0,"docs":{},"u":{"c":{"df":0,"docs":{},"t":{"df":0,"docs":{},"o":{"df":0,"docs":{},"r":{"df":4,"docs":{"25":{"tf":2.23606797749979},"26":{"tf":1.7320508075688772},"55":{"tf":2.8284271247461903},"65":{"tf":1.0}}}}}},"df":0,"docs":{}}}}},"t":{"df":0,"docs":{},"r":{"a":{"d":{"df":0,"docs":{},"i":{"c":{"df":0,"docs":{},"t":{"df":5,"docs":{"13":{"tf":1.0},"14":{"tf":1.0},"27":{"tf":2.6457513110645907},"47":{"tf":1.0},"74":{"tf":1.0}}}},"df":0,"docs":{}}},"df":0,"docs":{}},"df":0,"docs":{}}},"v":{"df":1,"docs":{"28":{"tf":2.0}},"e":{"df":0,"docs":{},"r":{"df":0,"docs":{},"t":{"df":1,"docs":{"29":{"tf":2.23606797749979}}}}}}}}},"d":{"df":3,"docs":{"56":{"tf":1.4142135623730951},"61":{"tf":1.7320508075688772},"66":{"tf":2.23606797749979}},"e":{"df":0,"docs":{},"f":{"df":4,"docs":{"36":{"tf":1.4142135623730951},"42":{"tf":1.0},"70":{"tf":1.0},"71":{"tf":1.0}}},"p":{"df":0,"docs":{},"e":{"df":0,"docs":{},"n":{"d":{"df":1,"docs":{"10":{"tf":1.0}}},"df":0,"docs":{}}}}},"o":{"df":0,"docs":{},"n":{"df":0,"docs":{},"e":{"df":4,"docs":{"10":{"tf":1.4142135623730951},"30":{"tf":2.0},"33":{"tf":1.0},"4":{"tf":1.0}}}}},"s":{"df":0,"docs":{},"i":{"df":0,"docs":{},"m":{"df":0,"docs":{},"p":{"df":2,"docs":{"36":{"tf":1.0},"69":{"tf":1.7320508075688772}}}}}}},"df":0,"docs":{},"e":{"df":2,"docs":{"61":{"tf":1.7320508075688772},"66":{"tf":1.4142135623730951}},"v":{"df":0,"docs":{},"e":{"df":0,"docs":{},"n":{"df":1,"docs":{"57":{"tf":1.7320508075688772}}}}},"x":{"a":{"c":{"df":0,"docs":{},"t":{"df":30,"docs":{"10":{"tf":1.0},"12":{"tf":1.7320508075688772},"15":{"tf":1.0},"16":{"tf":1.0},"18":{"tf":1.4142135623730951},"19":{"tf":1.4142135623730951},"21":{"tf":1.0},"22":{"tf":1.0},"23":{"tf":1.0},"24":{"tf":1.0},"25":{"tf":1.7320508075688772},"29":{"tf":1.4142135623730951},"31":{"tf":2.6457513110645907},"32":{"tf":1.7320508075688772},"33":{"tf":3.605551275463989},"37":{"tf":1.0},"38":{"tf":1.4142135623730951},"4":{"tf":1.0},"46":{"tf":1.0},"5":{"tf":1.7320508075688772},"52":{"tf":1.0},"53":{"tf":1.4142135623730951},"55":{"tf":2.449489742783178},"6":{"tf":1.0},"62":{"tf":1.0},"63":{"tf":2.23606797749979},"65":{"tf":1.4142135623730951},"72":{"tf":1.0},"73":{"tf":1.4142135623730951},"8":{"tf":1.7320508075688772}}}},"df":0,"docs":{},"m":{"df":0,"docs":{},"p":{"df":0,"docs":{},"l":{"df":60,"docs":{"10":{"tf":1.0},"11":{"tf":1.0},"13":{"tf":1.0},"14":{"tf":1.0},"15":{"tf":1.4142135623730951},"16":{"tf":1.0},"18":{"tf":1.0},"19":{"tf":1.0},"20":{"tf":1.0},"21":{"tf":1.4142135623730951},"22":{"tf":1.0},"23":{"tf":1.0},"24":{"tf":1.4142135623730951},"25":{"tf":1.4142135623730951},"26":{"tf":1.0},"27":{"tf":2.0},"29":{"tf":1.0},"3":{"tf":1.4142135623730951},"31":{"tf":1.4142135623730951},"33":{"tf":1.4142135623730951},"34":{"tf":1.0},"35":{"tf":1.0},"36":{"tf":1.0},"37":{"tf":1.0},"38":{"tf":1.0},"4":{"tf":1.4142135623730951},"40":{"tf":1.0},"41":{"tf":1.0},"42":{"tf":1.0},"43":{"tf":1.0},"44":{"tf":1.0},"45":{"tf":1.0},"46":{"tf":1.4142135623730951},"47":{"tf":1.0},"48":{"tf":1.4142135623730951},"49":{"tf":1.4142135623730951},"5":{"tf":1.4142135623730951},"50":{"tf":1.0},"51":{"tf":1.0},"52":{"tf":1.4142135623730951},"53":{"tf":1.0},"54":{"tf":1.0},"55":{"tf":1.4142135623730951},"56":{"tf":1.4142135623730951},"57":{"tf":1.0},"58":{"tf":1.4142135623730951},"59":{"tf":1.7320508075688772},"6":{"tf":1.0},"60":{"tf":1.4142135623730951},"61":{"tf":1.0},"62":{"tf":1.0},"63":{"tf":1.4142135623730951},"65":{"tf":1.0},"66":{"tf":1.0},"71":{"tf":1.0},"72":{"tf":1.0},"73":{"tf":2.0},"74":{"tf":1.4142135623730951},"75":{"tf":1.0},"8":{"tf":1.0}}}}}},"df":0,"docs":{},"i":{"df":0,"docs":{},"s":{"df":0,"docs":{},"t":{"df":5,"docs":{"23":{"tf":1.0},"34":{"tf":2.449489742783178},"41":{"tf":1.0},"52":{"tf":1.0},"57":{"tf":1.0}}}}},"p":{"df":0,"docs":{},"l":{"df":0,"docs":{},"o":{"df":0,"docs":{},"s":{"df":0,"docs":{},"i":{"df":0,"docs":{},"o":{"df":0,"docs":{},"n":{")":{"df":0,"docs":{},"と":{"df":0,"docs":{},"呼":{"df":0,"docs":{},"び":{"df":0,"docs":{},"ま":{"df":0,"docs":{},"す":{"df":0,"docs":{},"が":{"df":0,"docs":{},"，":{"c":{"df":0,"docs":{},"o":{"df":0,"docs":{},"n":{"df":0,"docs":{},"t":{"df":0,"docs":{},"r":{"a":{"d":{"df":0,"docs":{},"i":{"c":{"df":0,"docs":{},"t":{"df":1,"docs":{"27":{"tf":1.0}}}},"df":0,"docs":{}}},"df":0,"docs":{}},"df":0,"docs":{}}}}}},"df":0,"docs":{}}}}}}}}},"df":0,"docs":{}}}}}}}},"t":{"df":1,"docs":{"35":{"tf":2.449489742783178}},"e":{"df":0,"docs":{},"n":{"df":0,"docs":{},"s":{"df":0,"docs":{},"i":{"df":0,"docs":{},"o":{"df":0,"docs":{},"n":{"df":1,"docs":{"35":{"tf":1.0}}}}}}}}}}},"f":{"a":{"c":{"df":2,"docs":{"42":{"tf":2.6457513110645907},"43":{"tf":1.7320508075688772}}},"df":0,"docs":{},"l":{"df":0,"docs":{},"s":{"df":7,"docs":{"14":{"tf":1.4142135623730951},"27":{"tf":1.4142135623730951},"4":{"tf":1.0},"47":{"tf":2.0},"50":{"tf":1.0},"6":{"tf":1.7320508075688772},"74":{"tf":1.0}}}}},"df":11,"docs":{"10":{"tf":2.23606797749979},"22":{"tf":2.8284271247461903},"23":{"tf":3.0},"24":{"tf":3.7416573867739413},"29":{"tf":1.7320508075688772},"3":{"tf":3.1622776601683795},"35":{"tf":1.7320508075688772},"36":{"tf":2.449489742783178},"61":{"tf":1.7320508075688772},"63":{"tf":2.23606797749979},"66":{"tf":3.605551275463989}},"e":{"df":0,"docs":{},"r":{"df":0,"docs":{},"m":{"a":{"df":0,"docs":{},"t":{"df":1,"docs":{"70":{"tf":1.0}},"l":{"a":{"df":0,"docs":{},"s":{"df":0,"docs":{},"t":{"df":0,"docs":{},"t":{"df":0,"docs":{},"h":{"df":0,"docs":{},"e":{"df":0,"docs":{},"o":{"df":0,"docs":{},"r":{"df":0,"docs":{},"e":{"df":0,"docs":{},"m":{"df":1,"docs":{"70":{"tf":1.4142135623730951}}}}}}}}}}}},"df":0,"docs":{}}}},"df":0,"docs":{}}}},"l":{"df":0,"docs":{},"t":{"df":1,"docs":{"70":{"tf":1.0}}}},"u":{"df":0,"docs":{},"n":{"c":{"df":0,"docs":{},"t":{"df":0,"docs":{},"i":{"df":0,"docs":{},"o":{"df":0,"docs":{},"n":{"df":1,"docs":{"3":{"tf":1.0}}}}}}},"df":4,"docs":{"15":{"tf":1.0},"16":{"tf":1.0},"23":{"tf":1.4142135623730951},"36":{"tf":1.4142135623730951}},"e":{"df":0,"docs":{},"x":{"df":0,"docs":{},"t":{"df":1,"docs":{"36":{"tf":2.23606797749979}}}}}}}},"g":{"df":9,"docs":{"10":{"tf":1.7320508075688772},"22":{"tf":2.8284271247461903},"24":{"tf":2.23606797749979},"3":{"tf":2.23606797749979},"35":{"tf":1.7320508075688772},"36":{"tf":2.449489742783178},"62":{"tf":1.7320508075688772},"63":{"tf":1.7320508075688772},"66":{"tf":2.6457513110645907}},"e":{"_":{"df":0,"docs":{},"i":{"df":0,"docs":{},"f":{"df":0,"docs":{},"f":{"_":{"df":0,"docs":{},"l":{"df":1,"docs":{"71":{"tf":1.4142135623730951}}}},"df":0,"docs":{}}}}},"df":0,"docs":{},"n":{"df":0,"docs":{},"e":{"df":0,"docs":{},"r":{"a":{"df":0,"docs":{},"r":{"df":1,"docs":{"75":{"tf":1.0}}}},"df":1,"docs":{"44":{"tf":1.0}}}}}},"o":{"a":{"df":0,"docs":{},"l":{"df":1,"docs":{"25":{"tf":1.0}}}},"df":0,"docs":{}},"r":{"df":0,"docs":{},"o":{"df":0,"docs":{},"u":{"df":0,"docs":{},"p":{"df":2,"docs":{"10":{"tf":1.4142135623730951},"62":{"tf":1.0}}}}}},"u":{"a":{"df":0,"docs":{},"r":{"d":{"_":{"df":0,"docs":{},"h":{"df":0,"docs":{},"y":{"df":0,"docs":{},"p":{"df":8,"docs":{"13":{"tf":1.4142135623730951},"22":{"tf":1.4142135623730951},"37":{"tf":2.23606797749979},"44":{"tf":1.7320508075688772},"45":{"tf":1.0},"57":{"tf":1.4142135623730951},"71":{"tf":1.4142135623730951},"75":{"tf":1.7320508075688772}}}}},"m":{"df":0,"docs":{},"s":{"df":0,"docs":{},"g":{"df":1,"docs":{"10":{"tf":1.0}}}}}},"df":0,"docs":{}},"df":0,"docs":{}}},"df":0,"docs":{}}},"h":{".":{"df":0,"docs":{},"l":{"df":0,"docs":{},"e":{"df":0,"docs":{},"f":{"df":0,"docs":{},"t":{"df":1,"docs":{"25":{"tf":1.4142135623730951}}}}}},"r":{"df":0,"docs":{},"i":{"df":0,"docs":{},"g":{"df":0,"docs":{},"h":{"df":0,"docs":{},"t":{"df":1,"docs":{"25":{"tf":1.0}}}}}}}},"1":{"df":4,"docs":{"49":{"tf":1.0},"50":{"tf":1.0},"56":{"tf":2.0},"61":{"tf":1.4142135623730951}}},"2":{"df":4,"docs":{"49":{"tf":1.0},"50":{"tf":1.0},"56":{"tf":1.4142135623730951},"61":{"tf":1.4142135623730951}}},"a":{"b":{"df":1,"docs":{"61":{"tf":1.7320508075688772}}},"df":0,"docs":{}},"c":{"df":1,"docs":{"29":{"tf":1.4142135623730951}}},"df":30,"docs":{"10":{"tf":1.4142135623730951},"13":{"tf":1.0},"14":{"tf":2.0},"15":{"tf":1.0},"18":{"tf":2.23606797749979},"19":{"tf":1.7320508075688772},"20":{"tf":1.4142135623730951},"21":{"tf":2.449489742783178},"22":{"tf":1.4142135623730951},"23":{"tf":1.7320508075688772},"24":{"tf":2.0},"25":{"tf":1.4142135623730951},"27":{"tf":1.7320508075688772},"29":{"tf":3.0},"38":{"tf":1.4142135623730951},"44":{"tf":1.7320508075688772},"46":{"tf":1.4142135623730951},"47":{"tf":1.7320508075688772},"5":{"tf":2.8284271247461903},"51":{"tf":1.0},"52":{"tf":1.4142135623730951},"54":{"tf":1.7320508075688772},"57":{"tf":1.7320508075688772},"61":{"tf":2.449489742783178},"66":{"tf":3.1622776601683795},"71":{"tf":3.1622776601683795},"73":{"tf":1.4142135623730951},"74":{"tf":1.0},"75":{"tf":2.23606797749979},"8":{"tf":1.4142135623730951}},"e":{"a":{"d":{"df":1,"docs":{"4":{"tf":1.4142135623730951}}},"df":0,"docs":{}},"df":0,"docs":{},"l":{"df":0,"docs":{},"p":{"df":1,"docs":{"1":{"tf":1.0}}}}},"f":{"df":2,"docs":{"22":{"tf":2.0},"24":{"tf":1.4142135623730951}}},"g":{"df":1,"docs":{"22":{"tf":1.7320508075688772}},"f":{"df":0,"docs":{},"i":{"df":0,"docs":{},"n":{"df":0,"docs":{},"j":{"df":2,"docs":{"3":{"tf":1.7320508075688772},"63":{"tf":1.4142135623730951}}}}}}},"k":{"df":1,"docs":{"57":{"tf":2.6457513110645907}}},"n":{"df":2,"docs":{"57":{"tf":1.4142135623730951},"6":{"tf":2.0}},"e":{"_":{"df":0,"docs":{},"s":{"df":0,"docs":{},"t":{"df":1,"docs":{"23":{"tf":1.4142135623730951}}}}},"df":0,"docs":{}},"n":{"df":0,"docs":{},"p":{"df":1,"docs":{"13":{"tf":1.0}}}},"p":{"df":1,"docs":{"27":{"tf":1.0}}},"q":{"df":2,"docs":{"14":{"tf":1.4142135623730951},"47":{"tf":1.4142135623730951}}}},"o":{"df":0,"docs":{},"g":{"df":0,"docs":{},"e":{"df":1,"docs":{"66":{"tf":1.0}}}},"m":{"df":1,"docs":{"66":{"tf":4.0}}}},"p":{"df":27,"docs":{"11":{"tf":1.0},"13":{"tf":1.7320508075688772},"14":{"tf":1.0},"15":{"tf":2.0},"16":{"tf":2.0},"18":{"tf":1.4142135623730951},"19":{"tf":1.4142135623730951},"20":{"tf":1.4142135623730951},"21":{"tf":2.23606797749979},"25":{"tf":1.4142135623730951},"27":{"tf":1.0},"31":{"tf":2.8284271247461903},"37":{"tf":1.7320508075688772},"38":{"tf":1.7320508075688772},"4":{"tf":1.4142135623730951},"40":{"tf":1.0},"46":{"tf":1.7320508075688772},"47":{"tf":2.0},"48":{"tf":1.4142135623730951},"5":{"tf":2.23606797749979},"53":{"tf":1.4142135623730951},"54":{"tf":1.4142135623730951},"55":{"tf":2.0},"6":{"tf":1.4142135623730951},"63":{"tf":1.4142135623730951},"65":{"tf":1.4142135623730951},"8":{"tf":1.4142135623730951}},"q":{"df":10,"docs":{"15":{"tf":2.0},"16":{"tf":1.7320508075688772},"33":{"tf":1.4142135623730951},"38":{"tf":1.7320508075688772},"4":{"tf":1.7320508075688772},"40":{"tf":1.4142135623730951},"46":{"tf":1.7320508075688772},"54":{"tf":1.4142135623730951},"61":{"tf":2.0},"63":{"tf":1.4142135623730951}}},"r":{"df":4,"docs":{"18":{"tf":1.4142135623730951},"19":{"tf":1.4142135623730951},"20":{"tf":1.4142135623730951},"21":{"tf":1.4142135623730951}}}},"q":{"df":15,"docs":{"18":{"tf":1.4142135623730951},"19":{"tf":1.4142135623730951},"20":{"tf":1.4142135623730951},"21":{"tf":2.23606797749979},"25":{"tf":1.4142135623730951},"31":{"tf":1.7320508075688772},"33":{"tf":1.4142135623730951},"38":{"tf":1.7320508075688772},"4":{"tf":1.0},"40":{"tf":1.0},"46":{"tf":1.7320508075688772},"47":{"tf":1.4142135623730951},"53":{"tf":1.4142135623730951},"55":{"tf":2.0},"65":{"tf":1.4142135623730951}},"n":{"df":1,"docs":{"4":{"tf":1.4142135623730951}}},"r":{"df":11,"docs":{"15":{"tf":2.0},"16":{"tf":1.7320508075688772},"18":{"tf":1.4142135623730951},"19":{"tf":1.4142135623730951},"20":{"tf":1.4142135623730951},"21":{"tf":1.4142135623730951},"33":{"tf":1.4142135623730951},"38":{"tf":1.7320508075688772},"4":{"tf":1.0},"46":{"tf":1.7320508075688772},"63":{"tf":1.4142135623730951}}}},"r":{"df":2,"docs":{"55":{"tf":2.0},"63":{"tf":1.4142135623730951}}},"x":{"df":3,"docs":{"26":{"tf":1.4142135623730951},"41":{"tf":2.0},"71":{"tf":1.7320508075688772}}},"y":{"df":1,"docs":{"41":{"tf":1.4142135623730951}},"p":{"df":1,"docs":{"46":{"tf":1.0}}}}},"i":{"d":{"_":{"c":{"df":0,"docs":{},"o":{"df":0,"docs":{},"m":{"df":0,"docs":{},"p":{"df":1,"docs":{"66":{"tf":1.4142135623730951}}}}}},"df":0,"docs":{}},"df":2,"docs":{"49":{"tf":1.7320508075688772},"66":{"tf":2.449489742783178}}},"df":0,"docs":{},"f":{"df":0,"docs":{},"f":{".":{"df":0,"docs":{},"m":{"df":0,"docs":{},"p":{"df":0,"docs":{},"r":{"df":1,"docs":{"72":{"tf":1.0}}}}}},"df":0,"docs":{}}},"h":{"df":4,"docs":{"42":{"tf":1.0},"43":{"tf":1.7320508075688772},"44":{"tf":1.4142135623730951},"45":{"tf":1.4142135623730951}}},"m":{"df":0,"docs":{},"p":{"df":0,"docs":{},"o":{"df":0,"docs":{},"r":{"df":0,"docs":{},"t":{"df":26,"docs":{"10":{"tf":1.7320508075688772},"14":{"tf":1.0},"16":{"tf":1.0},"20":{"tf":1.0},"21":{"tf":1.0},"22":{"tf":1.0},"29":{"tf":1.0},"3":{"tf":1.7320508075688772},"33":{"tf":1.0},"35":{"tf":1.0},"37":{"tf":1.0},"4":{"tf":1.4142135623730951},"43":{"tf":1.0},"48":{"tf":1.0},"49":{"tf":1.0},"51":{"tf":1.0},"52":{"tf":1.0},"56":{"tf":1.0},"57":{"tf":1.0},"58":{"tf":1.7320508075688772},"59":{"tf":1.0},"60":{"tf":1.0},"62":{"tf":1.0},"63":{"tf":1.0},"73":{"tf":1.0},"75":{"tf":1.0}}}}}}},"n":{"d":{"df":0,"docs":{},"u":{"c":{"df":0,"docs":{},"t":{"df":5,"docs":{"42":{"tf":2.6457513110645907},"43":{"tf":2.23606797749979},"44":{"tf":1.7320508075688772},"45":{"tf":1.4142135623730951},"58":{"tf":1.0}}}},"df":0,"docs":{}}},"df":0,"docs":{},"f":{"df":0,"docs":{},"i":{"df":0,"docs":{},"x":{"df":0,"docs":{},"r":{":":{"8":{"0":{"df":1,"docs":{"66":{"tf":1.0}}},"df":0,"docs":{}},"df":0,"docs":{}},"df":0,"docs":{}}}},"o":{"df":1,"docs":{"10":{"tf":1.0}},"v":{"df":0,"docs":{},"i":{"df":0,"docs":{},"e":{"df":0,"docs":{},"w":{"df":1,"docs":{"63":{"tf":1.0}}}}}}}},"j":{"df":0,"docs":{},"e":{"c":{"df":0,"docs":{},"t":{"df":2,"docs":{"3":{"tf":2.6457513110645907},"63":{"tf":1.7320508075688772}}}},"df":0,"docs":{}}},"l":{"df":4,"docs":{"13":{"tf":1.0},"18":{"tf":1.7320508075688772},"19":{"tf":1.4142135623730951},"71":{"tf":1.0}}},"r":{"df":4,"docs":{"13":{"tf":1.0},"18":{"tf":1.7320508075688772},"19":{"tf":1.4142135623730951},"71":{"tf":1.0}}},"s":{"df":0,"docs":{},"e":{"df":0,"docs":{},"r":{"df":0,"docs":{},"t":{"df":1,"docs":{"18":{"tf":1.4142135623730951}}}}}},"t":{"df":5,"docs":{"24":{"tf":2.0},"52":{"tf":1.4142135623730951},"56":{"tf":1.4142135623730951},"57":{"tf":1.0},"71":{"tf":1.7320508075688772}},"r":{"df":0,"docs":{},"o":{"d":{"df":0,"docs":{},"u":{"c":{"df":1,"docs":{"46":{"tf":1.0}}},"df":0,"docs":{}}},"df":19,"docs":{"13":{"tf":1.0},"14":{"tf":1.0},"15":{"tf":1.0},"16":{"tf":1.0},"18":{"tf":1.0},"19":{"tf":1.0},"20":{"tf":1.0},"21":{"tf":1.4142135623730951},"23":{"tf":1.0},"26":{"tf":1.0},"3":{"tf":1.4142135623730951},"35":{"tf":1.0},"38":{"tf":1.0},"4":{"tf":1.0},"46":{"tf":2.8284271247461903},"47":{"tf":2.0},"52":{"tf":1.0},"57":{"tf":1.0},"63":{"tf":1.0}}}}}},"t":{"df":0,"docs":{},"e":{"_":{"df":0,"docs":{},"f":{"a":{"df":0,"docs":{},"l":{"df":0,"docs":{},"s":{"df":1,"docs":{"71":{"tf":1.0}}}}},"df":0,"docs":{}},"t":{"df":0,"docs":{},"r":{"df":0,"docs":{},"u":{"df":1,"docs":{"71":{"tf":1.0}}}}}},"df":0,"docs":{}}}},"k":{"df":3,"docs":{"43":{"tf":1.4142135623730951},"45":{"tf":1.7320508075688772},"57":{"tf":3.3166247903554}}},"l":{".":{"df":0,"docs":{},"l":{"df":0,"docs":{},"e":{"df":0,"docs":{},"n":{"df":0,"docs":{},"g":{"df":0,"docs":{},"t":{"df":0,"docs":{},"h":{"df":1,"docs":{"44":{"tf":1.0}}}}}}}}},"df":1,"docs":{"44":{"tf":3.1622776601683795}},"e":{"a":{"df":0,"docs":{},"n":{".":{"df":0,"docs":{},"m":{"df":0,"docs":{},"v":{"a":{"df":0,"docs":{},"r":{"df":0,"docs":{},"i":{"d":{".":{"df":0,"docs":{},"r":{"df":0,"docs":{},"e":{"df":0,"docs":{},"f":{"df":0,"docs":{},"l":{"df":1,"docs":{"59":{"tf":1.0}}}}},"f":{"df":0,"docs":{},"l":{"df":1,"docs":{"59":{"tf":1.0}}}}}},"df":0,"docs":{}},"df":0,"docs":{}}}},"df":0,"docs":{}}}},"4":{"df":5,"docs":{"0":{"tf":1.7320508075688772},"1":{"tf":1.0},"17":{"tf":1.0},"2":{"tf":1.0},"28":{"tf":1.0}}},"df":8,"docs":{"0":{"tf":1.0},"15":{"tf":1.0},"2":{"tf":2.0},"42":{"tf":1.0},"47":{"tf":1.0},"6":{"tf":1.0},"71":{"tf":1.0},"75":{"tf":1.0}}}},"df":0,"docs":{},"f":{"df":0,"docs":{},"t":{"df":3,"docs":{"18":{"tf":1.0},"25":{"tf":1.0},"48":{"tf":2.449489742783178}}}}},"i":{"df":0,"docs":{},"n":{"a":{"df":0,"docs":{},"r":{"df":0,"docs":{},"i":{"df":0,"docs":{},"t":{"df":0,"docs":{},"h":{"df":5,"docs":{"49":{"tf":3.3166247903554},"50":{"tf":1.7320508075688772},"51":{"tf":1.7320508075688772},"52":{"tf":1.0},"71":{"tf":1.4142135623730951}}}}}}},"df":0,"docs":{},"e":{"a":{"df":0,"docs":{},"r":{"df":2,"docs":{"49":{"tf":1.0},"51":{"tf":1.0}}}},"df":0,"docs":{}}},"s":{"df":0,"docs":{},"t":{".":{"df":0,"docs":{},"l":{"df":0,"docs":{},"e":{"df":0,"docs":{},"n":{"df":0,"docs":{},"g":{"df":0,"docs":{},"t":{"df":0,"docs":{},"h":{"df":1,"docs":{"44":{"tf":1.7320508075688772}}}}}}}}},"df":1,"docs":{"44":{"tf":1.7320508075688772}}}}},"o":{"df":0,"docs":{},"s":{"df":0,"docs":{},"s":{"df":1,"docs":{"75":{"tf":1.0}}}}}},"m":{"a":{"df":0,"docs":{},"t":{"c":{"df":0,"docs":{},"h":{"df":1,"docs":{"45":{"tf":1.0}}}},"df":0,"docs":{},"h":{"df":0,"docs":{},"e":{"df":0,"docs":{},"m":{"a":{"df":0,"docs":{},"t":{"df":1,"docs":{"2":{"tf":1.0}}}},"df":0,"docs":{}}},"l":{"df":0,"docs":{},"i":{"b":{".":{"a":{"df":0,"docs":{},"l":{"df":0,"docs":{},"g":{"df":0,"docs":{},"e":{"b":{"df":0,"docs":{},"r":{"a":{".":{"df":0,"docs":{},"g":{"df":0,"docs":{},"r":{"df":0,"docs":{},"o":{"df":0,"docs":{},"u":{"df":0,"docs":{},"p":{".":{"d":{"df":0,"docs":{},"e":{"df":0,"docs":{},"f":{"df":1,"docs":{"10":{"tf":1.0}}}}},"df":0,"docs":{}},"df":0,"docs":{}}}}}},"h":{"df":0,"docs":{},"o":{"df":0,"docs":{},"m":{".":{"df":0,"docs":{},"g":{"df":0,"docs":{},"r":{"df":0,"docs":{},"o":{"df":0,"docs":{},"u":{"df":0,"docs":{},"p":{".":{"d":{"df":0,"docs":{},"e":{"df":0,"docs":{},"f":{"df":1,"docs":{"10":{"tf":1.0}}}}},"df":0,"docs":{}},"df":0,"docs":{}}}}}}},"df":0,"docs":{}}}}},"df":0,"docs":{}},"df":0,"docs":{}}},"df":0,"docs":{}}}}},"d":{"a":{"df":0,"docs":{},"t":{"a":{".":{"df":0,"docs":{},"n":{"a":{"df":0,"docs":{},"t":{".":{"b":{"a":{"df":0,"docs":{},"s":{"df":1,"docs":{"58":{"tf":1.0}}}},"df":0,"docs":{}},"df":0,"docs":{}},"df":0,"docs":{}}},"df":0,"docs":{}},"s":{"df":0,"docs":{},"e":{"df":0,"docs":{},"t":{"df":0,"docs":{},"l":{"df":0,"docs":{},"i":{"df":0,"docs":{},"k":{"df":0,"docs":{},"e":{".":{"b":{"a":{"df":0,"docs":{},"s":{"df":1,"docs":{"35":{"tf":1.0}}}},"df":0,"docs":{}},"df":0,"docs":{}},"df":0,"docs":{}}}}}}}}},"df":0,"docs":{}},"df":0,"docs":{}}},"df":0,"docs":{}},"df":0,"docs":{},"i":{"df":0,"docs":{},"n":{"df":0,"docs":{},"i":{"df":0,"docs":{},"t":{".":{"df":0,"docs":{},"f":{"df":0,"docs":{},"u":{"df":0,"docs":{},"n":{"c":{"df":0,"docs":{},"t":{"df":1,"docs":{"3":{"tf":1.0}}}},"df":0,"docs":{}}}}},"df":0,"docs":{}}}}},"t":{"a":{"c":{"df":0,"docs":{},"t":{"df":0,"docs":{},"i":{"c":{".":{"b":{"df":0,"docs":{},"y":{"c":{"df":0,"docs":{},"o":{"df":0,"docs":{},"n":{"df":0,"docs":{},"t":{"df":0,"docs":{},"r":{"a":{"df":1,"docs":{"14":{"tf":1.0}}},"df":0,"docs":{}}}}}},"df":0,"docs":{}}},"c":{"a":{"df":0,"docs":{},"s":{"df":2,"docs":{"20":{"tf":1.0},"43":{"tf":1.0}}}},"df":0,"docs":{},"h":{"df":0,"docs":{},"o":{"df":0,"docs":{},"o":{"df":0,"docs":{},"s":{"df":1,"docs":{"22":{"tf":1.0}}}}}},"o":{"df":0,"docs":{},"n":{"df":0,"docs":{},"v":{"df":0,"docs":{},"e":{"df":0,"docs":{},"r":{"df":0,"docs":{},"t":{"df":1,"docs":{"29":{"tf":1.0}}}}}}}}},"df":0,"docs":{},"g":{"c":{"df":0,"docs":{},"o":{"df":0,"docs":{},"n":{"df":0,"docs":{},"g":{"df":0,"docs":{},"r":{"df":1,"docs":{"56":{"tf":1.0}}}}}}},"df":0,"docs":{}},"l":{"df":0,"docs":{},"e":{"df":0,"docs":{},"f":{"df":0,"docs":{},"t":{"df":0,"docs":{},"r":{"df":0,"docs":{},"i":{"df":0,"docs":{},"g":{"df":0,"docs":{},"h":{"df":0,"docs":{},"t":{"df":1,"docs":{"48":{"tf":1.0}}}}}}}}}},"i":{"b":{"df":0,"docs":{},"r":{"a":{"df":0,"docs":{},"r":{"df":0,"docs":{},"y":{"df":0,"docs":{},"s":{"df":0,"docs":{},"e":{"a":{"df":0,"docs":{},"r":{"c":{"df":0,"docs":{},"h":{"df":2,"docs":{"10":{"tf":1.0},"33":{"tf":1.0}}}},"df":0,"docs":{}}},"df":0,"docs":{}}}}}},"df":0,"docs":{}}},"df":0,"docs":{},"n":{"a":{"df":0,"docs":{},"r":{"df":0,"docs":{},"i":{"df":0,"docs":{},"t":{"df":0,"docs":{},"h":{"df":2,"docs":{"49":{"tf":1.0},"51":{"tf":1.0}}}}}}},"df":0,"docs":{}}}},"n":{"df":0,"docs":{},"t":{"df":0,"docs":{},"h":{"df":0,"docs":{},"r":{"df":0,"docs":{},"e":{"df":0,"docs":{},"w":{"df":0,"docs":{},"r":{"df":0,"docs":{},"i":{"df":0,"docs":{},"t":{"df":1,"docs":{"62":{"tf":1.0}}}}}}}}}}},"p":{"df":0,"docs":{},"u":{"df":0,"docs":{},"s":{"df":0,"docs":{},"h":{"df":0,"docs":{},"n":{"df":0,"docs":{},"e":{"df":0,"docs":{},"g":{"df":1,"docs":{"52":{"tf":1.0}}}}}}}}},"r":{"df":1,"docs":{"60":{"tf":1.0}},"e":{"df":0,"docs":{},"l":{"a":{"df":0,"docs":{},"t":{"df":0,"docs":{},"i":{"df":0,"docs":{},"o":{"df":0,"docs":{},"n":{".":{"df":0,"docs":{},"r":{"df":0,"docs":{},"f":{"df":0,"docs":{},"l":{"df":2,"docs":{"58":{"tf":1.0},"59":{"tf":1.4142135623730951}}}}}},"df":0,"docs":{}}}}}},"df":0,"docs":{}}}},"s":{"a":{"df":0,"docs":{},"y":{"df":2,"docs":{"3":{"tf":1.0},"63":{"tf":1.0}}}},"df":0,"docs":{},"o":{"df":0,"docs":{},"l":{"df":0,"docs":{},"v":{"df":0,"docs":{},"e":{"b":{"df":0,"docs":{},"y":{"df":0,"docs":{},"e":{"df":0,"docs":{},"l":{"df":0,"docs":{},"i":{"df":0,"docs":{},"m":{"df":1,"docs":{"4":{"tf":1.4142135623730951}}}}}}}},"df":0,"docs":{}}}}}},"t":{"a":{"df":0,"docs":{},"u":{"df":0,"docs":{},"t":{"df":0,"docs":{},"o":{"df":1,"docs":{"73":{"tf":1.0}}}}}},"df":0,"docs":{}},"w":{"df":0,"docs":{},"l":{"df":0,"docs":{},"o":{"df":0,"docs":{},"g":{"df":1,"docs":{"75":{"tf":1.0}}}}}}},"df":0,"docs":{}},"df":0,"docs":{}}}},"df":0,"docs":{}},"df":0,"docs":{}}},"4":{"df":2,"docs":{"2":{"tf":1.0},"48":{"tf":1.0}}},"df":0,"docs":{}},"df":0,"docs":{}}}}}},"df":1,"docs":{"45":{"tf":1.7320508075688772}},"o":{"df":0,"docs":{},"n":{"df":0,"docs":{},"o":{"df":0,"docs":{},"i":{"d":{"df":0,"docs":{},"h":{"df":0,"docs":{},"o":{"df":0,"docs":{},"m":{".":{"df":0,"docs":{},"m":{"a":{"df":0,"docs":{},"p":{"_":{"df":0,"docs":{},"m":{"df":0,"docs":{},"u":{"df":0,"docs":{},"l":{"df":1,"docs":{"10":{"tf":1.0}}}}}},"df":0,"docs":{}}},"df":0,"docs":{}}},"df":0,"docs":{}}}}},"df":0,"docs":{}}}}},"u":{"df":0,"docs":{},"l":{"_":{"df":0,"docs":{},"i":{"df":0,"docs":{},"n":{"df":0,"docs":{},"v":{"_":{"df":0,"docs":{},"e":{"df":0,"docs":{},"q":{"_":{"df":0,"docs":{},"i":{"df":0,"docs":{},"f":{"df":0,"docs":{},"f":{"_":{"df":0,"docs":{},"e":{"df":0,"docs":{},"q":{"_":{"df":0,"docs":{},"m":{"df":0,"docs":{},"u":{"df":0,"docs":{},"l":{"df":1,"docs":{"62":{"tf":1.4142135623730951}}}}}},"df":0,"docs":{}}}},"df":0,"docs":{}}}}},"df":0,"docs":{}}}},"df":0,"docs":{}}}},"n":{"df":0,"docs":{},"e":{"df":0,"docs":{},"g":{"df":1,"docs":{"71":{"tf":1.0}}}}}},"df":0,"docs":{}}},"y":{"a":{"b":{"df":1,"docs":{"71":{"tf":2.23606797749979}}},"df":0,"docs":{}},"df":0,"docs":{},"e":{"df":0,"docs":{},"q":{".":{"df":0,"docs":{},"r":{"df":0,"docs":{},"e":{"df":0,"docs":{},"f":{"df":0,"docs":{},"l":{"df":1,"docs":{"58":{"tf":1.0}}}}}}},"df":1,"docs":{"58":{"tf":1.7320508075688772}}}}}},"n":{"a":{"df":0,"docs":{},"m":{"df":0,"docs":{},"e":{"df":11,"docs":{"21":{"tf":1.0},"24":{"tf":1.0},"35":{"tf":1.0},"46":{"tf":1.0},"49":{"tf":1.0},"51":{"tf":1.0},"52":{"tf":1.0},"56":{"tf":1.0},"58":{"tf":1.0},"73":{"tf":1.0},"75":{"tf":1.0}}}},"t":{".":{"d":{"df":0,"docs":{},"v":{"d":{"_":{"df":0,"docs":{},"i":{"df":0,"docs":{},"f":{"df":0,"docs":{},"f":{"_":{"d":{"df":0,"docs":{},"i":{"df":0,"docs":{},"v":{"_":{"df":0,"docs":{},"m":{"df":0,"docs":{},"u":{"df":0,"docs":{},"l":{"_":{"df":0,"docs":{},"e":{"df":0,"docs":{},"q":{"df":1,"docs":{"72":{"tf":1.0}}}}},"df":0,"docs":{}}}}},"df":0,"docs":{}}}},"df":0,"docs":{}},"df":0,"docs":{}}}}},"df":0,"docs":{}},"df":0,"docs":{}}},"df":0,"docs":{},"l":{"df":0,"docs":{},"t":{".":{"b":{"a":{"df":0,"docs":{},"s":{"df":1,"docs":{"33":{"tf":1.0}}}},"df":0,"docs":{}},"df":0,"docs":{}},"df":0,"docs":{}}},"m":{"df":0,"docs":{},"u":{"df":0,"docs":{},"l":{"_":{"a":{"df":0,"docs":{},"s":{"df":0,"docs":{},"s":{"df":0,"docs":{},"o":{"c":{"df":1,"docs":{"61":{"tf":1.4142135623730951}}},"df":0,"docs":{}}}}},"df":0,"docs":{}},"df":0,"docs":{}}}},"s":{"df":0,"docs":{},"t":{"df":0,"docs":{},"r":{"df":0,"docs":{},"o":{"df":0,"docs":{},"n":{"df":0,"docs":{},"g":{"_":{"df":0,"docs":{},"i":{"df":0,"docs":{},"n":{"d":{"df":0,"docs":{},"u":{"c":{"df":0,"docs":{},"t":{"df":0,"docs":{},"i":{"df":0,"docs":{},"o":{"df":0,"docs":{},"n":{"_":{"df":0,"docs":{},"o":{"df":0,"docs":{},"n":{"df":1,"docs":{"45":{"tf":1.0}}}}},"df":0,"docs":{}}}}}},"df":0,"docs":{}}},"df":0,"docs":{}}}},"df":0,"docs":{}}}}}}}},"df":15,"docs":{"10":{"tf":1.0},"26":{"tf":1.0},"27":{"tf":1.0},"29":{"tf":1.4142135623730951},"34":{"tf":1.0},"36":{"tf":1.4142135623730951},"42":{"tf":2.8284271247461903},"43":{"tf":1.0},"45":{"tf":1.4142135623730951},"46":{"tf":1.0},"51":{"tf":1.0},"58":{"tf":1.0},"61":{"tf":1.0},"70":{"tf":1.0},"75":{"tf":1.4142135623730951}}}},"df":8,"docs":{"42":{"tf":3.872983346207417},"43":{"tf":1.7320508075688772},"44":{"tf":2.0},"45":{"tf":3.3166247903554},"46":{"tf":1.7320508075688772},"57":{"tf":3.7416573867739413},"58":{"tf":2.449489742783178},"70":{"tf":2.23606797749979}},"e":{"df":0,"docs":{},"e":{"d":{"df":22,"docs":{"14":{"tf":1.0},"16":{"tf":1.0},"20":{"tf":1.0},"21":{"tf":1.0},"22":{"tf":1.0},"29":{"tf":1.0},"35":{"tf":1.0},"37":{"tf":1.0},"4":{"tf":1.0},"43":{"tf":1.0},"48":{"tf":1.0},"49":{"tf":1.0},"51":{"tf":1.0},"52":{"tf":1.0},"56":{"tf":1.0},"57":{"tf":1.0},"58":{"tf":1.0},"60":{"tf":1.0},"62":{"tf":1.0},"63":{"tf":1.0},"73":{"tf":1.0},"75":{"tf":1.0}}},"df":0,"docs":{}},"g":{"a":{"df":0,"docs":{},"t":{"df":1,"docs":{"52":{"tf":1.0}}}},"df":0,"docs":{}}},"l":{"df":0,"docs":{},"i":{"df":0,"docs":{},"n":{"a":{"df":0,"docs":{},"r":{"df":0,"docs":{},"i":{"df":0,"docs":{},"t":{"df":0,"docs":{},"h":{"df":1,"docs":{"51":{"tf":2.23606797749979}}}}}}},"df":0,"docs":{}}}},"o":{"df":0,"docs":{},"n":{"c":{"df":0,"docs":{},"o":{"df":0,"docs":{},"m":{"df":0,"docs":{},"p":{"df":0,"docs":{},"u":{"df":0,"docs":{},"t":{"df":1,"docs":{"23":{"tf":1.0}}}}}}}},"df":1,"docs":{"51":{"tf":1.0}},"e":{"df":0,"docs":{},"m":{"df":0,"docs":{},"p":{"df":0,"docs":{},"t":{"df":0,"docs":{},"i":{"df":1,"docs":{"23":{"tf":1.0}}}}}}}}},"t":{"df":0,"docs":{},"h":{"_":{"df":0,"docs":{},"r":{"df":0,"docs":{},"w":{"df":2,"docs":{"57":{"tf":1.0},"62":{"tf":1.7320508075688772}}}}},"df":0,"docs":{}}}},"o":{"b":{"df":0,"docs":{},"t":{"a":{"df":0,"docs":{},"i":{"df":0,"docs":{},"n":{"df":1,"docs":{"57":{"tf":1.0}}}}},"df":0,"docs":{}}},"df":0,"docs":{},"n":{"df":0,"docs":{},"e":{"_":{"df":0,"docs":{},"m":{"df":0,"docs":{},"u":{"df":0,"docs":{},"l":{"df":1,"docs":{"62":{"tf":1.4142135623730951}}}}}},"df":0,"docs":{}}},"p":{"df":0,"docs":{},"e":{"df":0,"docs":{},"n":{"df":2,"docs":{"3":{"tf":1.0},"66":{"tf":1.0}}}},"t":{"df":0,"docs":{},"i":{"df":0,"docs":{},"o":{"df":0,"docs":{},"n":{"df":1,"docs":{"1":{"tf":1.0}}}}}}},"r":{".":{"df":0,"docs":{},"i":{"df":0,"docs":{},"n":{"df":0,"docs":{},"l":{"df":1,"docs":{"48":{"tf":1.4142135623730951}}},"r":{"df":1,"docs":{"48":{"tf":1.0}}}}}},"df":0,"docs":{}}},"p":{"(":{"0":{"df":1,"docs":{"45":{"tf":1.0}}},"df":0,"docs":{},"x":{"df":2,"docs":{"22":{"tf":1.4142135623730951},"46":{"tf":1.0}}}},"df":43,"docs":{"11":{"tf":1.7320508075688772},"13":{"tf":3.3166247903554},"14":{"tf":2.6457513110645907},"15":{"tf":2.8284271247461903},"16":{"tf":1.4142135623730951},"18":{"tf":2.449489742783178},"19":{"tf":1.7320508075688772},"20":{"tf":1.4142135623730951},"21":{"tf":3.0},"23":{"tf":2.449489742783178},"25":{"tf":3.0},"26":{"tf":1.0},"27":{"tf":2.6457513110645907},"31":{"tf":2.449489742783178},"33":{"tf":1.7320508075688772},"34":{"tf":1.7320508075688772},"37":{"tf":1.7320508075688772},"38":{"tf":3.0},"4":{"tf":2.449489742783178},"40":{"tf":2.23606797749979},"41":{"tf":1.4142135623730951},"42":{"tf":2.0},"44":{"tf":2.23606797749979},"45":{"tf":2.449489742783178},"46":{"tf":4.242640687119285},"47":{"tf":3.3166247903554},"48":{"tf":2.449489742783178},"5":{"tf":3.7416573867739413},"52":{"tf":3.4641016151377544},"53":{"tf":2.0},"54":{"tf":2.23606797749979},"55":{"tf":2.6457513110645907},"57":{"tf":1.0},"6":{"tf":2.6457513110645907},"61":{"tf":1.7320508075688772},"63":{"tf":1.4142135623730951},"65":{"tf":2.23606797749979},"66":{"tf":1.4142135623730951},"71":{"tf":1.7320508075688772},"72":{"tf":1.0},"73":{"tf":3.0},"74":{"tf":1.0},"8":{"tf":2.0}},"h":{"df":0,"docs":{},"r":{"a":{"df":0,"docs":{},"s":{"df":0,"docs":{},"e":{"b":{"df":0,"docs":{},"o":{"df":0,"docs":{},"o":{"df":0,"docs":{},"k":{"df":1,"docs":{"2":{"tf":1.0}}}}}},"df":0,"docs":{}}}},"df":0,"docs":{}}},"o":{"df":0,"docs":{},"s":{"df":0,"docs":{},"i":{"df":0,"docs":{},"t":{"df":2,"docs":{"42":{"tf":1.0},"43":{"tf":1.0}}}}}},"r":{"df":0,"docs":{},"i":{"df":0,"docs":{},"n":{"df":0,"docs":{},"t":{"df":1,"docs":{"10":{"tf":1.0}}}}},"o":{"df":0,"docs":{},"p":{"df":9,"docs":{"13":{"tf":1.0},"21":{"tf":1.0},"23":{"tf":1.0},"33":{"tf":1.0},"4":{"tf":1.0},"44":{"tf":1.0},"45":{"tf":1.0},"46":{"tf":1.0},"58":{"tf":1.0}}},"v":{"df":0,"docs":{},"e":{"df":2,"docs":{"17":{"tf":1.0},"28":{"tf":1.0}}}}}},"u":{"df":0,"docs":{},"s":{"df":0,"docs":{},"h":{"_":{"df":0,"docs":{},"n":{"df":0,"docs":{},"e":{"df":0,"docs":{},"g":{"df":1,"docs":{"52":{"tf":2.449489742783178}}}}}},"df":1,"docs":{"52":{"tf":1.0}}}}},"y":{"df":1,"docs":{"23":{"tf":1.4142135623730951}}}},"q":{"(":{"df":0,"docs":{},"i":{"df":1,"docs":{"46":{"tf":1.0}}}},"df":32,"docs":{"11":{"tf":1.0},"14":{"tf":2.23606797749979},"15":{"tf":2.0},"16":{"tf":1.4142135623730951},"18":{"tf":2.449489742783178},"19":{"tf":1.7320508075688772},"20":{"tf":1.4142135623730951},"21":{"tf":3.0},"25":{"tf":2.8284271247461903},"26":{"tf":1.0},"27":{"tf":1.0},"31":{"tf":1.4142135623730951},"33":{"tf":1.7320508075688772},"38":{"tf":2.6457513110645907},"4":{"tf":2.449489742783178},"40":{"tf":2.23606797749979},"42":{"tf":2.0},"46":{"tf":3.872983346207417},"47":{"tf":3.0},"48":{"tf":2.0},"5":{"tf":3.4641016151377544},"52":{"tf":3.1622776601683795},"53":{"tf":1.4142135623730951},"54":{"tf":2.0},"55":{"tf":2.8284271247461903},"61":{"tf":1.4142135623730951},"63":{"tf":1.4142135623730951},"65":{"tf":1.7320508075688772},"71":{"tf":1.7320508075688772},"72":{"tf":2.6457513110645907},"73":{"tf":2.23606797749979},"8":{"tf":2.0}}},"r":{"c":{"a":{"df":0,"docs":{},"s":{"df":0,"docs":{},"e":{"df":1,"docs":{"21":{"tf":2.23606797749979}}}}},"df":0,"docs":{}},"df":13,"docs":{"15":{"tf":2.449489742783178},"16":{"tf":1.4142135623730951},"18":{"tf":1.7320508075688772},"19":{"tf":1.7320508075688772},"20":{"tf":1.7320508075688772},"21":{"tf":2.0},"33":{"tf":1.4142135623730951},"38":{"tf":2.23606797749979},"4":{"tf":1.7320508075688772},"46":{"tf":2.6457513110645907},"55":{"tf":2.8284271247461903},"63":{"tf":1.4142135623730951},"73":{"tf":1.4142135623730951}},"e":{"c":{"df":0,"docs":{},"u":{"df":0,"docs":{},"r":{"df":0,"docs":{},"s":{"df":1,"docs":{"21":{"tf":1.0}}}}}},"df":0,"docs":{},"f":{"df":0,"docs":{},"i":{"df":0,"docs":{},"n":{"df":4,"docs":{"10":{"tf":1.0},"53":{"tf":2.23606797749979},"54":{"tf":2.23606797749979},"55":{"tf":2.0}}}},"l":{"df":2,"docs":{"58":{"tf":2.0},"59":{"tf":1.0}},"e":{"df":0,"docs":{},"x":{"df":1,"docs":{"58":{"tf":1.0}}}}}},"l":{"a":{"df":0,"docs":{},"t":{"df":1,"docs":{"56":{"tf":1.0}}}},"df":1,"docs":{"56":{"tf":2.6457513110645907}}},"p":{"df":0,"docs":{},"e":{"a":{"df":0,"docs":{},"t":{"df":1,"docs":{"4":{"tf":1.7320508075688772}}}},"df":0,"docs":{}},"l":{"a":{"c":{"df":2,"docs":{"57":{"tf":2.449489742783178},"71":{"tf":1.0}}},"df":0,"docs":{}},"df":0,"docs":{}}}},"f":{"df":0,"docs":{},"l":{"df":5,"docs":{"49":{"tf":1.0},"58":{"tf":2.449489742783178},"59":{"tf":2.23606797749979},"72":{"tf":1.4142135623730951},"74":{"tf":1.0}}}},"i":{"df":0,"docs":{},"g":{"df":0,"docs":{},"h":{"df":0,"docs":{},"t":{"df":3,"docs":{"18":{"tf":1.0},"25":{"tf":1.0},"48":{"tf":2.23606797749979}}}}},"n":{"df":0,"docs":{},"g":{"df":4,"docs":{"36":{"tf":1.0},"41":{"tf":1.0},"57":{"tf":2.0},"60":{"tf":2.6457513110645907}}}}},"w":{"df":10,"docs":{"26":{"tf":1.0},"29":{"tf":1.0},"3":{"tf":1.4142135623730951},"41":{"tf":1.0},"46":{"tf":1.0},"57":{"tf":1.4142135623730951},"61":{"tf":3.7416573867739413},"62":{"tf":1.4142135623730951},"63":{"tf":1.0},"67":{"tf":1.0}}}},"s":{"a":{"df":0,"docs":{},"y":{"df":0,"docs":{},"s":{".":{"df":0,"docs":{},"n":{"df":0,"docs":{},"o":{"_":{"df":0,"docs":{},"v":{"df":0,"docs":{},"e":{"df":0,"docs":{},"r":{"df":0,"docs":{},"i":{"df":0,"docs":{},"f":{"df":0,"docs":{},"y":{"_":{"df":0,"docs":{},"i":{"df":0,"docs":{},"n":{"_":{"c":{"df":0,"docs":{},"i":{"df":2,"docs":{"3":{"tf":1.0},"64":{"tf":1.0}}}},"df":0,"docs":{}},"df":0,"docs":{}}}},"df":0,"docs":{}}}}}}}},"df":0,"docs":{}}},"v":{"df":0,"docs":{},"e":{"df":0,"docs":{},"r":{"df":0,"docs":{},"i":{"df":0,"docs":{},"f":{"df":0,"docs":{},"i":{"df":1,"docs":{"64":{"tf":1.0}}}}}}}}},"df":0,"docs":{}}}},"df":2,"docs":{"35":{"tf":2.449489742783178},"63":{"tf":1.4142135623730951}},"e":{"df":0,"docs":{},"t":{"_":{"df":0,"docs":{},"o":{"df":0,"docs":{},"p":{"df":0,"docs":{},"t":{"df":2,"docs":{"1":{"tf":1.0},"3":{"tf":1.0}}}}}},"df":1,"docs":{"35":{"tf":1.0}}}},"h":{"df":0,"docs":{},"o":{"df":0,"docs":{},"w":{"_":{"df":0,"docs":{},"t":{"df":0,"docs":{},"e":{"df":0,"docs":{},"r":{"df":0,"docs":{},"m":{"df":1,"docs":{"60":{"tf":1.4142135623730951}}}}}}},"df":16,"docs":{"14":{"tf":1.0},"24":{"tf":1.4142135623730951},"29":{"tf":1.0},"3":{"tf":1.0},"4":{"tf":1.7320508075688772},"44":{"tf":1.4142135623730951},"46":{"tf":1.4142135623730951},"47":{"tf":1.0},"5":{"tf":1.0},"52":{"tf":1.4142135623730951},"53":{"tf":1.0},"54":{"tf":1.0},"55":{"tf":2.6457513110645907},"65":{"tf":2.449489742783178},"71":{"tf":1.7320508075688772},"75":{"tf":1.4142135623730951}}}}},"i":{"df":0,"docs":{},"m":{"df":0,"docs":{},"p":{"_":{"a":{"df":0,"docs":{},"l":{"df":4,"docs":{"26":{"tf":1.0},"3":{"tf":1.0},"63":{"tf":1.0},"68":{"tf":1.7320508075688772}}}},"df":0,"docs":{}},"df":11,"docs":{"24":{"tf":1.4142135623730951},"3":{"tf":1.0},"42":{"tf":1.4142135623730951},"43":{"tf":1.4142135623730951},"60":{"tf":1.0},"63":{"tf":1.0},"66":{"tf":3.1622776601683795},"67":{"tf":2.0},"68":{"tf":1.4142135623730951},"69":{"tf":1.4142135623730951},"71":{"tf":2.449489742783178}}}}},"o":{"df":0,"docs":{},"r":{"df":0,"docs":{},"r":{"df":0,"docs":{},"i":{"df":4,"docs":{"10":{"tf":1.4142135623730951},"44":{"tf":1.4142135623730951},"45":{"tf":1.4142135623730951},"70":{"tf":2.449489742783178}}},"y":{"a":{"df":0,"docs":{},"x":{"df":1,"docs":{"10":{"tf":1.7320508075688772}}}},"df":0,"docs":{}}}}},"p":{"df":0,"docs":{},"l":{"df":0,"docs":{},"i":{"df":0,"docs":{},"t":{"df":1,"docs":{"71":{"tf":2.6457513110645907}}}}}},"t":{"d":{".":{"df":0,"docs":{},"t":{"a":{"c":{"df":0,"docs":{},"t":{"df":0,"docs":{},"i":{"c":{".":{"df":0,"docs":{},"e":{"df":0,"docs":{},"x":{"df":0,"docs":{},"t":{"df":1,"docs":{"35":{"tf":1.0}}}}},"g":{"df":0,"docs":{},"u":{"a":{"df":0,"docs":{},"r":{"d":{"df":0,"docs":{},"e":{"df":0,"docs":{},"x":{"df":0,"docs":{},"p":{"df":0,"docs":{},"r":{"df":1,"docs":{"37":{"tf":1.0}}}}}}},"df":0,"docs":{}}},"df":0,"docs":{}}},"r":{"c":{"a":{"df":0,"docs":{},"s":{"df":1,"docs":{"21":{"tf":1.0}}}},"df":0,"docs":{}},"df":0,"docs":{},"e":{"df":0,"docs":{},"p":{"df":0,"docs":{},"l":{"a":{"c":{"df":1,"docs":{"57":{"tf":1.0}}},"df":0,"docs":{}},"df":0,"docs":{}}}}},"s":{"df":0,"docs":{},"h":{"df":0,"docs":{},"o":{"df":0,"docs":{},"w":{"df":0,"docs":{},"t":{"df":0,"docs":{},"e":{"df":0,"docs":{},"r":{"df":0,"docs":{},"m":{"df":1,"docs":{"16":{"tf":1.0}}}}}}}}}}},"df":0,"docs":{}},"df":0,"docs":{}}}},"df":0,"docs":{}},"df":0,"docs":{}}},"df":0,"docs":{}},"df":0,"docs":{}},"u":{"c":{"c":{"df":2,"docs":{"42":{"tf":2.6457513110645907},"44":{"tf":1.0}}},"df":0,"docs":{}},"df":0,"docs":{},"f":{"df":0,"docs":{},"f":{"df":0,"docs":{},"i":{"c":{"df":1,"docs":{"72":{"tf":3.0}}},"df":0,"docs":{}}}}}},"t":{"a":{"c":{"df":0,"docs":{},"t":{"df":0,"docs":{},"i":{"c":{"df":1,"docs":{"2":{"tf":1.0}}},"df":0,"docs":{}}}},"df":0,"docs":{},"u":{"df":0,"docs":{},"t":{"df":0,"docs":{},"o":{"df":1,"docs":{"73":{"tf":2.8284271247461903}},"l":{"df":0,"docs":{},"o":{"df":0,"docs":{},"g":{"df":1,"docs":{"73":{"tf":1.0}}}}}}}}},"df":2,"docs":{"10":{"tf":1.7320508075688772},"35":{"tf":2.449489742783178}},"h":{"df":0,"docs":{},"e":{"df":0,"docs":{},"o":{"df":0,"docs":{},"r":{"df":0,"docs":{},"e":{"df":0,"docs":{},"m":{"df":4,"docs":{"10":{"tf":1.0},"17":{"tf":1.0},"28":{"tf":1.0},"70":{"tf":1.0}}}},"i":{"df":1,"docs":{"2":{"tf":1.0}}}}}}},"r":{"df":0,"docs":{},"i":{"df":7,"docs":{"16":{"tf":1.0},"29":{"tf":1.0},"33":{"tf":1.4142135623730951},"49":{"tf":1.0},"51":{"tf":1.0},"63":{"tf":1.7320508075688772},"73":{"tf":1.4142135623730951}},"v":{"df":0,"docs":{},"i":{"a":{"df":0,"docs":{},"l":{"df":1,"docs":{"74":{"tf":2.8284271247461903}}}},"df":0,"docs":{}}}},"u":{"df":0,"docs":{},"e":{"df":3,"docs":{"1":{"tf":1.0},"3":{"tf":1.0},"64":{"tf":1.4142135623730951}}}}},"y":{"df":0,"docs":{},"p":{"df":0,"docs":{},"e":{"df":6,"docs":{"2":{"tf":1.0},"3":{"tf":1.0},"35":{"tf":1.0},"58":{"tf":1.0},"59":{"tf":1.0},"66":{"tf":1.7320508075688772}}}}}},"u":{"df":2,"docs":{"58":{"tf":1.0},"66":{"tf":1.7320508075688772}},"n":{"df":0,"docs":{},"f":{"df":0,"docs":{},"o":{"df":0,"docs":{},"l":{"d":{"df":1,"docs":{"71":{"tf":1.0}}},"df":0,"docs":{}}}},"i":{"df":0,"docs":{},"v":{"df":0,"docs":{},"e":{"df":0,"docs":{},"r":{"df":0,"docs":{},"s":{"df":1,"docs":{"66":{"tf":1.0}}}}}}}},"s":{"df":2,"docs":{"22":{"tf":1.4142135623730951},"45":{"tf":1.0}}}},"v":{"a":{"df":0,"docs":{},"r":{"df":0,"docs":{},"i":{"a":{"b":{"df":0,"docs":{},"l":{"df":10,"docs":{"21":{"tf":1.0},"23":{"tf":1.0},"3":{"tf":1.0},"33":{"tf":1.0},"35":{"tf":1.4142135623730951},"4":{"tf":1.0},"45":{"tf":1.0},"59":{"tf":1.0},"62":{"tf":1.0},"66":{"tf":1.0}}}},"df":0,"docs":{}},"df":0,"docs":{}}}},"df":1,"docs":{"66":{"tf":1.7320508075688772}}},"w":{"a":{"df":0,"docs":{},"r":{"df":0,"docs":{},"n":{"df":1,"docs":{"1":{"tf":1.0}},"i":{"df":0,"docs":{},"n":{"df":0,"docs":{},"g":{"a":{"df":0,"docs":{},"s":{"df":0,"docs":{},"e":{"df":0,"docs":{},"r":{"df":0,"docs":{},"r":{"df":0,"docs":{},"o":{"df":0,"docs":{},"r":{"df":1,"docs":{"1":{"tf":1.0}}}}}}}}},"df":0,"docs":{}}}}}}},"df":0,"docs":{},"i":{"df":0,"docs":{},"t":{"df":0,"docs":{},"h":{"df":0,"docs":{},"o":{"df":0,"docs":{},"u":{"df":0,"docs":{},"t":{"df":1,"docs":{"75":{"tf":1.0}}}}}}}},"l":{"df":0,"docs":{},"o":{"df":0,"docs":{},"g":{"df":1,"docs":{"75":{"tf":2.23606797749979}}}}}},"x":{")":{".":{"df":0,"docs":{},"p":{"df":0,"docs":{},"r":{"df":0,"docs":{},"o":{"df":0,"docs":{},"p":{"df":0,"docs":{},"e":{"df":0,"docs":{},"r":{"df":0,"docs":{},"t":{"df":0,"docs":{},"i":{"df":1,"docs":{"23":{"tf":1.0}}}}}}}}}},"v":{"a":{"df":0,"docs":{},"l":{"df":1,"docs":{"23":{"tf":1.0}}}},"df":0,"docs":{}}},"df":0,"docs":{}},"`":{"df":0,"docs":{},"が":{"df":0,"docs":{},"偶":{"df":0,"docs":{},"数":{"df":0,"docs":{},"の":{"df":0,"docs":{},"と":{"df":0,"docs":{},"き":{"`":{"3":{"df":1,"docs":{"41":{"tf":1.0}}},"df":0,"docs":{}},"df":0,"docs":{}}}}}}}},"df":23,"docs":{"10":{"tf":1.7320508075688772},"22":{"tf":3.1622776601683795},"23":{"tf":4.358898943540674},"24":{"tf":3.4641016151377544},"26":{"tf":2.6457513110645907},"27":{"tf":1.7320508075688772},"3":{"tf":2.23606797749979},"33":{"tf":1.7320508075688772},"34":{"tf":3.3166247903554},"35":{"tf":2.6457513110645907},"36":{"tf":3.872983346207417},"41":{"tf":3.4641016151377544},"46":{"tf":2.449489742783178},"49":{"tf":2.8284271247461903},"50":{"tf":1.4142135623730951},"52":{"tf":3.1622776601683795},"56":{"tf":2.23606797749979},"59":{"tf":1.7320508075688772},"60":{"tf":2.449489742783178},"63":{"tf":2.8284271247461903},"64":{"tf":1.4142135623730951},"70":{"tf":1.7320508075688772},"71":{"tf":5.196152422706632}}},"y":{"df":13,"docs":{"10":{"tf":1.7320508075688772},"22":{"tf":4.0},"23":{"tf":3.3166247903554},"3":{"tf":2.449489742783178},"41":{"tf":2.449489742783178},"46":{"tf":3.3166247903554},"49":{"tf":1.4142135623730951},"50":{"tf":1.4142135623730951},"52":{"tf":2.0},"60":{"tf":2.449489742783178},"63":{"tf":2.6457513110645907},"64":{"tf":2.0},"70":{"tf":1.7320508075688772}}},"z":{"df":5,"docs":{"3":{"tf":2.0},"41":{"tf":1.4142135623730951},"49":{"tf":1.4142135623730951},"63":{"tf":1.0},"70":{"tf":1.7320508075688772}},"e":{"df":0,"docs":{},"r":{"df":0,"docs":{},"o":{"df":2,"docs":{"42":{"tf":1.7320508075688772},"44":{"tf":1.0}}}}}}}},"title":{"root":{"a":{"df":0,"docs":{},"e":{"df":0,"docs":{},"s":{"df":0,"docs":{},"o":{"df":0,"docs":{},"p":{"df":1,"docs":{"3":{"tf":1.0}}}}}},"p":{"df":0,"docs":{},"p":{"df":0,"docs":{},"l":{"df":0,"docs":{},"i":{"df":3,"docs":{"10":{"tf":1.0},"5":{"tf":1.0},"54":{"tf":1.0}}},"y":{"_":{"a":{"df":0,"docs":{},"s":{"df":0,"docs":{},"s":{"df":0,"docs":{},"u":{"df":0,"docs":{},"m":{"df":0,"docs":{},"p":{"df":0,"docs":{},"t":{"df":2,"docs":{"4":{"tf":1.0},"9":{"tf":1.0}}}}}}}}},"df":0,"docs":{}},"df":0,"docs":{}}}}},"s":{"df":0,"docs":{},"s":{"df":0,"docs":{},"u":{"df":0,"docs":{},"m":{"df":0,"docs":{},"p":{"df":0,"docs":{},"t":{"df":2,"docs":{"11":{"tf":1.0},"32":{"tf":1.0}}}}}}}}},"b":{"df":0,"docs":{},"y":{"_":{"c":{"a":{"df":0,"docs":{},"s":{"df":1,"docs":{"13":{"tf":1.0}}}},"df":0,"docs":{},"o":{"df":0,"docs":{},"n":{"df":0,"docs":{},"t":{"df":0,"docs":{},"r":{"a":{"df":1,"docs":{"14":{"tf":1.0}}},"df":0,"docs":{}}}}}},"df":0,"docs":{}},"df":0,"docs":{}}},"c":{"a":{"df":0,"docs":{},"l":{"c":{"df":1,"docs":{"17":{"tf":1.0}}},"df":0,"docs":{}},"s":{"df":0,"docs":{},"e":{"df":3,"docs":{"18":{"tf":1.0},"19":{"tf":1.0},"20":{"tf":1.0}}}}},"df":0,"docs":{},"h":{"df":0,"docs":{},"o":{"df":0,"docs":{},"o":{"df":0,"docs":{},"s":{"df":1,"docs":{"22":{"tf":1.0}}}}}},"o":{"df":0,"docs":{},"n":{"df":0,"docs":{},"g":{"df":0,"docs":{},"r":{"df":1,"docs":{"24":{"tf":1.0}}}},"s":{"df":0,"docs":{},"t":{"df":0,"docs":{},"r":{"df":0,"docs":{},"u":{"c":{"df":0,"docs":{},"t":{"df":0,"docs":{},"o":{"df":0,"docs":{},"r":{"df":2,"docs":{"25":{"tf":1.0},"55":{"tf":1.0}}}}}},"df":0,"docs":{}}}}},"t":{"df":0,"docs":{},"r":{"a":{"d":{"df":0,"docs":{},"i":{"c":{"df":0,"docs":{},"t":{"df":1,"docs":{"27":{"tf":1.0}}}},"df":0,"docs":{}}},"df":0,"docs":{}},"df":0,"docs":{}}},"v":{"df":1,"docs":{"28":{"tf":1.0}},"e":{"df":0,"docs":{},"r":{"df":0,"docs":{},"t":{"df":1,"docs":{"29":{"tf":1.0}}}}}}}}},"d":{"df":0,"docs":{},"o":{"df":0,"docs":{},"n":{"df":0,"docs":{},"e":{"df":1,"docs":{"30":{"tf":1.0}}}}},"s":{"df":0,"docs":{},"i":{"df":0,"docs":{},"m":{"df":0,"docs":{},"p":{"df":1,"docs":{"69":{"tf":1.0}}}}}}},"df":0,"docs":{},"e":{"df":0,"docs":{},"x":{"a":{"c":{"df":0,"docs":{},"t":{"df":4,"docs":{"12":{"tf":1.0},"31":{"tf":1.0},"33":{"tf":1.0},"8":{"tf":1.0}}}},"df":0,"docs":{}},"df":0,"docs":{},"i":{"df":0,"docs":{},"s":{"df":0,"docs":{},"t":{"df":1,"docs":{"34":{"tf":1.0}}}}},"t":{"df":1,"docs":{"35":{"tf":1.0}}}}},"f":{"df":0,"docs":{},"u":{"df":0,"docs":{},"n":{"df":0,"docs":{},"e":{"df":0,"docs":{},"x":{"df":0,"docs":{},"t":{"df":1,"docs":{"36":{"tf":1.0}}}}}}}},"g":{"df":0,"docs":{},"u":{"a":{"df":0,"docs":{},"r":{"d":{"_":{"df":0,"docs":{},"h":{"df":0,"docs":{},"y":{"df":0,"docs":{},"p":{"df":1,"docs":{"37":{"tf":1.0}}}}}},"df":0,"docs":{}},"df":0,"docs":{}}},"df":0,"docs":{}}},"i":{"df":0,"docs":{},"n":{"d":{"df":0,"docs":{},"u":{"c":{"df":0,"docs":{},"t":{"df":2,"docs":{"42":{"tf":1.0},"43":{"tf":1.0}}}},"df":0,"docs":{}}},"df":0,"docs":{},"t":{"df":0,"docs":{},"r":{"df":0,"docs":{},"o":{"df":1,"docs":{"46":{"tf":1.0}}}}}}},"l":{"df":0,"docs":{},"e":{"a":{"df":0,"docs":{},"n":{"4":{"df":1,"docs":{"0":{"tf":1.0}}},"df":0,"docs":{}}},"df":0,"docs":{},"f":{"df":0,"docs":{},"t":{"df":1,"docs":{"48":{"tf":1.0}}}}},"i":{"df":0,"docs":{},"n":{"a":{"df":0,"docs":{},"r":{"df":0,"docs":{},"i":{"df":0,"docs":{},"t":{"df":0,"docs":{},"h":{"df":1,"docs":{"49":{"tf":1.0}}}}}}},"df":0,"docs":{}}}},"n":{"df":0,"docs":{},"l":{"df":0,"docs":{},"i":{"df":0,"docs":{},"n":{"a":{"df":0,"docs":{},"r":{"df":0,"docs":{},"i":{"df":0,"docs":{},"t":{"df":0,"docs":{},"h":{"df":1,"docs":{"51":{"tf":1.0}}}}}}},"df":0,"docs":{}}}},"t":{"df":0,"docs":{},"h":{"_":{"df":0,"docs":{},"r":{"df":0,"docs":{},"w":{"df":1,"docs":{"62":{"tf":1.0}}}}},"df":0,"docs":{}}}},"p":{"df":0,"docs":{},"u":{"df":0,"docs":{},"s":{"df":0,"docs":{},"h":{"_":{"df":0,"docs":{},"n":{"df":0,"docs":{},"e":{"df":0,"docs":{},"g":{"df":1,"docs":{"52":{"tf":1.0}}}}}},"df":0,"docs":{}}}}},"r":{"c":{"a":{"df":0,"docs":{},"s":{"df":0,"docs":{},"e":{"df":1,"docs":{"21":{"tf":1.0}}}}},"df":0,"docs":{}},"df":0,"docs":{},"e":{"df":0,"docs":{},"f":{"df":0,"docs":{},"i":{"df":0,"docs":{},"n":{"df":1,"docs":{"53":{"tf":1.0}}}}},"l":{"df":1,"docs":{"56":{"tf":1.0}}},"p":{"df":0,"docs":{},"l":{"a":{"c":{"df":1,"docs":{"57":{"tf":1.0}}},"df":0,"docs":{}},"df":0,"docs":{}}}},"f":{"df":0,"docs":{},"l":{"df":1,"docs":{"58":{"tf":1.0}}}},"i":{"df":0,"docs":{},"g":{"df":0,"docs":{},"h":{"df":0,"docs":{},"t":{"df":1,"docs":{"48":{"tf":1.0}}}}},"n":{"df":0,"docs":{},"g":{"df":1,"docs":{"60":{"tf":1.0}}}}},"w":{"df":1,"docs":{"61":{"tf":1.0}}}},"s":{"df":0,"docs":{},"h":{"df":0,"docs":{},"o":{"df":0,"docs":{},"w":{"df":1,"docs":{"65":{"tf":1.0}}}}},"i":{"df":0,"docs":{},"m":{"df":0,"docs":{},"p":{"_":{"a":{"df":0,"docs":{},"l":{"df":1,"docs":{"68":{"tf":1.0}}}},"df":0,"docs":{}},"df":2,"docs":{"66":{"tf":1.0},"67":{"tf":1.0}}}}},"o":{"df":0,"docs":{},"r":{"df":0,"docs":{},"r":{"df":0,"docs":{},"i":{"df":1,"docs":{"70":{"tf":1.0}}}}}},"p":{"df":0,"docs":{},"l":{"df":0,"docs":{},"i":{"df":0,"docs":{},"t":{"df":1,"docs":{"71":{"tf":1.0}}}}}},"u":{"df":0,"docs":{},"f":{"df":0,"docs":{},"f":{"df":0,"docs":{},"i":{"c":{"df":1,"docs":{"72":{"tf":1.0}}},"df":0,"docs":{}}}}}},"t":{"a":{"df":0,"docs":{},"u":{"df":0,"docs":{},"t":{"df":0,"docs":{},"o":{"df":1,"docs":{"73":{"tf":1.0}}}}}},"df":0,"docs":{},"r":{"df":0,"docs":{},"i":{"df":0,"docs":{},"v":{"df":0,"docs":{},"i":{"a":{"df":0,"docs":{},"l":{"df":1,"docs":{"74":{"tf":1.0}}}},"df":0,"docs":{}}}}}},"w":{"df":0,"docs":{},"l":{"df":0,"docs":{},"o":{"df":0,"docs":{},"g":{"df":1,"docs":{"75":{"tf":1.0}}}}}}}}},"lang":"English","pipeline":["trimmer","stopWordFilter","stemmer"],"ref":"id","version":"0.9.5"},"results_options":{"limit_results":30,"teaser_word_count":30},"search_options":{"bool":"OR","expand":true,"fields":{"body":{"boost":1},"breadcrumbs":{"boost":1},"title":{"boost":2}}}});
\ No newline at end of file
diff --git a/searchindex.json b/searchindex.json
index 52a0eaeb..3ce57a82 100644
--- a/searchindex.json
+++ b/searchindex.json
@@ -1 +1 @@
-{"doc_urls":["index.html#lean4-タクティク逆引きリスト","index.html#オプションについて","index.html#リンク集","aesop.html#aesop","aesop.html#aesop-1","apply_assumption.html#apply_assumption","apply.html#apply","apply.html#否定--について","apply.html#よくあるエラー","apply.html#exact-との関連","apply.html#apply_assumption-との関連","apply_question.html#apply","apply_question.html#補足","assumption.html#assumption","assumption.html#exact-との関連","by_cases.html#by_cases","by_contra.html#by_contra","by.html#by","by.html#by-1","calc.html#calc","cases.html#cases","cases.html#case-を書かない","cases.html#cases-1","cases.html#rcases","choose.html#choose","choose.html#補足","congr.html#congr","constructor.html#constructor","constructor.html#同値を示す","contradiction.html#contradiction","conv.html#conv","convert.html#convert","done.html#done","exact.html#exact","exact.html#assumption-との関連","exact_question.html#exact","exists.html#exists","ext.html#ext","funext.html#funext","guard_hyp.html#guard_hyp","have.html#have","have.html#パターンマッチ","have.html#論理積-","have.html#存在-","induction.html#induction","induction.html#induction-1","induction.html#一般のについての帰納法","induction.html#強い帰納法","intro.html#intro","intro.html#否定--について","left_right.html#left-right","linarith.html#linarith","linarith.html#補足","nlinarith.html#nlinarith","push_neg.html#push_neg","refine.html#refine","refine.html#apply-との関連","refine.html#constructor-との関連","rel.html#rel","replace.html#replace","rfl.html#rfl","rfl.html#補足","ring.html#ring","rw.html#rw","rw.html#nth_rewrite","says.html#says","says.html#オプション","show.html#show","simp.html#simp","simp.html#simp-1","simp.html#simp_all","simp.html#dsimp","sorry.html#sorry","split.html#split","suffices.html#suffices","tauto.html#tauto","trivial.html#trivial","wlog.html#wlog"],"index":{"documentStore":{"docInfo":{"0":{"body":1,"breadcrumbs":2,"title":1},"1":{"body":6,"breadcrumbs":1,"title":0},"10":{"body":3,"breadcrumbs":2,"title":1},"11":{"body":24,"breadcrumbs":2,"title":1},"12":{"body":60,"breadcrumbs":1,"title":0},"13":{"body":9,"breadcrumbs":2,"title":1},"14":{"body":2,"breadcrumbs":2,"title":1},"15":{"body":30,"breadcrumbs":2,"title":1},"16":{"body":31,"breadcrumbs":2,"title":1},"17":{"body":37,"breadcrumbs":0,"title":0},"18":{"body":24,"breadcrumbs":0,"title":0},"19":{"body":4,"breadcrumbs":2,"title":1},"2":{"body":10,"breadcrumbs":1,"title":0},"20":{"body":49,"breadcrumbs":2,"title":1},"21":{"body":33,"breadcrumbs":2,"title":1},"22":{"body":26,"breadcrumbs":2,"title":1},"23":{"body":61,"breadcrumbs":2,"title":1},"24":{"body":64,"breadcrumbs":2,"title":1},"25":{"body":67,"breadcrumbs":1,"title":0},"26":{"body":75,"breadcrumbs":2,"title":1},"27":{"body":36,"breadcrumbs":2,"title":1},"28":{"body":27,"breadcrumbs":1,"title":0},"29":{"body":31,"breadcrumbs":2,"title":1},"3":{"body":25,"breadcrumbs":2,"title":1},"30":{"body":4,"breadcrumbs":2,"title":1},"31":{"body":37,"breadcrumbs":2,"title":1},"32":{"body":1,"breadcrumbs":2,"title":1},"33":{"body":25,"breadcrumbs":2,"title":1},"34":{"body":3,"breadcrumbs":2,"title":1},"35":{"body":35,"breadcrumbs":2,"title":1},"36":{"body":23,"breadcrumbs":2,"title":1},"37":{"body":48,"breadcrumbs":2,"title":1},"38":{"body":40,"breadcrumbs":2,"title":1},"39":{"body":13,"breadcrumbs":2,"title":1},"4":{"body":23,"breadcrumbs":2,"title":1},"40":{"body":39,"breadcrumbs":0,"title":0},"41":{"body":0,"breadcrumbs":0,"title":0},"42":{"body":17,"breadcrumbs":0,"title":0},"43":{"body":38,"breadcrumbs":0,"title":0},"44":{"body":67,"breadcrumbs":2,"title":1},"45":{"body":22,"breadcrumbs":2,"title":1},"46":{"body":51,"breadcrumbs":1,"title":0},"47":{"body":40,"breadcrumbs":1,"title":0},"48":{"body":101,"breadcrumbs":2,"title":1},"49":{"body":42,"breadcrumbs":1,"title":0},"5":{"body":44,"breadcrumbs":2,"title":1},"50":{"body":29,"breadcrumbs":4,"title":2},"51":{"body":43,"breadcrumbs":2,"title":1},"52":{"body":13,"breadcrumbs":1,"title":0},"53":{"body":21,"breadcrumbs":2,"title":1},"54":{"body":62,"breadcrumbs":2,"title":1},"55":{"body":17,"breadcrumbs":2,"title":1},"56":{"body":26,"breadcrumbs":2,"title":1},"57":{"body":62,"breadcrumbs":2,"title":1},"58":{"body":36,"breadcrumbs":2,"title":1},"59":{"body":81,"breadcrumbs":2,"title":1},"6":{"body":49,"breadcrumbs":2,"title":1},"60":{"body":34,"breadcrumbs":2,"title":1},"61":{"body":27,"breadcrumbs":1,"title":0},"62":{"body":33,"breadcrumbs":2,"title":1},"63":{"body":55,"breadcrumbs":2,"title":1},"64":{"body":34,"breadcrumbs":2,"title":1},"65":{"body":70,"breadcrumbs":0,"title":0},"66":{"body":13,"breadcrumbs":0,"title":0},"67":{"body":19,"breadcrumbs":2,"title":1},"68":{"body":142,"breadcrumbs":2,"title":1},"69":{"body":2,"breadcrumbs":2,"title":1},"7":{"body":21,"breadcrumbs":1,"title":0},"70":{"body":2,"breadcrumbs":2,"title":1},"71":{"body":2,"breadcrumbs":2,"title":1},"72":{"body":26,"breadcrumbs":2,"title":1},"73":{"body":115,"breadcrumbs":2,"title":1},"74":{"body":38,"breadcrumbs":2,"title":1},"75":{"body":39,"breadcrumbs":2,"title":1},"76":{"body":16,"breadcrumbs":2,"title":1},"77":{"body":42,"breadcrumbs":2,"title":1},"8":{"body":1,"breadcrumbs":1,"title":0},"9":{"body":17,"breadcrumbs":2,"title":1}},"docs":{"0":{"body":"「普段の数学を Lean でどうやって実現するんだろう」という疑問に答えるために，よく使うタクティクをユースケースから逆引きできるようにまとめたリストです． なお，タクティクの説明に付記している名前の由来についての説明は公式に説明があったものではなく，あくまで憶測であることをお断りしておきます．","breadcrumbs":"Lean4 タクティク逆引きリスト » Lean4 タクティク逆引きリスト","id":"0","title":"Lean4 タクティク逆引きリスト"},"1":{"body":"タクティクによっては，オプションを設定することで挙動を変更することができます．オプションの設定には，set_option を使用します．たとえば，set_option warningAsError true と書くと，warning(警告) がエラーとして扱われるようになります． 使用できるオプションの一覧は #help option または こちらのリスト で確認することができます．","breadcrumbs":"Lean4 タクティク逆引きリスト » オプションについて","id":"1","title":"オプションについて"},"10":{"body":"apply は常にどの命題を使うか明示する必要がありますが，「ゴールに apply が適用できるような命題をローカルコンテキストから自動で探す」 apply_assumption というタクティクもあります．","breadcrumbs":"apply: 含意→を使う » apply_assumption との関連","id":"10","title":"apply_assumption との関連"},"11":{"body":"needs: import Mathlib.Tactic.LibrarySearch apply? は，ゴールを閉じるのに必要な命題をライブラリから検索してきて，提案してくれるタクティクです． -- 群準同型は積を保つ\nexample [Group G] [Group H] (f : G →* H) (a b : G) : f (a * b) = f a * f b := by -- `exact MonoidHom.map_mul f a b` を提案してくれる apply? 複数の候補が提案されたときは，どれを選ぶとゴールが何に変わるのか表示されるので，その中から好ましいものを選ぶと良いでしょう．","breadcrumbs":"apply?: ライブラリ検索で後方推論 » apply?","id":"11","title":"apply?"},"12":{"body":"apply? はあくまで証明を書くときに補助として使うものです．sorry と同じように，清書した証明に残してはいけません． sorry と同じと言いましたが，実際 apply? は sorryAx [1] を裏で使用します．これは，#explode で証明の中身を出力させれば分かります．sorry を使っているという旨の警告も出ます． theorem T (x y : Nat) (_: x ≤ y) : 2 ^ x ≤ 2 ^ y := by apply? -- `apply?` しただけで `done` が通り，示せているように見える done /-\nT : ∀ (x y : ℕ), x ≤ y → 2 ^ x ≤ 2 ^ y 0│ │ x ├ ℕ\n1│ │ y ├ ℕ\n2│ │ h ├ x ≤ y\n3│ │ sorryAx │ 2 ^ x ≤ 2 ^ y\n4│0,1,2,3│ ∀I │ ∀ (x y : ℕ), x ≤ y → 2 ^ x ≤ 2 ^ y\n-/\n#explode T [1] sorry が裏で使用している公理のこと","breadcrumbs":"apply?: ライブラリ検索で後方推論 » 補足","id":"12","title":"補足"},"13":{"body":"assumption は，現在のゴール ⊢ P がローカルコンテキストにあるとき，ゴールを閉じます． example (hP: P) (_: Q) : P := by assumption","breadcrumbs":"assumption: 仮定からゴールを閉じる » assumption","id":"13","title":"assumption"},"14":{"body":"assumption による証明は，どの仮定を使うか明示すれば exact で書き直すことができます．","breadcrumbs":"assumption: 仮定からゴールを閉じる » exact との関連","id":"14","title":"exact との関連"},"15":{"body":"by_cases は排中律を使って場合分けをするタクティクです． by_cases h: P とすると，P が成り立つときと成り立たないときのゴールがそれぞれ生成されます． example (P: Prop) : ¬¬P → P := by intro hnnP -- `P` が成り立つかどうかで場合分けする by_cases hP: P case inl => -- `P` が成り立つとき guard_hyp hP : P assumption case inr => -- `¬ P` が成り立つとき guard_hyp hP : ¬P contradiction","breadcrumbs":"by_cases: 排中律 » by_cases","id":"15","title":"by_cases"},"16":{"body":"needs: import Mathlib.Tactic.ByContra by_contra は，背理法を使いたいときに役立つタクティクです． ゴールが ⊢ P であるときに by_contra h を実行すると，h : ¬ P がローカルコンテキストに追加されて，同時にゴールが ⊢ False になります． example (h: ¬Q → ¬P) : P → Q := by -- `P` であると仮定する intro hP -- `¬Q` であると仮定して矛盾を導きたい by_contra hnQ show False -- `¬ Q → ¬ P` と `¬Q` から `¬P` が導かれる have := h hnQ -- これは仮定に矛盾 contradiction","breadcrumbs":"by_contra: 背理法 » by_contra","id":"16","title":"by_contra"},"17":{"body":"Lean においては，命題は型で，証明はその項です．命題 P の証明を構成するとは項 h : P を構成するということです．by は，証明の構成をタクティクで行いたいときに使います． -- `P → R` というのは `P` の証明を与えられたときに `R` の証明を返す関数の型\n-- したがって，その証明は関数となる\nexample (hPQ : P → Q) (hQR : Q → R) : P → R := fun hP ↦ hQR (hPQ hP) -- 同じ命題をタクティクで示した例\nexample (hPQ : P → Q) (hQR : Q → R) : P → R := by intro hP exact hQR (hPQ hP)","breadcrumbs":"by: タクティクモードに入る » by","id":"17","title":"by"},"18":{"body":"needs: import Std.Tactic.ShowTerm by? を使うとタクティクモードで構成した証明を直接構成した証明に変換してくれます． example (hPQ : P → Q) (hQR : Q → R) : P → R := by? -- `Try this: fun hP => hQR (hPQ hP)` と提案してくれる intro hP exact hQR (hPQ hP)","breadcrumbs":"by: タクティクモードに入る » by?","id":"18","title":"by?"},"19":{"body":"calc は計算モードに入るためのタクティクです．詳細については Theorem Proving in Lean4 をご参照ください．","breadcrumbs":"calc: 計算モードに入る » calc","id":"19","title":"calc"},"2":{"body":"Mathematics in type Theory 日本語訳 このリストでは「命題は型，証明はその項」という型理論を基礎として数学を実装する際の事実は既知としています．こういった話に全く馴染みがない方は，まずこちらの記事を読まれると良いと思います． mathlib4-all-tactics 全タクティクの網羅的なリスト． 数学系のためのLean勉強会 Lean で数学をどのように実装するのか，実際に実装する過程を追うことで学べる教材です．いくつかコード例を拝借させていただきました． Lean phrasebook 英語ですが，数学でのよくある推論ステップが，Lean にどのように翻訳されるかがよくまとめられたリストです．","breadcrumbs":"Lean4 タクティク逆引きリスト » リンク集","id":"2","title":"リンク集"},"20":{"body":"cases は場合分けを行います．ローカルコンテキストに h: P ∨ Q があるときに cases h とすると，仮定に P を付け加えたゴール inl と，仮定に Q を付け加えたゴール inr を生成します．それぞれ，insert left と insert right の略ではないかと思います． example : P ∨ Q → (P → R) → (Q → R) → R := by -- `h: P ∨ Q` intro h hPR hQR -- `case inl` と `case inr` の２つのゴールを生成する cases h -- `P` が成り立つ場合 case inl hP => exact hPR hP -- `Q` が成り立つ場合 case inr hQ => exact hQR hQ","breadcrumbs":"cases: 論理和∨を使う » cases","id":"20","title":"cases"},"21":{"body":"上記の例では case を場合分けの枝ごとに書いていますが，下の例のように case を書かずに済ませることもできます． example : P ∨ Q → (P → R) → (Q → R) → R := by -- `h: P ∨ Q` intro h hPR hQR -- `case inl` と `case inr` の２つのゴールを生成する cases h with | inl hP => exact hPR hP | inr hQ => exact hQR hQ","breadcrumbs":"cases: 論理和∨を使う » case を書かない","id":"21","title":"case を書かない"},"22":{"body":"needs: import Mathlib.Tactic.Cases cases' を使用すると分解した仮定に簡潔に名前をつけることができます． example : P ∨ Q → (P → R) → (Q → R) → R := by intro h hPR hQR -- 場合分けをする cases' h with hP hQ · apply hPR hP · apply hQR hQ","breadcrumbs":"cases: 論理和∨を使う » cases'","id":"22","title":"cases'"},"23":{"body":"needs: import Std.Tactic.RCases named after: 再帰的(recursive) cases rcases は cases をパターンに従って再帰的に適用します．論理和∨以外にも使うことができます． variable (P Q R : Prop) example : P ∨ Q → (P → R) → (Q → R) → R := by intro h hPR hQR -- 場合分けをする rcases h with hP | hQ · apply hPR hP · apply hQR hQ example : P ∧ Q → Q ∧ P := by -- `h: P ∧ Q` と仮定する intro h -- `h: P ∧ Q` を `hP: P` と `hQ: Q` に分解する rcases h with ⟨hP, hQ⟩ -- `Q ∧ P` を証明する exact ⟨hQ, hP⟩","breadcrumbs":"cases: 論理和∨を使う » rcases","id":"23","title":"rcases"},"24":{"body":"needs: import Mathlib.Tactic.Choose h : ∀ x, ∃ y, P(x, y) が成り立っているときに，choose f hf using h は写像 f: X → Y と f が満たす性質 hf : ∀ x, P(x, f x) のペアを作ります． example (f : X → Y) (hf : ∀ y, ∃ x, f x = y) : ∃ g : Y → X, ∀ y, f (g y) = y := by -- 写像 `g : Y → X` を構成する choose g hg using hf -- `g` が満たす条件がローカルコンテキストに追加される guard_hyp g: Y → X guard_hyp hg: ∀ (y : Y), f (g y) = y exact ⟨g, hg⟩","breadcrumbs":"choose: 選択関数を得る » choose","id":"24","title":"choose"},"25":{"body":"choose が自動で示してくれることは選択原理 Classical.choice を使って手動で示すことができます．たとえば次のようになります． variable (P : X → Y → Prop) noncomputable example (h : ∀ x, ∃ y, P x y) : ∃ f : X → Y, ∀ x, P x (f x) := by -- `f` を作る let f' : (x : X) → {y // P x y} := fun x ↦ have hne_st : Nonempty {y // P x y} := let ⟨y, py⟩ := h x; ⟨⟨y, py⟩⟩ Classical.choice hne_st let f : X → Y := fun x ↦ (f' x).val -- 上記で作った関数が条件を満たすことを示す have h₁ : ∀ x, P x (f x) := by intro x exact (f' x).property exists f","breadcrumbs":"choose: 選択関数を得る » 補足","id":"25","title":"補足"},"26":{"body":"named after: 合同(congruence) congr は，⊢ f as = f bs という形のゴールがあったときに，ゴールを ⊢ as = bs に変えます．再帰的に適用されるので，⊢ g (f as) = g (f bs) という形のゴールでも同じ結果になります． example (f : Int → X) (h : x = 0) : f (2 + x) = f 2 := by congr show 2 + x = 2 simp only [h, add_zero] congr が適用される再帰の深さを引数として渡すことができます．これは，主に単に congr とするだけだと「行き過ぎ」になるときに調整する目的で使用されます． example (f : Int → Int) (g : Int → X) (h : x = 0) (hf : ∀ x, f x = f (- x)) : g (f (2 + x)) = g (f (- 2)) := by -- 仮に `congr` とすると -- ゴールが `⊢ 2 + x = -2` になってしまう congr 1 show f (2 + x) = f (-2) simp only [h, add_zero] exact hf _","breadcrumbs":"congr: ゴールの差異に注目する » congr","id":"26","title":"congr"},"27":{"body":"ゴールが ⊢ P ∧ Q であるとき，constructor を実行すると，ゴールが２つのゴール ⊢ P と ⊢ Q に分割されます． example (hP: P) (hQ: Q) : P ∧ Q := by -- goal が `left` と `right` に分割される constructor · -- `P` を示す exact hP · -- `Q` を示す exact hQ なお h: P ∧ Q から P や Q の証明を得るのは，それぞれ h.left と h.right で可能です． example (h: P ∧ Q) : P := by exact h.left","breadcrumbs":"constructor: 論理積∧を示す » constructor","id":"27","title":"constructor"},"28":{"body":"constructor はゴールが ⊢ P ↔ Q であるときにも使用できます． example (x : Nat) : x = 0 ↔ x + 1 = 1 := by constructor · -- `x = 0 → x + 1 = 1` を示す intro hx rw [hx] · -- `x + 1 = 1 → x = 0` を示す simp_all","breadcrumbs":"constructor: 論理積∧を示す » 同値を示す","id":"28","title":"同値を示す"},"29":{"body":"矛盾からはどんな命題でも証明することができます．これを爆発律(principle of explosion)と呼びますが，contradiction は，この爆発律を使ってゴールを閉じるタクティクです． ローカルコンテキストに P と ¬ P が同時にあるなど，矛盾した状況にあるときにゴールを閉じます． -- `False`\nexample (h : False) : P := by contradiction -- 明らかに偽な等式\nexample (h : 2 + 2 = 3) : P := by contradiction -- 明らかに偽な等式\nexample (x : Nat) (h : x ≠ x) : P := by contradiction -- 矛盾する仮定\nexample (hP : P) (hnP : ¬ P) : Q := by contradiction","breadcrumbs":"contradiction: 爆発律 » contradiction","id":"29","title":"contradiction"},"3":{"body":"needs: import Aesop aesop は，intro や simp を使用してルーチンな証明を自動で行おうとします． -- 合成 `g ∘ f` が単射なら，`f` も単射\nexample {f : X → Y} {g : Y → Z} (hgfinj : Injective (g ∘ f)) : Injective f := by rw [Injective] aesop","breadcrumbs":"aesop: ルーチン自動化 » aesop","id":"3","title":"aesop"},"30":{"body":"conv は変換モードに入るためのタクティクです．詳細については Theorem Proving in Lean4 をご参照ください．","breadcrumbs":"conv: 変換モードに入る » conv","id":"30","title":"conv"},"31":{"body":"needs: import Mathlib.Tactic.Convert ローカルコンテキストに現在のゴールに近いけれども等しくはない h があるとき，exact h としても失敗します．しかし convert h は成功する可能性があり，成功した場合は h とゴールの差分を新たなゴールとします． example (f : Nat → Nat) (h : f (a + b) = 0) (hc: a + b = c) : f (c) = 0 := by -- `h` はゴールと等しくないので失敗する try exact [h] -- `h` とゴールの差分を新たなゴールにする convert h -- ゴールが `⊢ c = a + b` に変わっている show c = a + b rw [hc]","breadcrumbs":"convert: 惜しい補題を使う » convert","id":"31","title":"convert"},"32":{"body":"done は，証明終了の合図です．証明すべきゴールが残っていない時に成功し，それ以外の時にはエラーになります．QED のようなものです．","breadcrumbs":"done: 証明終了を宣言 » done","id":"32","title":"done"},"33":{"body":"ゴールが P で，ローカルコンテキストに hP: P があるときに，exact hP はゴールを閉じます． example (hP: P) : P := by exact hP hP がゴールの証明になっていないときには，失敗してエラーになります． exact ⟨ hP, hQ ⟩ のようにすると，論理積∧の形をした命題を証明することができます． example (hP: P) (hQ: Q) : P ∧ Q := by exact ⟨ hP, hQ ⟩","breadcrumbs":"exact: 証明を直接構成 » exact","id":"33","title":"exact"},"34":{"body":"exact は常にどの命題を使うか明示する必要がありますが，「ゴールを exact で閉じることができるような命題をローカルコンテキストから自動で探す」 assumption というタクティクもあります．","breadcrumbs":"exact: 証明を直接構成 » assumption との関連","id":"34","title":"assumption との関連"},"35":{"body":"needs: import Mathlib.Tactic.LibrarySearch exact? は，ライブラリとローカルコンテキストにある命題を使って，ゴールを閉じることができないか探索します． -- `exact?` はライブラリ検索を行う\nexample : x < x + 1 := by -- `Try this: exact Nat.lt.base x` と出力される exact? apply? と似ていますが，apply? とは異なりゴールを変形するのではなくて exact で直接閉じようとします． -- ローカルコンテキストにある仮定を自動で使ってゴールを導いてくれる\nexample (hPQ : P → Q) (hQR : Q → R) (hQ : P) : R := by -- `Try this: exact hQR (hPQ hQ)` と出力される exact? -- 証明は `exact?` だけで終わっている done","breadcrumbs":"exact?: ゴールをライブラリ検索 » exact?","id":"35","title":"exact?"},"36":{"body":"exists は，「～という x が存在する」という命題を示すために，「この x を使え」と指示するコマンドです． ゴールが ⊢ ∃ x, P x のとき，x: X がローカルコンテキストにあれば，exists x によりゴールが P x に変わります．同時に，P x が自明な場合は証明が終了します． example : ∃ x : Nat, 3 * x + 1 = 7 := by exists 2","breadcrumbs":"exists: 存在∃を示す » exists","id":"36","title":"exists"},"37":{"body":"needs: import Std.Tactic.Ext named after: 外延性(extensionality) ext は，外延性を使うタクティクです．外延性とは，「同じものから作られているものは同じである」という主張のことです．たとえば 集合 A, B ⊂ α について A = B は x ∈ A ↔ x ∈ B と同じ 2つの写像 f g : A → B があるとき f = g は ∀ a ∈ A, f a = g a と同じ といったことを指します． @[ext] で登録されたルールを使用するため，集合の等式 A = B を示すときは Mathlib.Data.SetLike.Basic も必要です． variable {α : Type} -- `s` と `t` は `α` の部分集合\nvariable (s t : Set α) example : s ∩ t = t ∩ s := by -- `x ∈ α` を取る．` x ∈ s ∩ t ↔ x ∈ t ∩ s` を証明すればよい ext x aesop なお A ⊂ B を示すために元を取るのは intro x で可能です．","breadcrumbs":"ext: 外延性を使う » ext","id":"37","title":"ext"},"38":{"body":"関数 f と g が等しいことを示す際に，引数 x をとって f x = g x を示そうとすることがありますが，funext はそれを行うタクティクです. def f := fun (x : Nat) ↦ x + x def g := fun (x : Nat) ↦ 2 * x example : f = g := by -- 引数 `x` を取る funext x -- `f x` と `g x` を展開する dsimp [f, g] -- `x + x` と `2 * x` が等しいことを証明する ring","breadcrumbs":"funext: 関数等式を示す » funext","id":"38","title":"funext"},"39":{"body":"needs: import Std.Tactic.GuardExpr guard_hyp は，ローカルコンテキストにある命題を確認するタクティクです．指定した仮定が存在すれば成功し，そうでなければ失敗します． example (hP : P) : P := by -- 現在ローカルコンテキストにある命題を確認できる guard_hyp hP : P exact hP 通常の証明で使うことはあまりないかもしれません．このタクティクリストでは，ローカルコンテキストの変化を説明するために使用することがあります．","breadcrumbs":"guard_hyp: 仮定や補題を確認 » guard_hyp","id":"39","title":"guard_hyp"},"4":{"body":"aesop が成功したとき，aesop? に置き換えると，ゴールを達成するのにどんなタクティクを使用したか教えてくれます． example {f : X → Y} {g : Y → Z} (hgfinj : Injective (g ∘ f)) : Injective f := by rw [Injective] -- `aesop?` は以下を返す intro a₁ a₂ a apply hgfinj simp_all only [comp_apply]","breadcrumbs":"aesop: ルーチン自動化 » aesop?","id":"4","title":"aesop?"},"40":{"body":"have は，証明の途中でわかることをローカルコンテキストに追加するコマンドです． have h: P := ... で P という命題の証明を構成し，その証明に h という名前を付けることができます． example (hPQ: P → Q) (hQR: Q → R) : P → R := by -- 示したいことが `P → R` なので，`P` だと仮定する intro hP -- 仮定 `hPQ : P → Q` と `hP : P` から `Q` が導かれる have hQ : Q := by exact hPQ hP -- 仮定 `hQR : Q → R` と `hQ : Q` から `R` が導かれる exact hQR hQ 名前を省略して have : P := ... とすると，自動的に this という名前になります．","breadcrumbs":"have: 補題を用意する » have","id":"40","title":"have"},"41":{"body":"補題を示すだけでなく，ある特定の形をした主張を分解するのにも have は使うことができます．","breadcrumbs":"have: 補題を用意する » パターンマッチ","id":"41","title":"パターンマッチ"},"42":{"body":"次のように，P ∧ Q という命題から P と Q を取り出すことができます． example (hPQ: P ∧ Q) : P := by -- `P ∧ Q` という仮定を分解する -- `hQ: Q` は不要なのでアンダースコアに置き換える have ⟨ hP, _ ⟩ := hPQ assumption","breadcrumbs":"have: 補題を用意する » 論理積 ∧","id":"42","title":"論理積 ∧"},"43":{"body":"次のように，∃ x: X, P x という命題から，条件を満たす x を取り出すことができます．x: X と hx: P x がローカルコンテキストに追加されます． -- `x`が偶数のとき`3 * x`も偶数\nexample (x : ℕ) (hx : ∃ y, x = 2 * y) : ∃ z, 3 * x = 2 * z := by -- `hx` で存在が主張されている `y` と， -- `x = 2 * y` という命題を得る have ⟨y, hy⟩ := hx exists 3 * y rw [hy] ring","breadcrumbs":"have: 補題を用意する » 存在 ∃","id":"43","title":"存在 ∃"},"44":{"body":"induction は，帰納法のためのタクティクです． 自然数を例に説明します．Lean では自然数は次のように帰納的に定義されています. inductive Nat | zero : Nat | succ (n : Nat) : Nat succ は後者関数と呼ばれる関数で，n + 1 := succ n です． n : Nat についてゴール P n ⊢ Q n があったとします．このとき induction n を行うと，コンストラクタ zero と succ のそれぞれに対して，対応するゴールを生成します．つまり P 0 ⊢ Q 0 (P (succ a)) (P a → Q a) ⊢ Q (succ a) の２つのゴールです． -- 階乗関数\ndef fac : Nat → Nat | 0 => 1 | n + 1 => (n + 1) * fac n example (n : Nat) : 0 < fac n := by -- `n` についての帰納法で示す induction n with | zero => -- `fac` の定義から従う simp [fac] | succ n ih => -- `fac` の定義から従う simp [fac] positivity","breadcrumbs":"induction: 帰納法 » induction","id":"44","title":"induction"},"45":{"body":"needs: import Mathlib.Tactic.Cases induction' というタクティクもあります．こちらは箇条書きによる，より簡潔な書き方が可能です． example (n : Nat) : 0 < fac n := by -- `ih` は帰納法の仮定 -- `k` は `ih` に登場する変数 induction' n with k ih · simp [fac] · simp [fac] positivity","breadcrumbs":"induction: 帰納法 » induction'","id":"45","title":"induction'"},"46":{"body":"また，induction' では「リストの長さに対する帰納法」のようなより複雑な帰納法を行うことができます． example (l : List α) (P : List α → Prop) : P l := by -- リストの長さに対する帰納法 induction' h : l.length generalizing l case zero => -- リストの長さが 0 のとき guard_hyp h: List.length l = 0 show P l sorry case succ n IH => -- リストの長さが `n + 1` のとき guard_hyp h: List.length l = n + 1 -- 帰納法の仮定が使える guard_hyp IH: ∀ (l : List α), List.length l = n → P l show P l sorry","breadcrumbs":"induction: 帰納法 » 一般の～についての帰納法","id":"46","title":"一般の～についての帰納法"},"47":{"body":"時には，より強い帰納法が必要なこともあります．強い帰納法とは，たとえば P(0) を示す (∀ k < n, P (k)) → P (n) を示す したがって ∀ n, P (n) である という形式で表されるような帰納法のことです．これは超限帰納法の特別な場合です．これを使用するには，Nat.strong_induction_on を使って次のようにします． variable (P : Nat → Prop) example (n : Nat) : P n := by -- `n` についての強い帰納法で示す induction' n using Nat.strong_induction_on with n ih -- 仮定が追加される guard_hyp ih : ∀ (m : ℕ), m < n → P m match n with | 0 => sorry | k + 1 => sorry","breadcrumbs":"induction: 帰納法 » 強い帰納法","id":"47","title":"強い帰納法"},"48":{"body":"named after: 導入(introduce) intro は数学で慣習的に行われる P → Q を示すときに最初に P を仮定する ∀ x ∈ A, P(x) を示すときに最初に x ∈ A が与えられたと仮定する といった導入を実行します． 具体的には，intro は ゴールが ⊢ P → Q という形であるときに P をローカルコンテキストに追加して，ゴールを ⊢ Q に変える ゴールが ⊢ ∀ x, P x という形であるときに x をローカルコンテキストに追加してゴールを ⊢ P x に変える といった挙動をします． example (hPQ: P → Q) (hQR: Q → R) : P → R := by -- 示したいことが `P → R` なので，`P` だと仮定する intro hP -- `R` を示したい show R -- 仮定 `hPQ : P → Q` と `hP : P` から `Q` が導かれる have hQ : Q := hPQ hP -- 仮定 `hQR : Q → R` と `hQ : Q` から `R` が導かれる exact hQR hQ もう一つ使用例を挙げておきます： example (P Q : Nat → Prop) (h : ∀ n, P n ↔ Q n) : ∀ y, P (y + 1) → Q (y + 1) := by -- 任意の `y` について示すので，`intro` で `y` を導入する -- そして `P (y + 1) → Q(y + 1)` を示したいので，`P (y + 1)` を仮定する intro y hyP -- `Q (y + 1)` を示せば良い show Q (y + 1) -- 同値を使ってゴールを書き換える rw [← h] -- 仮定 `P (y + 1)` より従う assumption","breadcrumbs":"intro: 含意→や全称∀を示す » intro","id":"48","title":"intro"},"49":{"body":"Lean では否定 ¬ P は P → False として定義されているので，ゴールが ¬ P のときに intro すると P が仮定に追加されて，ゴールが False に変わります． False は矛盾を導けば証明できます． example (h: P → Q) : ¬Q → ¬P := by -- 示したいことが `¬Q → ¬P` なので，`¬Q` だと仮定する -- そうするとゴールが `¬P` になるので， -- さらに `intro` を行って仮定 `hP : P` を導入する intro hnQ hP -- 矛盾を示したい show False -- `hP : P` と `h : P → Q` から `Q` が導かれる have hQ : Q := h hP -- `hQ : Q` と `hnQ : ¬Q` から矛盾が導かれる contradiction","breadcrumbs":"intro: 含意→や全称∀を示す » 否定 ¬ について","id":"49","title":"否定 ¬ について"},"5":{"body":"needs: import Mathlib.Tactic.SolveByElim apply_assumption は，ゴールが ⊢ head であるときに，... → ∀ _, ... → head という形の命題をローカルコンテキストから探し，それを用いてゴールを書き換えます． example (hPQ : P → Q) : ¬ Q → ¬ P := by intro hQn hP -- 矛盾を示したい show False -- 自動で `hQn` を適用 apply_assumption show Q -- 自動で `hPQ` を適用 apply_assumption show P -- 自動で `hP` を適用 apply_assumption done タクティクを繰り返すことを指示するタクティク repeat と組み合わせると，「ローカルコンテキストにある仮定を適切に選んで apply, exact することを繰り返し，ゴールを閉じる」ことができます． example (hPQ : P → Q) (hQR : Q → R) (hQ : P) : R := by repeat apply_assumption","breadcrumbs":"apply_assumption: 仮定から後方推論 » apply_assumption","id":"5","title":"apply_assumption"},"50":{"body":"needs: import Mathlib.Tactic.LeftRight ゴールが ⊢ P ∨ Q であるとき，left はゴールを ⊢ P に，right はゴールを ⊢ Q に変えます． example (hP: P) : P ∨ Q := by left assumption left, right を使わずに Mathlib4 なしで同じことをするには，Or.inl または Or.inr を使用します． example (hP: P) : P ∨ Q := by apply Or.inl assumption","breadcrumbs":"left, right: 論理和∨を示す » left, right","id":"50","title":"left, right"},"51":{"body":"needs: import Mathlib.Tactic.Linarith named after: 線形算術(linear arithmetic) linarith は線形な(不)等式を導くことができます． example (h1 : 2 * x < 3 * y) (h2 : -4 * x + 2 * z < 0): 12 * y - 4 * z ≥ 0 := by linarith linarith はローカルコンテキストを読み取ってくれるので，linarith が通らないとき補題を追加してあげると通るようになることがあります． example : id x ≤ x := by -- `linarith` で示すことはできない try linarith have : id x = x := rfl -- `id x = x` だと教えてあげると `linarith` で示せる linarith","breadcrumbs":"linarith: 線形(不)等式を示す » linarith","id":"51","title":"linarith"},"52":{"body":"もう少し詳細に書くと，linarith は「ロールコンテキストにある線形な(不)等式系に矛盾があるか調べる」タクティクなので，次のような使い方もできます． example (h1: x = 2 * y) (h2 : - x + 2 * y = 1) : False := by linarith","breadcrumbs":"linarith: 線形(不)等式を示す » 補足","id":"52","title":"補足"},"53":{"body":"needs: import Mathlib.Tactic.Linarith named after: non-linear(非線形) arithmetic(算術) nlinarith は非線形な式も扱えるように linarith にいくつか前処理を追加したものです． example (a b: Nat) (h : a ≤ b) : a ^ 2 ≤ b ^ 2 := by -- `linarith` では示すことができない try linarith nlinarith","breadcrumbs":"nlinarith: 非線形な(不)等式を示す » nlinarith","id":"53","title":"nlinarith"},"54":{"body":"needs: import Mathlib.Tactic.PushNeg named after: 押し込む(push) 否定(negation) push_neg はドモルガン則を使って，否定を式の中に押し込みます．たとえば ¬ (P ∧ Q) は P → ¬ Q に， ¬ ∀ x, P x は ∃ x, ¬ P x に という調子で変形します． [1] example (h: P → Q) : ¬ (P ∧ ¬ Q) := by -- ドモルガン則を適用して，`¬` を内側に押し込む push_neg -- `¬` を内側に押し込んだ結果，`¬ P ∨ Q` が得られる -- これは `P → Q` と同値 show P → Q exact h example : ¬ ∃ x : Int , ∀ y : Int, (x + y = 0) := by -- ドモルガン則を適用して，`¬` を内側に押し込む push_neg -- `¬` を内側に押し込んだ結果，ゴールが変わる show ∀ x, ∃ y, ¬ (x + y = 0) intro x exists (- x + 1) linarith [1] モードによって ¬ (P ∧ Q) を P → ¬ Q としたり，¬ P ∨ ¬ Q としたりします．","breadcrumbs":"push_neg: ドモルガン » push_neg","id":"54","title":"push_neg"},"55":{"body":"refine は exact と同様に機能しますが，プレースホルダを受け入れて新しいゴールを生成するという違いがあります． example (hP: P) (hQ: Q) : P ∧ Q := by -- 穴埋め形式で証明を作ることができる refine ⟨?_, hQ⟩ -- ゴールが `⊢ P` になる show P exact hP","breadcrumbs":"refine: 一般の後方推論 » refine","id":"55","title":"refine"},"56":{"body":"h : P → Q という命題があって，ゴールが ⊢ Q であるとき refine h ?_ は apply h と同様に機能するので，refine で apply を代用することができます． example (hPQ : P → Q) (hP : P) : Q := by refine hPQ ?_ -- ゴールが `⊢ P` になる show P refine hP","breadcrumbs":"refine: 一般の後方推論 » apply との関連","id":"56","title":"apply との関連"},"57":{"body":"refine は constructor の代わりに使うこともできます．実際 refine は constructor よりも柔軟で，⊢ P ∧ Q ∧ R のような形のゴールは constructor よりも簡潔に分割できます． example (hP: P) (hQ: Q) (hR : R) : P ∧ Q ∧ R := by -- ゴールを３つに分割する refine ⟨?_, ?_, ?_⟩ · show P exact hP · show Q exact hQ · show R exact hR -- `constructor` を使った場合\n-- 一度に２つのゴールに分割することしかできない\nexample (hP: P) (hQ: Q) (hR : R) : P ∧ Q ∧ R := by constructor · show P exact hP · show Q ∧ R constructor · show Q exact hQ · show R exact hR","breadcrumbs":"refine: 一般の後方推論 » constructor との関連","id":"57","title":"constructor との関連"},"58":{"body":"needs: import Mathlib.Tactic.GCongr named after: 関係(relation) rel は，不等式を代入して適用し，不等式を示します． example (h1 : a ≤ b) (h2 : c ≤ d) : a + c ≤ b + d := by rel [h1, h2] rel は，たとえば整数 x: Int に対して 0 ≤ x ^ 2 であることを自動的に適用するなど, 多少の推論を行います． example (x: Int) (h1 : a ≤ b) : x ^ 2 * a ≤ x ^ 2 * b := by rel [h1]","breadcrumbs":"rel: 不等式を使う » rel","id":"58","title":"rel"},"59":{"body":"needs: import Std.Tactic.Replace replace は have と同じく補題を入手するためのタクティクですが，have とは異なりローカルコンテキストにすでにある命題を置き換えることができます． have を使った場合，ローカルコンテキストにすでに h : P がある状態で，再び h という名前で別の命題を示すと，古い方の h はアクセス不能になって † が付いた状態になってしまいます． replace であれば，古い方が新しい方に置き換えられ，† の付いた命題は出現しません． example : ∀ (n : Int), Even (5 * n) → Even n := by intro n hn -- `Even (5 * n)` という仮定を分解 obtain ⟨ k, hk ⟩ := hn -- 以下がローカルコンテキストに追加される guard_hyp hk: 5 * n = k + k -- `k + k` という形が使いづらいので，`2 * k` に置き換える replace hk : 5 * n = 2 * k := by rw [hk] ring -- `hk` の内容が変化している guard_hyp hk: 5 * n = 2 * k -- 計算をする have := by calc n _ = 5 * n - 4 * n := by ring _ = 2 * k - 4 * n := by rw [hk] _ = 2 * (k - 2 * n) := by ring exists k - 2 * n nth_rewrite 1 [this] ring","breadcrumbs":"replace: 補題の入れ替え » replace","id":"59","title":"replace"},"6":{"body":"apply は含意 → をゴールに適用するタクティクです． ゴールが ⊢ Q で，ローカルコンテキストに h: P → Q があるときに，apply h を実行するとゴールが ⊢ P に書き換わります． -- `P → Q` かつ `P` ならば `Q`\nexample (h: P → Q) (hP: P) : Q := by apply h -- ゴールが `P` に変わっている show P exact hP 注意点として，h: P → Q は P の証明を受け取って Q の証明を返す関数でもあるので，上記の例は apply を使わずに exact h hP で閉じることもできます． -- `P → Q` かつ `P` ならば `Q`\nexample (h: P → Q) (hP: P) : Q := by exact h hP","breadcrumbs":"apply: 含意→を使う » apply","id":"6","title":"apply"},"60":{"body":"needs: import Mathlib.Tactic.Relation.Rfl named after: 反射律(reflexivity) rfl は，refl attribute の付けられた定理を用いて関係の反射性を示すタクティクです． inductive MyEq {α : Type u} : α → α → Prop | refl (a : α) : MyEq a a attribute [refl] MyEq.refl example (n : ℕ) : MyEq n n := by rfl @[refl] で登録された定理を用いるので，追加でライブラリを import することにより示すことができる命題が増えます． -- `import Mathlib.Data.Nat.Basic` が必要\nexample (n : Nat) : n ≤ n := by rfl","breadcrumbs":"rfl: 関係の反射性を示す » rfl","id":"60","title":"rfl"},"61":{"body":"実は Mathlib.Tactic.Relation.Rfl を import するかどうかにより，内部で呼び出されるタクティクが変わります． Mathlib.Tactic.Relation.Rfl ありなら Lean.MVarId.rfl が， なしなら Lean.MVarId.refl が それぞれ参照されます．後者は @[refl] が付けられた一般の関係の反射性にアクセスできず，等号 = の反射性しか使うことができません． 後者の場合 rfl は，単に定義から等しいものが等しいことを示すタクティクになります． variable (α : Type) example : 1 + 1 = 2 := by rfl example (x : α) : x = x := by rfl example : (2 ^ 70 + 3 ^ 70) % 13 = 0 := by rfl","breadcrumbs":"rfl: 関係の反射性を示す » 補足","id":"61","title":"補足"},"62":{"body":"needs: import Mathlib.Tactic.Ring ring は，可換環の等式を示します． example : (x + y) ^ 2 = x ^ 2 + 2 * x * y + y ^ 2 := by ring simp 等と異なり，ring? タクティクは用意されていませんが，show_term で具体的にどんなルールが適用されたのかを知ることができます．ただし，その出力結果は非常に長く読みづらいものであることがしばしばです．例えば， example : (x + y) ^ 2 = x ^ 2 + 2 * x * y + y ^ 2 := by show_term ring の出力をここに掲載すると100行を超えてしまいます．","breadcrumbs":"ring: 環の等式を示す » ring","id":"62","title":"ring"},"63":{"body":"rw は rewrite（書き換え）を行うタクティクです．等式や同値をもとに書き換えを行います． hab: a = b や hPQ : P ↔ Q がローカルコンテキストにあるとき， rw [hab] はゴールの中の a をすべて b に置き換え， rw [hPQ] はゴールの中の P をすべて Q に置き換えます． 順番は重要で，b を a に置き換えたいときなどは rw [← hab] のように ← をつけます． h1, h2, ... について続けて置き換えを行いたいときは，rw [h1, h2, ...] のようにします． ゴールではなく，ローカルコンテキストにある h: P を書き換えたいときには at をつけて rw [hPQ] at h とします．すべての箇所で置き換えたいときは rw [hPQ] at * とします． example (a b c d e f : Nat) (h : a * b = c * d) (h' : e = f) : a * (b * e) = c * (d * f) := by rw [h'] -- 結合法則を使う rw [← Nat.mul_assoc] rw [h] -- 結合法則を使う rw [Nat.mul_assoc]","breadcrumbs":"rw: 同値変形 » rw","id":"63","title":"rw"},"64":{"body":"needs: import Mathlib.Tactic.NthRewrite rw はマッチした項をすべて置き換えてしまいます．特定の項だけを書き換えたいとき，nth_rewrite が使用できます．対象の式中に現れる順番を1始まりで指定することで，項を指定します．指定された順番が式中の対象の項の数よりも多い場合はエラーになります． -- `G` は群\nvariable [Group G] example (a b : G) : a * b⁻¹ = 1 ↔ a = b := by -- `one_mul: 1 * b = b` を使って `b` を `1 * b` に書き換える -- `b` は2回出現するが，2番目だけ置き換える nth_rewrite 2 [← one_mul b] -- `mul_inv_eq_iff_eq_mul: a * b⁻¹ = c ↔ a = c * b` を使う exact mul_inv_eq_iff_eq_mul","breadcrumbs":"rw: 同値変形 » nth_rewrite","id":"64","title":"nth_rewrite"},"65":{"body":"needs: import Mathlib.Tactic.Says exact? や apply? は証明を書いている過程で使用することを想定したタクティクです．Try this: という提案をクリックして採用したら，exact? や apply? は提案内容で上書きされて，最終的な証明には残りません． では，証明のある部分が apply? などにより提案された内容であることを明示したい場合はどうしたら良いでしょうか？says タクティクはまさにその問題を解決するタクティクです． example (hPQ : P → Q) (hQR : Q → R) (hRS : R → S) (hP : P) : S := by -- `exact?` は実行されない exact? says exact hRS (hQR (hPQ hP)) また，simp? や aesop? などに対しても使用することができ，やはりドキュメントとして役に立ちます． -- 合成 `g ∘ f` が単射なら，`f` も単射\nexample {f : X → Y} {g : Y → Z} (hgfinj : Injective (g ∘ f)) : Injective f := by rw [Injective] aesop? says intro a₁ a₂ a apply hgfinj simp_all only [comp_apply] より詳細には，検索タクティク X があり，その提案内容が Try this: Y だったとき，X says とすると says は Try this: Y の代わりに Try this: X says Y という提案を infoview 上で出します．それをクリックすると，X says の内容が X says Y で置換されます．そして，X says Y が実行されるときには X は飛ばされます．","breadcrumbs":"says: タクティク提案の痕跡を残す » says","id":"65","title":"says"},"66":{"body":"says.verify : Bool : true にすると，X says Y の Y のところに，実際には提案されていないタクティクを入れたときにエラーになります． says.no_verify_in_CI : Bool : true にすると，CI 環境で X says Y の Y の部分が実際に提案されている内容と一致するかのチェックが走らなくなります．","breadcrumbs":"says: タクティク提案の痕跡を残す » オプション","id":"66","title":"オプション"},"67":{"body":"show P は, ゴールの中に ⊢ P があるときにそれをメインのゴールにします． たとえば，証明中にこれから示すべきことを明示し，コードを読みやすくする目的で使うことができます． example (hP: P) (hQ: Q) : P ∧ Q := by constructor · show P exact hP · show Q exact hQ","breadcrumbs":"show: 示すべきことを宣言 » show","id":"67","title":"show"},"68":{"body":"simp は，ターゲットを決められた規則に基づいて自動で簡約（simplify）するタクティクです．カスタマイズすることが可能で，簡約に使ってほしい命題を登録することができます． universe u v -- 圏の公理\nclass Category (C : Type u) where -- 射 Hom : C → C → Type v -- 射の合成 comp : ∀ {a b c : C}, Hom a b → Hom b c → Hom a c -- 恒等射. `id a` が `a` 上の恒等射を意味する id : ∀ (a : C), Hom a a -- 恒等射の性質 id_comp : ∀ {a b : C} (f : Hom a b), comp (id a) f = f comp_id : ∀ {a b : C} (f : Hom a b), comp f (id b) = f -- 射の結合律 assoc : ∀ {a b c d : C} (f : Hom a b) (g : Hom b c) (h : Hom c d), comp (comp f g) h = comp f (comp g h) -- `f : Hom a b`と`g : Hom b c`の合成を`f ≫ g`と書く\ninfixr:80 \" ≫ \" => Category.comp -- `Category.hoge` ではなく `hoge` で呼び出せるようにする\nopen Category -- 公理の等式が `simp` で使えるようにする\nattribute [simp] id_comp comp_id assoc -- 変数の定義\nvariable {C : Type u} [Category.{u, v} C] {a b c d e : C} example (f : Hom a b) (g : Hom b c) (h : Hom c d) (i : Hom d e) : (f ≫ (id b ≫ g)) ≫ (h ≫ i) = f ≫ (g ≫ ((id c ≫ h) ≫ i)) := by -- 上で `simp` で使えるようにした等式を使って自動で簡約する simp 既知の h: P という証明を使って簡約させたいときは，明示的に simp [h] と指定することで可能です． 何も指定しなければゴールを簡約しますが，ローカルコンテキストにある h: P を簡約させたければ simp at h と指定することで可能です．","breadcrumbs":"simp: 簡約 » simp","id":"68","title":"simp"},"69":{"body":"simp は自動的に証明を行ってくれますが，何が使われたのか知りたいときもあります．simp? は簡約に何が使われたのかを示してくれるので，rw などを用いて明示的に書き直すことができます．","breadcrumbs":"simp: 簡約 » simp?","id":"69","title":"simp?"},"7":{"body":"また，Lean では否定 ¬ P は P → False として実装されているため，ゴールが ⊢ False であるときに hn: ¬P に対して apply hn とするとゴールが ⊢ P に書き換わります． -- 矛盾\nexample (hn: ¬ P) (hP: P) : False := by -- ゴールが `P` に変わる apply hn exact hP","breadcrumbs":"apply: 含意→を使う » 否定 ¬ について","id":"7","title":"否定 ¬ について"},"70":{"body":"simp_all は simp [*] at * の強化版で，ローカルコンテキストとゴールをこれ以上簡約できなくなるまですべて簡約します．","breadcrumbs":"simp: 簡約 » simp_all","id":"70","title":"simp_all"},"71":{"body":"dsimp は，定義上(definitionally)等しいもの同士しか簡約しないという制約付きの simp です．","breadcrumbs":"simp: 簡約 » dsimp","id":"71","title":"dsimp"},"72":{"body":"証明の細部を埋める前にコンパイルが通るようにしたいとき，証明で埋めるべき箇所に sorry と書くとコンパイルが通るようになります．ただし，sorry を使用しているという旨の警告が出ます． -- Fermat の最終定理\ndef FermatLastTheorem := ∀ x y z n : Nat, n > 2 ∧ x * y * z ≠ 0 → x ^ n + y ^ n ≠ z ^ n theorem flt : FermatLastTheorem := sorry","breadcrumbs":"sorry: 証明したことにする » sorry","id":"72","title":"sorry"},"73":{"body":"ゴールにある if ... then ... else 式を扱うのに有用なタクティクです． if 式を扱う必要が生じるのは，典型的には Lean で定義したアルゴリズムや関数に関して，何か性質を証明しようとしたときです． ゴールが ⊢ Q (if P then a else b) であったときに，split を使用すると2つのサブゴールが生成されます．具体的には 1つはローカルコンテキストに † : P が追加され，ゴールが ⊢ Q (a) 1つはローカルコンテキストに † : ¬ P が追加され，ゴールが ⊢ Q (b) というサブゴールです．split によって追加される仮定は名前がついているとは限りません．名前がついていなかった場合，case などで名前を付けることができます． -- if 式を使って関数を定義する\ndef myabs (x : Int) : Int := if x ≥ 0 then x else - x example (x : Int) : myabs (2 * x) = 2 * myabs x := by -- `myabs` の定義を展開する unfold myabs -- ゴールの中に if 式があって複雑 show (if 2 * x ≥ 0 then 2 * x else -(2 * x)) = 2 * if x ≥ 0 then x else -x -- `split` タクティクでケース分割する split case inl h => -- `2 * x ≥ 0` の場合 guard_hyp h: 2 * x ≥ 0 -- 左辺にあった if 式が消えた show 2 * x = 2 * if x ≥ 0 then x else -x replace h : x ≥ 0 := by linarith [h] -- `simp` で if を消すことができる simp? [h] says simp only [ge_iff_le, h, ite_true] case inr h => -- `2 * x < 0` の場合 guard_hyp h: ¬2 * x ≥ 0 -- 左辺にあった if 式が消えた show -(2 * x) = 2 * if x ≥ 0 then x else -x -- if 式を消すための補題を準備する have hx : ¬ x ≥ 0 := by linarith [h] -- `simp` で簡約 simp? [h, hx] says simp only [ge_iff_le, hx, ite_false, mul_neg]","breadcrumbs":"split: if 式を含む命題を示す » split","id":"73","title":"split"},"74":{"body":"suffices は，数学でよくある「～を示せば十分である」という推論を行うタクティクです． ゴールが ⊢ P であるときに suffices Q from を実行すると， suffices Q from のブロック内では，仮定に this: Q が追加され， suffices Q from 以降では，ゴールが ⊢ Q に書き換えられます． apply と似ていますが，apply と違って「十分条件になっていること」の証明が明らかでないときにも使うことができます． example : 13 ∣ (2 ^ 70 + 3 ^ 70) := by -- 余りがゼロであることを示せば十分 suffices (2 ^ 70 + 3 ^ 70) % 13 = 0 from by exact Iff.mpr (Nat.dvd_iff_div_mul_eq (2 ^ 70 + 3 ^ 70) 13) rfl rfl suffices Q from ... という形式の場合は，証明を直接構成することが必要です．suffices Q from by ... とすると，タクティクによって証明を構成するモードになります．","breadcrumbs":"suffices: 十分条件に帰着 » suffices","id":"74","title":"suffices"},"75":{"body":"needs: import Mathlib.Tactic.Tauto named after: トートロジー(tautology) tauto は， トートロジー(恒真式)であることに基づいてゴールを閉じるタクティクです． ゴールを閉じることができなければエラーになります． -- 含意の導入\nexample (h : P) : Q → P := by tauto -- フレーゲの3段論法\nexample : (P → (Q → R)) → ((P → Q) → (P → R)) := by tauto -- 排中律\nexample : P ∨ ¬ P := by -- `aesop` では示すことができない try aesop tauto -- 対偶\nexample (h : P → Q) : ¬ Q → ¬ P := by -- `exact?` では示すことができない try exact? tauto","breadcrumbs":"tauto: トートロジーを示す » tauto","id":"75","title":"tauto"},"76":{"body":"trivial は明らかなことを示します． trivial は，rfl や contradiction などのタクティクを実行して，現在のゴールを閉じようとします． -- 定義から明らかな等式\nexample : 1 + 1 = 2 := by trivial -- 矛盾があるので, どんな命題でも証明できる\nexample (h: False) : P := by trivial 普段の数学でいう「自明」な命題は trivial では示せないことがほとんどだと思います． aesop を試してみてください．","breadcrumbs":"trivial: 自明 » trivial","id":"76","title":"trivial"},"77":{"body":"needs: import Mathlib.Tactic.WLOG named after: 一般性を失わずに(without loss of generarity) wlog は，数学でよく使われる「一般性を失うことなく～と仮定してよい」というフレーズの Lean での対応物です． example (a b : Nat) : a + b = b + a := by -- `a ≤ b` だと仮定しても一般性を失わない wlog h : a ≤ b with H -- `a ≤ b` なら成り立つと仮定して，そうでないときにも成り立つことを示す · show a + b = b + a guard_hyp H : ∀ (a b : Nat), a ≤ b → a + b = b + a guard_hyp h : ¬a ≤ b abel -- `a ≤ b` であるときに成り立つことを示す · show a + b = b + a guard_hyp h: a ≤ b abel","breadcrumbs":"wlog: 一般性を失わずに特殊化 » wlog","id":"77","title":"wlog"},"8":{"body":"apply には引数が必須なのですが，省略しても近くにエラーが出ません．一般に，構文的に間違った証明を書いた場合には，エラーがわかりやすい場所に出てくれる保証はありません．","breadcrumbs":"apply: 含意→を使う » よくあるエラー","id":"8","title":"よくあるエラー"},"9":{"body":"exact の代わりに apply を使うことができます． -- `P → Q` かつ `P` ならば `Q`\nexample (h: P → Q) (hP: P) : Q := by apply h apply hP","breadcrumbs":"apply: 含意→を使う » exact との関連","id":"9","title":"exact との関連"}},"length":78,"save":true},"fields":["title","body","breadcrumbs"],"index":{"body":{"root":{"0":{"df":15,"docs":{"12":{"tf":1.0},"26":{"tf":1.4142135623730951},"28":{"tf":1.7320508075688772},"31":{"tf":1.4142135623730951},"44":{"tf":2.0},"45":{"tf":1.0},"46":{"tf":1.4142135623730951},"47":{"tf":1.0},"51":{"tf":1.4142135623730951},"54":{"tf":1.4142135623730951},"58":{"tf":1.0},"61":{"tf":1.0},"72":{"tf":1.0},"73":{"tf":3.3166247903554},"74":{"tf":1.0}}},"1":{"0":{"0":{"df":1,"docs":{"62":{"tf":1.0}}},"df":0,"docs":{}},"2":{"df":1,"docs":{"51":{"tf":1.0}}},"3":{"df":2,"docs":{"61":{"tf":1.0},"74":{"tf":1.7320508075688772}}},"df":16,"docs":{"12":{"tf":1.7320508075688772},"26":{"tf":1.0},"28":{"tf":2.449489742783178},"35":{"tf":1.0},"36":{"tf":1.0},"44":{"tf":2.0},"46":{"tf":1.4142135623730951},"47":{"tf":1.0},"48":{"tf":2.8284271247461903},"52":{"tf":1.0},"54":{"tf":1.7320508075688772},"59":{"tf":1.0},"61":{"tf":1.4142135623730951},"64":{"tf":1.7320508075688772},"73":{"tf":1.4142135623730951},"76":{"tf":1.4142135623730951}}},"2":{"df":19,"docs":{"12":{"tf":3.0},"26":{"tf":3.1622776601683795},"29":{"tf":1.4142135623730951},"36":{"tf":1.0},"37":{"tf":1.0},"38":{"tf":1.4142135623730951},"43":{"tf":1.7320508075688772},"51":{"tf":1.4142135623730951},"52":{"tf":1.4142135623730951},"53":{"tf":1.4142135623730951},"58":{"tf":1.7320508075688772},"59":{"tf":2.6457513110645907},"61":{"tf":1.4142135623730951},"62":{"tf":2.8284271247461903},"64":{"tf":1.0},"72":{"tf":1.0},"73":{"tf":3.872983346207417},"74":{"tf":1.7320508075688772},"76":{"tf":1.0}},"回":{"df":0,"docs":{},"出":{"df":0,"docs":{},"現":{"df":0,"docs":{},"す":{"df":0,"docs":{},"る":{"df":0,"docs":{},"が":{"df":0,"docs":{},"，":{"2":{"df":1,"docs":{"64":{"tf":1.0}}},"df":0,"docs":{}}}}}}}}},"3":{"df":8,"docs":{"12":{"tf":1.0},"29":{"tf":1.0},"36":{"tf":1.0},"43":{"tf":1.4142135623730951},"51":{"tf":1.0},"61":{"tf":1.0},"74":{"tf":1.7320508075688772},"75":{"tf":1.0}}},"4":{"df":2,"docs":{"51":{"tf":1.4142135623730951},"59":{"tf":1.4142135623730951}},"│":{"0":{",":{"1":{",":{"2":{",":{"3":{"df":1,"docs":{"12":{"tf":1.0}}},"df":0,"docs":{}},"df":0,"docs":{}},"df":0,"docs":{}},"df":0,"docs":{}},"df":0,"docs":{}},"df":0,"docs":{}},"df":0,"docs":{}}},"5":{"df":1,"docs":{"59":{"tf":2.449489742783178}}},"7":{"0":{"df":2,"docs":{"61":{"tf":1.4142135623730951},"74":{"tf":2.449489742783178}}},"df":1,"docs":{"36":{"tf":1.0}}},"_":{"df":9,"docs":{"12":{"tf":1.0},"13":{"tf":1.0},"26":{"tf":1.0},"42":{"tf":1.0},"5":{"tf":1.0},"55":{"tf":1.0},"56":{"tf":1.4142135623730951},"57":{"tf":1.7320508075688772},"59":{"tf":1.7320508075688772}}},"a":{"b":{"df":0,"docs":{},"e":{"df":0,"docs":{},"l":{"df":1,"docs":{"77":{"tf":1.4142135623730951}}}}},"d":{"d":{"_":{"df":0,"docs":{},"z":{"df":0,"docs":{},"e":{"df":0,"docs":{},"r":{"df":0,"docs":{},"o":{"df":1,"docs":{"26":{"tf":1.4142135623730951}}}}}}},"df":0,"docs":{}},"df":0,"docs":{}},"df":0,"docs":{},"e":{"df":0,"docs":{},"s":{"df":0,"docs":{},"o":{"df":0,"docs":{},"p":{"df":6,"docs":{"3":{"tf":2.0},"37":{"tf":1.0},"4":{"tf":2.0},"65":{"tf":1.4142135623730951},"75":{"tf":1.4142135623730951},"76":{"tf":1.0}}}}}},"p":{"df":0,"docs":{},"p":{"df":0,"docs":{},"l":{"df":0,"docs":{},"i":{"df":16,"docs":{"10":{"tf":1.4142135623730951},"11":{"tf":1.7320508075688772},"12":{"tf":2.0},"22":{"tf":1.4142135623730951},"23":{"tf":1.4142135623730951},"35":{"tf":1.4142135623730951},"4":{"tf":1.0},"5":{"tf":1.0},"50":{"tf":1.0},"56":{"tf":1.7320508075688772},"6":{"tf":2.23606797749979},"65":{"tf":2.0},"7":{"tf":1.4142135623730951},"74":{"tf":1.4142135623730951},"8":{"tf":1.0},"9":{"tf":1.7320508075688772}}},"y":{"_":{"a":{"df":0,"docs":{},"s":{"df":0,"docs":{},"s":{"df":0,"docs":{},"u":{"df":0,"docs":{},"m":{"df":0,"docs":{},"p":{"df":0,"docs":{},"t":{"df":2,"docs":{"10":{"tf":1.4142135623730951},"5":{"tf":2.449489742783178}}}}}}}}},"df":0,"docs":{}},"df":0,"docs":{}}}}},"r":{"df":0,"docs":{},"i":{"df":0,"docs":{},"t":{"df":0,"docs":{},"h":{"df":0,"docs":{},"m":{"df":0,"docs":{},"e":{"df":0,"docs":{},"t":{"df":2,"docs":{"51":{"tf":1.0},"53":{"tf":1.0}}}}}}}}},"s":{"df":0,"docs":{},"s":{"df":0,"docs":{},"o":{"c":{"df":1,"docs":{"68":{"tf":1.4142135623730951}}},"df":0,"docs":{}},"u":{"df":0,"docs":{},"m":{"df":0,"docs":{},"p":{"df":0,"docs":{},"t":{"df":7,"docs":{"13":{"tf":1.7320508075688772},"14":{"tf":1.0},"15":{"tf":1.0},"34":{"tf":1.4142135623730951},"42":{"tf":1.0},"48":{"tf":1.0},"50":{"tf":1.4142135623730951}}}}}}}},"t":{"df":0,"docs":{},"t":{"df":0,"docs":{},"r":{"df":0,"docs":{},"i":{"b":{"df":0,"docs":{},"u":{"df":0,"docs":{},"t":{"df":2,"docs":{"60":{"tf":1.4142135623730951},"68":{"tf":1.0}}}}},"df":0,"docs":{}}}}}},"b":{"`":{"df":0,"docs":{},"と":{"`":{"df":0,"docs":{},"g":{"df":1,"docs":{"68":{"tf":1.0}}}},"df":0,"docs":{}}},"df":10,"docs":{"11":{"tf":2.0},"31":{"tf":2.0},"37":{"tf":2.449489742783178},"53":{"tf":1.7320508075688772},"58":{"tf":2.0},"63":{"tf":2.449489742783178},"64":{"tf":3.3166247903554},"68":{"tf":4.0},"73":{"tf":1.4142135623730951},"77":{"tf":4.123105625617661}},"o":{"df":0,"docs":{},"o":{"df":0,"docs":{},"l":{"df":1,"docs":{"66":{"tf":1.4142135623730951}}}}},"s":{"df":1,"docs":{"26":{"tf":1.7320508075688772}}},"y":{"_":{"c":{"a":{"df":0,"docs":{},"s":{"df":1,"docs":{"15":{"tf":2.0}}}},"df":0,"docs":{},"o":{"df":0,"docs":{},"n":{"df":0,"docs":{},"t":{"df":0,"docs":{},"r":{"a":{"df":1,"docs":{"16":{"tf":2.0}}},"df":0,"docs":{}}}}}},"df":0,"docs":{}},"df":0,"docs":{}}},"c":{"`":{"df":0,"docs":{},"の":{"df":0,"docs":{},"合":{"df":0,"docs":{},"成":{"df":0,"docs":{},"を":{"`":{"df":0,"docs":{},"f":{"df":1,"docs":{"68":{"tf":1.0}}}},"df":0,"docs":{}}}}}},"a":{"df":0,"docs":{},"l":{"c":{"df":2,"docs":{"19":{"tf":1.4142135623730951},"59":{"tf":1.0}}},"df":0,"docs":{}},"s":{"df":0,"docs":{},"e":{"df":7,"docs":{"15":{"tf":1.4142135623730951},"20":{"tf":2.8284271247461903},"21":{"tf":2.449489742783178},"22":{"tf":1.7320508075688772},"23":{"tf":1.4142135623730951},"46":{"tf":1.4142135623730951},"73":{"tf":1.4142135623730951}}}},"t":{"df":0,"docs":{},"e":{"df":0,"docs":{},"g":{"df":0,"docs":{},"o":{"df":0,"docs":{},"r":{"df":0,"docs":{},"i":{"df":1,"docs":{"68":{"tf":1.4142135623730951}}},"y":{".":{"c":{"df":0,"docs":{},"o":{"df":0,"docs":{},"m":{"df":0,"docs":{},"p":{"df":1,"docs":{"68":{"tf":1.0}}}}}},"df":0,"docs":{},"h":{"df":0,"docs":{},"o":{"df":0,"docs":{},"g":{"df":1,"docs":{"68":{"tf":1.0}}}}},"{":{"df":0,"docs":{},"u":{"df":1,"docs":{"68":{"tf":1.0}}}}},"df":0,"docs":{}}}}}}}},"df":5,"docs":{"31":{"tf":2.0},"58":{"tf":1.4142135623730951},"63":{"tf":1.7320508075688772},"64":{"tf":1.4142135623730951},"68":{"tf":4.58257569495584}},"h":{"df":0,"docs":{},"o":{"df":0,"docs":{},"o":{"df":0,"docs":{},"s":{"df":2,"docs":{"24":{"tf":1.7320508075688772},"25":{"tf":1.0}}}}}},"i":{"df":1,"docs":{"66":{"tf":1.0}}},"l":{"a":{"df":0,"docs":{},"s":{"df":0,"docs":{},"s":{"df":1,"docs":{"68":{"tf":1.0}},"i":{"c":{"a":{"df":0,"docs":{},"l":{".":{"c":{"df":0,"docs":{},"h":{"df":0,"docs":{},"o":{"df":0,"docs":{},"i":{"c":{"df":1,"docs":{"25":{"tf":1.4142135623730951}}},"df":0,"docs":{}}}}},"df":0,"docs":{}},"df":0,"docs":{}}},"df":0,"docs":{}},"df":0,"docs":{}}}}},"df":0,"docs":{}},"o":{"df":0,"docs":{},"m":{"df":0,"docs":{},"p":{"_":{"a":{"df":0,"docs":{},"p":{"df":0,"docs":{},"p":{"df":0,"docs":{},"l":{"df":0,"docs":{},"i":{"df":2,"docs":{"4":{"tf":1.0},"65":{"tf":1.0}}}}}}},"df":0,"docs":{},"i":{"d":{"df":1,"docs":{"68":{"tf":1.4142135623730951}}},"df":0,"docs":{}}},"df":1,"docs":{"68":{"tf":2.6457513110645907}}}},"n":{"df":0,"docs":{},"g":{"df":0,"docs":{},"r":{"df":1,"docs":{"26":{"tf":2.6457513110645907}},"u":{"df":0,"docs":{},"e":{"df":0,"docs":{},"n":{"c":{"df":1,"docs":{"26":{"tf":1.0}}},"df":0,"docs":{}}}}}},"s":{"df":0,"docs":{},"t":{"df":0,"docs":{},"r":{"df":0,"docs":{},"u":{"c":{"df":0,"docs":{},"t":{"df":0,"docs":{},"o":{"df":0,"docs":{},"r":{"df":4,"docs":{"27":{"tf":1.7320508075688772},"28":{"tf":1.4142135623730951},"57":{"tf":2.6457513110645907},"67":{"tf":1.0}}}}}},"df":0,"docs":{}}}}},"t":{"df":0,"docs":{},"r":{"a":{"d":{"df":0,"docs":{},"i":{"c":{"df":0,"docs":{},"t":{"df":5,"docs":{"15":{"tf":1.0},"16":{"tf":1.0},"29":{"tf":2.23606797749979},"49":{"tf":1.0},"76":{"tf":1.0}}}},"df":0,"docs":{}}},"df":0,"docs":{}},"df":0,"docs":{}}},"v":{"df":1,"docs":{"30":{"tf":1.4142135623730951}},"e":{"df":0,"docs":{},"r":{"df":0,"docs":{},"t":{"df":1,"docs":{"31":{"tf":1.7320508075688772}}}}}}}}},"d":{"df":3,"docs":{"58":{"tf":1.4142135623730951},"63":{"tf":1.7320508075688772},"68":{"tf":2.23606797749979}},"e":{"df":0,"docs":{},"f":{"df":4,"docs":{"38":{"tf":1.4142135623730951},"44":{"tf":1.0},"72":{"tf":1.0},"73":{"tf":1.0}}}},"o":{"df":0,"docs":{},"n":{"df":0,"docs":{},"e":{"df":4,"docs":{"12":{"tf":1.4142135623730951},"32":{"tf":1.4142135623730951},"35":{"tf":1.0},"5":{"tf":1.0}}}}},"s":{"df":0,"docs":{},"i":{"df":0,"docs":{},"m":{"df":0,"docs":{},"p":{"df":2,"docs":{"38":{"tf":1.0},"71":{"tf":1.4142135623730951}}}}}}},"df":0,"docs":{},"e":{"df":2,"docs":{"63":{"tf":1.7320508075688772},"68":{"tf":1.4142135623730951}},"v":{"df":0,"docs":{},"e":{"df":0,"docs":{},"n":{"df":1,"docs":{"59":{"tf":1.7320508075688772}}}}},"x":{"a":{"c":{"df":0,"docs":{},"t":{"df":30,"docs":{"11":{"tf":1.0},"14":{"tf":1.4142135623730951},"17":{"tf":1.0},"18":{"tf":1.0},"20":{"tf":1.4142135623730951},"21":{"tf":1.4142135623730951},"23":{"tf":1.0},"24":{"tf":1.0},"25":{"tf":1.0},"26":{"tf":1.0},"27":{"tf":1.7320508075688772},"31":{"tf":1.4142135623730951},"33":{"tf":2.23606797749979},"34":{"tf":1.4142135623730951},"35":{"tf":3.0},"39":{"tf":1.0},"40":{"tf":1.4142135623730951},"48":{"tf":1.0},"5":{"tf":1.0},"54":{"tf":1.0},"55":{"tf":1.4142135623730951},"57":{"tf":2.449489742783178},"6":{"tf":1.7320508075688772},"64":{"tf":1.0},"65":{"tf":2.23606797749979},"67":{"tf":1.4142135623730951},"7":{"tf":1.0},"74":{"tf":1.0},"75":{"tf":1.4142135623730951},"9":{"tf":1.4142135623730951}}}},"df":0,"docs":{},"m":{"df":0,"docs":{},"p":{"df":0,"docs":{},"l":{"df":61,"docs":{"11":{"tf":1.0},"13":{"tf":1.0},"15":{"tf":1.0},"16":{"tf":1.0},"17":{"tf":1.4142135623730951},"18":{"tf":1.0},"20":{"tf":1.0},"21":{"tf":1.0},"22":{"tf":1.0},"23":{"tf":1.4142135623730951},"24":{"tf":1.0},"25":{"tf":1.0},"26":{"tf":1.4142135623730951},"27":{"tf":1.4142135623730951},"28":{"tf":1.0},"29":{"tf":2.0},"3":{"tf":1.0},"31":{"tf":1.0},"33":{"tf":1.4142135623730951},"35":{"tf":1.4142135623730951},"36":{"tf":1.0},"37":{"tf":1.0},"38":{"tf":1.0},"39":{"tf":1.0},"4":{"tf":1.0},"40":{"tf":1.0},"42":{"tf":1.0},"43":{"tf":1.0},"44":{"tf":1.0},"45":{"tf":1.0},"46":{"tf":1.0},"47":{"tf":1.0},"48":{"tf":1.4142135623730951},"49":{"tf":1.0},"5":{"tf":1.4142135623730951},"50":{"tf":1.4142135623730951},"51":{"tf":1.4142135623730951},"52":{"tf":1.0},"53":{"tf":1.0},"54":{"tf":1.4142135623730951},"55":{"tf":1.0},"56":{"tf":1.0},"57":{"tf":1.4142135623730951},"58":{"tf":1.4142135623730951},"59":{"tf":1.0},"6":{"tf":1.4142135623730951},"60":{"tf":1.4142135623730951},"61":{"tf":1.7320508075688772},"62":{"tf":1.4142135623730951},"63":{"tf":1.0},"64":{"tf":1.0},"65":{"tf":1.4142135623730951},"67":{"tf":1.0},"68":{"tf":1.0},"7":{"tf":1.0},"73":{"tf":1.0},"74":{"tf":1.0},"75":{"tf":2.0},"76":{"tf":1.4142135623730951},"77":{"tf":1.0},"9":{"tf":1.0}}}}}},"df":0,"docs":{},"i":{"df":0,"docs":{},"s":{"df":0,"docs":{},"t":{"df":5,"docs":{"25":{"tf":1.0},"36":{"tf":2.0},"43":{"tf":1.0},"54":{"tf":1.0},"59":{"tf":1.0}}}}},"p":{"df":0,"docs":{},"l":{"df":0,"docs":{},"o":{"d":{"df":1,"docs":{"12":{"tf":1.4142135623730951}}},"df":0,"docs":{},"s":{"df":0,"docs":{},"i":{"df":0,"docs":{},"o":{"df":0,"docs":{},"n":{")":{"df":0,"docs":{},"と":{"df":0,"docs":{},"呼":{"df":0,"docs":{},"び":{"df":0,"docs":{},"ま":{"df":0,"docs":{},"す":{"df":0,"docs":{},"が":{"df":0,"docs":{},"，":{"c":{"df":0,"docs":{},"o":{"df":0,"docs":{},"n":{"df":0,"docs":{},"t":{"df":0,"docs":{},"r":{"a":{"d":{"df":0,"docs":{},"i":{"c":{"df":0,"docs":{},"t":{"df":1,"docs":{"29":{"tf":1.0}}}},"df":0,"docs":{}}},"df":0,"docs":{}},"df":0,"docs":{}}}}}},"df":0,"docs":{}}}}}}}}},"df":0,"docs":{}}}}}}}},"t":{"df":1,"docs":{"37":{"tf":2.0}},"e":{"df":0,"docs":{},"n":{"df":0,"docs":{},"s":{"df":0,"docs":{},"i":{"df":0,"docs":{},"o":{"df":0,"docs":{},"n":{"df":1,"docs":{"37":{"tf":1.0}}}}}}}}}}},"f":{"a":{"c":{"df":2,"docs":{"44":{"tf":2.6457513110645907},"45":{"tf":1.7320508075688772}}},"df":0,"docs":{},"l":{"df":0,"docs":{},"s":{"df":7,"docs":{"16":{"tf":1.4142135623730951},"29":{"tf":1.4142135623730951},"49":{"tf":2.0},"5":{"tf":1.0},"52":{"tf":1.0},"7":{"tf":1.7320508075688772},"76":{"tf":1.0}}}}},"df":12,"docs":{"11":{"tf":2.23606797749979},"24":{"tf":2.8284271247461903},"25":{"tf":3.0},"26":{"tf":3.7416573867739413},"3":{"tf":2.23606797749979},"31":{"tf":1.7320508075688772},"37":{"tf":1.7320508075688772},"38":{"tf":2.449489742783178},"4":{"tf":1.7320508075688772},"63":{"tf":1.7320508075688772},"65":{"tf":2.23606797749979},"68":{"tf":3.605551275463989}},"e":{"df":0,"docs":{},"r":{"df":0,"docs":{},"m":{"a":{"df":0,"docs":{},"t":{"df":1,"docs":{"72":{"tf":1.0}},"l":{"a":{"df":0,"docs":{},"s":{"df":0,"docs":{},"t":{"df":0,"docs":{},"t":{"df":0,"docs":{},"h":{"df":0,"docs":{},"e":{"df":0,"docs":{},"o":{"df":0,"docs":{},"r":{"df":0,"docs":{},"e":{"df":0,"docs":{},"m":{"df":1,"docs":{"72":{"tf":1.4142135623730951}}}}}}}}}}}},"df":0,"docs":{}}}},"df":0,"docs":{}}}},"l":{"df":0,"docs":{},"t":{"df":1,"docs":{"72":{"tf":1.0}}}},"u":{"df":0,"docs":{},"n":{"df":4,"docs":{"17":{"tf":1.0},"18":{"tf":1.0},"25":{"tf":1.4142135623730951},"38":{"tf":1.4142135623730951}},"e":{"df":0,"docs":{},"x":{"df":0,"docs":{},"t":{"df":1,"docs":{"38":{"tf":1.7320508075688772}}}}}}}},"g":{"df":10,"docs":{"11":{"tf":1.7320508075688772},"24":{"tf":2.8284271247461903},"26":{"tf":2.23606797749979},"3":{"tf":1.7320508075688772},"37":{"tf":1.7320508075688772},"38":{"tf":2.449489742783178},"4":{"tf":1.4142135623730951},"64":{"tf":1.7320508075688772},"65":{"tf":1.7320508075688772},"68":{"tf":2.6457513110645907}},"e":{"_":{"df":0,"docs":{},"i":{"df":0,"docs":{},"f":{"df":0,"docs":{},"f":{"_":{"df":0,"docs":{},"l":{"df":1,"docs":{"73":{"tf":1.4142135623730951}}}},"df":0,"docs":{}}}}},"df":0,"docs":{},"n":{"df":0,"docs":{},"e":{"df":0,"docs":{},"r":{"a":{"df":0,"docs":{},"r":{"df":1,"docs":{"77":{"tf":1.0}}}},"df":1,"docs":{"46":{"tf":1.0}}}}}},"o":{"a":{"df":0,"docs":{},"l":{"df":1,"docs":{"27":{"tf":1.0}}}},"df":0,"docs":{}},"r":{"df":0,"docs":{},"o":{"df":0,"docs":{},"u":{"df":0,"docs":{},"p":{"df":2,"docs":{"11":{"tf":1.4142135623730951},"64":{"tf":1.0}}}}}},"u":{"a":{"df":0,"docs":{},"r":{"d":{"_":{"df":0,"docs":{},"h":{"df":0,"docs":{},"y":{"df":0,"docs":{},"p":{"df":8,"docs":{"15":{"tf":1.4142135623730951},"24":{"tf":1.4142135623730951},"39":{"tf":1.7320508075688772},"46":{"tf":1.7320508075688772},"47":{"tf":1.0},"59":{"tf":1.4142135623730951},"73":{"tf":1.4142135623730951},"77":{"tf":1.7320508075688772}}}}}},"df":0,"docs":{}},"df":0,"docs":{}}},"df":0,"docs":{}}},"h":{".":{"df":0,"docs":{},"l":{"df":0,"docs":{},"e":{"df":0,"docs":{},"f":{"df":0,"docs":{},"t":{"df":1,"docs":{"27":{"tf":1.4142135623730951}}}}}},"r":{"df":0,"docs":{},"i":{"df":0,"docs":{},"g":{"df":0,"docs":{},"h":{"df":0,"docs":{},"t":{"df":1,"docs":{"27":{"tf":1.0}}}}}}}},"1":{"df":4,"docs":{"51":{"tf":1.0},"52":{"tf":1.0},"58":{"tf":2.0},"63":{"tf":1.4142135623730951}}},"2":{"df":4,"docs":{"51":{"tf":1.0},"52":{"tf":1.0},"58":{"tf":1.4142135623730951},"63":{"tf":1.4142135623730951}}},"a":{"b":{"df":1,"docs":{"63":{"tf":1.7320508075688772}}},"df":0,"docs":{}},"c":{"df":1,"docs":{"31":{"tf":1.4142135623730951}}},"df":31,"docs":{"11":{"tf":1.4142135623730951},"12":{"tf":1.0},"15":{"tf":1.0},"16":{"tf":2.0},"17":{"tf":1.0},"20":{"tf":2.23606797749979},"21":{"tf":1.7320508075688772},"22":{"tf":1.4142135623730951},"23":{"tf":2.449489742783178},"24":{"tf":1.4142135623730951},"25":{"tf":1.7320508075688772},"26":{"tf":2.0},"27":{"tf":1.4142135623730951},"29":{"tf":1.7320508075688772},"31":{"tf":3.0},"40":{"tf":1.4142135623730951},"46":{"tf":1.7320508075688772},"48":{"tf":1.4142135623730951},"49":{"tf":1.7320508075688772},"53":{"tf":1.0},"54":{"tf":1.4142135623730951},"56":{"tf":1.7320508075688772},"59":{"tf":1.7320508075688772},"6":{"tf":2.8284271247461903},"63":{"tf":2.449489742783178},"68":{"tf":3.1622776601683795},"73":{"tf":3.1622776601683795},"75":{"tf":1.4142135623730951},"76":{"tf":1.0},"77":{"tf":2.23606797749979},"9":{"tf":1.4142135623730951}},"e":{"a":{"d":{"df":1,"docs":{"5":{"tf":1.4142135623730951}}},"df":0,"docs":{}},"df":0,"docs":{},"l":{"df":0,"docs":{},"p":{"df":1,"docs":{"1":{"tf":1.0}}}}},"f":{"df":2,"docs":{"24":{"tf":2.0},"26":{"tf":1.4142135623730951}}},"g":{"df":1,"docs":{"24":{"tf":1.7320508075688772}},"f":{"df":0,"docs":{},"i":{"df":0,"docs":{},"n":{"df":0,"docs":{},"j":{"df":3,"docs":{"3":{"tf":1.0},"4":{"tf":1.4142135623730951},"65":{"tf":1.4142135623730951}}}}}}},"k":{"df":1,"docs":{"59":{"tf":2.6457513110645907}}},"n":{"df":2,"docs":{"59":{"tf":1.4142135623730951},"7":{"tf":2.0}},"e":{"_":{"df":0,"docs":{},"s":{"df":0,"docs":{},"t":{"df":1,"docs":{"25":{"tf":1.4142135623730951}}}}},"df":0,"docs":{}},"n":{"df":0,"docs":{},"p":{"df":1,"docs":{"15":{"tf":1.0}}}},"p":{"df":1,"docs":{"29":{"tf":1.0}}},"q":{"df":2,"docs":{"16":{"tf":1.4142135623730951},"49":{"tf":1.4142135623730951}}}},"o":{"df":0,"docs":{},"g":{"df":0,"docs":{},"e":{"df":1,"docs":{"68":{"tf":1.0}}}},"m":{"df":1,"docs":{"68":{"tf":4.0}}}},"p":{"df":27,"docs":{"13":{"tf":1.0},"15":{"tf":1.7320508075688772},"16":{"tf":1.0},"17":{"tf":2.0},"18":{"tf":2.0},"20":{"tf":1.4142135623730951},"21":{"tf":1.4142135623730951},"22":{"tf":1.4142135623730951},"23":{"tf":2.23606797749979},"27":{"tf":1.4142135623730951},"29":{"tf":1.0},"33":{"tf":2.8284271247461903},"39":{"tf":1.7320508075688772},"40":{"tf":1.7320508075688772},"42":{"tf":1.0},"48":{"tf":1.7320508075688772},"49":{"tf":2.0},"5":{"tf":1.4142135623730951},"50":{"tf":1.4142135623730951},"55":{"tf":1.4142135623730951},"56":{"tf":1.4142135623730951},"57":{"tf":2.0},"6":{"tf":2.23606797749979},"65":{"tf":1.4142135623730951},"67":{"tf":1.4142135623730951},"7":{"tf":1.4142135623730951},"9":{"tf":1.4142135623730951}},"q":{"df":10,"docs":{"17":{"tf":2.0},"18":{"tf":1.7320508075688772},"35":{"tf":1.4142135623730951},"40":{"tf":1.7320508075688772},"42":{"tf":1.4142135623730951},"48":{"tf":1.7320508075688772},"5":{"tf":1.7320508075688772},"56":{"tf":1.4142135623730951},"63":{"tf":2.0},"65":{"tf":1.4142135623730951}}},"r":{"df":4,"docs":{"20":{"tf":1.4142135623730951},"21":{"tf":1.4142135623730951},"22":{"tf":1.4142135623730951},"23":{"tf":1.4142135623730951}}}},"q":{"df":15,"docs":{"20":{"tf":1.4142135623730951},"21":{"tf":1.4142135623730951},"22":{"tf":1.4142135623730951},"23":{"tf":2.23606797749979},"27":{"tf":1.4142135623730951},"33":{"tf":1.7320508075688772},"35":{"tf":1.4142135623730951},"40":{"tf":1.7320508075688772},"42":{"tf":1.0},"48":{"tf":1.7320508075688772},"49":{"tf":1.4142135623730951},"5":{"tf":1.0},"55":{"tf":1.4142135623730951},"57":{"tf":2.0},"67":{"tf":1.4142135623730951}},"n":{"df":1,"docs":{"5":{"tf":1.4142135623730951}}},"r":{"df":11,"docs":{"17":{"tf":2.0},"18":{"tf":1.7320508075688772},"20":{"tf":1.4142135623730951},"21":{"tf":1.4142135623730951},"22":{"tf":1.4142135623730951},"23":{"tf":1.4142135623730951},"35":{"tf":1.4142135623730951},"40":{"tf":1.7320508075688772},"48":{"tf":1.7320508075688772},"5":{"tf":1.0},"65":{"tf":1.4142135623730951}}}},"r":{"df":2,"docs":{"57":{"tf":2.0},"65":{"tf":1.4142135623730951}}},"x":{"df":3,"docs":{"28":{"tf":1.4142135623730951},"43":{"tf":2.0},"73":{"tf":1.7320508075688772}}},"y":{"df":1,"docs":{"43":{"tf":1.4142135623730951}},"p":{"df":1,"docs":{"48":{"tf":1.0}}}}},"i":{"d":{"_":{"c":{"df":0,"docs":{},"o":{"df":0,"docs":{},"m":{"df":0,"docs":{},"p":{"df":1,"docs":{"68":{"tf":1.4142135623730951}}}}}},"df":0,"docs":{}},"df":2,"docs":{"51":{"tf":1.7320508075688772},"68":{"tf":2.449489742783178}}},"df":0,"docs":{},"f":{"df":0,"docs":{},"f":{".":{"df":0,"docs":{},"m":{"df":0,"docs":{},"p":{"df":0,"docs":{},"r":{"df":1,"docs":{"74":{"tf":1.0}}}}}},"df":0,"docs":{}}},"h":{"df":4,"docs":{"44":{"tf":1.0},"45":{"tf":1.7320508075688772},"46":{"tf":1.4142135623730951},"47":{"tf":1.4142135623730951}}},"m":{"df":0,"docs":{},"p":{"df":0,"docs":{},"o":{"df":0,"docs":{},"r":{"df":0,"docs":{},"t":{"df":26,"docs":{"11":{"tf":1.0},"16":{"tf":1.0},"18":{"tf":1.0},"22":{"tf":1.0},"23":{"tf":1.0},"24":{"tf":1.0},"3":{"tf":1.0},"31":{"tf":1.0},"35":{"tf":1.0},"37":{"tf":1.0},"39":{"tf":1.0},"45":{"tf":1.0},"5":{"tf":1.0},"50":{"tf":1.0},"51":{"tf":1.0},"53":{"tf":1.0},"54":{"tf":1.0},"58":{"tf":1.0},"59":{"tf":1.0},"60":{"tf":1.7320508075688772},"61":{"tf":1.0},"62":{"tf":1.0},"64":{"tf":1.0},"65":{"tf":1.0},"75":{"tf":1.0},"77":{"tf":1.0}}}}}}},"n":{"d":{"df":0,"docs":{},"u":{"c":{"df":0,"docs":{},"t":{"df":5,"docs":{"44":{"tf":2.23606797749979},"45":{"tf":1.7320508075688772},"46":{"tf":1.4142135623730951},"47":{"tf":1.0},"60":{"tf":1.0}}}},"df":0,"docs":{}}},"df":0,"docs":{},"f":{"df":0,"docs":{},"i":{"df":0,"docs":{},"x":{"df":0,"docs":{},"r":{":":{"8":{"0":{"df":1,"docs":{"68":{"tf":1.0}}},"df":0,"docs":{}},"df":0,"docs":{}},"df":0,"docs":{}}}},"o":{"df":0,"docs":{},"v":{"df":0,"docs":{},"i":{"df":0,"docs":{},"e":{"df":0,"docs":{},"w":{"df":1,"docs":{"65":{"tf":1.0}}}}}}}},"j":{"df":0,"docs":{},"e":{"c":{"df":0,"docs":{},"t":{"df":3,"docs":{"3":{"tf":1.7320508075688772},"4":{"tf":1.7320508075688772},"65":{"tf":1.7320508075688772}}}},"df":0,"docs":{}}},"l":{"df":4,"docs":{"15":{"tf":1.0},"20":{"tf":1.7320508075688772},"21":{"tf":1.4142135623730951},"73":{"tf":1.0}}},"r":{"df":4,"docs":{"15":{"tf":1.0},"20":{"tf":1.7320508075688772},"21":{"tf":1.4142135623730951},"73":{"tf":1.0}}},"s":{"df":0,"docs":{},"e":{"df":0,"docs":{},"r":{"df":0,"docs":{},"t":{"df":1,"docs":{"20":{"tf":1.4142135623730951}}}}}},"t":{"df":5,"docs":{"26":{"tf":2.0},"54":{"tf":1.4142135623730951},"58":{"tf":1.4142135623730951},"59":{"tf":1.0},"73":{"tf":1.7320508075688772}},"r":{"df":0,"docs":{},"o":{"d":{"df":0,"docs":{},"u":{"c":{"df":1,"docs":{"48":{"tf":1.0}}},"df":0,"docs":{}}},"df":20,"docs":{"15":{"tf":1.0},"16":{"tf":1.0},"17":{"tf":1.0},"18":{"tf":1.0},"20":{"tf":1.0},"21":{"tf":1.0},"22":{"tf":1.0},"23":{"tf":1.4142135623730951},"25":{"tf":1.0},"28":{"tf":1.0},"3":{"tf":1.0},"37":{"tf":1.0},"4":{"tf":1.0},"40":{"tf":1.0},"48":{"tf":2.449489742783178},"49":{"tf":1.7320508075688772},"5":{"tf":1.0},"54":{"tf":1.0},"59":{"tf":1.0},"65":{"tf":1.0}}}}}},"t":{"df":0,"docs":{},"e":{"_":{"df":0,"docs":{},"f":{"a":{"df":0,"docs":{},"l":{"df":0,"docs":{},"s":{"df":1,"docs":{"73":{"tf":1.0}}}}},"df":0,"docs":{}},"t":{"df":0,"docs":{},"r":{"df":0,"docs":{},"u":{"df":1,"docs":{"73":{"tf":1.0}}}}}},"df":0,"docs":{}}}},"k":{"df":3,"docs":{"45":{"tf":1.4142135623730951},"47":{"tf":1.7320508075688772},"59":{"tf":3.3166247903554}}},"l":{".":{"df":0,"docs":{},"l":{"df":0,"docs":{},"e":{"df":0,"docs":{},"n":{"df":0,"docs":{},"g":{"df":0,"docs":{},"t":{"df":0,"docs":{},"h":{"df":1,"docs":{"46":{"tf":1.0}}}}}}}}},"df":1,"docs":{"46":{"tf":3.1622776601683795}},"e":{"a":{"df":0,"docs":{},"n":{".":{"df":0,"docs":{},"m":{"df":0,"docs":{},"v":{"a":{"df":0,"docs":{},"r":{"df":0,"docs":{},"i":{"d":{".":{"df":0,"docs":{},"r":{"df":0,"docs":{},"e":{"df":0,"docs":{},"f":{"df":0,"docs":{},"l":{"df":1,"docs":{"61":{"tf":1.0}}}}},"f":{"df":0,"docs":{},"l":{"df":1,"docs":{"61":{"tf":1.0}}}}}},"df":0,"docs":{}},"df":0,"docs":{}}}},"df":0,"docs":{}}}},"4":{"df":3,"docs":{"0":{"tf":1.0},"19":{"tf":1.0},"30":{"tf":1.0}}},"df":8,"docs":{"0":{"tf":1.0},"17":{"tf":1.0},"2":{"tf":2.0},"44":{"tf":1.0},"49":{"tf":1.0},"7":{"tf":1.0},"73":{"tf":1.0},"77":{"tf":1.0}}}},"df":0,"docs":{},"f":{"df":0,"docs":{},"t":{"df":3,"docs":{"20":{"tf":1.0},"27":{"tf":1.0},"50":{"tf":2.0}}}}},"i":{"df":0,"docs":{},"n":{"a":{"df":0,"docs":{},"r":{"df":0,"docs":{},"i":{"df":0,"docs":{},"t":{"df":0,"docs":{},"h":{"df":5,"docs":{"51":{"tf":3.0},"52":{"tf":1.4142135623730951},"53":{"tf":1.7320508075688772},"54":{"tf":1.0},"73":{"tf":1.4142135623730951}}}}}}},"df":0,"docs":{},"e":{"a":{"df":0,"docs":{},"r":{"df":2,"docs":{"51":{"tf":1.0},"53":{"tf":1.0}}}},"df":0,"docs":{}}},"s":{"df":0,"docs":{},"t":{".":{"df":0,"docs":{},"l":{"df":0,"docs":{},"e":{"df":0,"docs":{},"n":{"df":0,"docs":{},"g":{"df":0,"docs":{},"t":{"df":0,"docs":{},"h":{"df":1,"docs":{"46":{"tf":1.7320508075688772}}}}}}}}},"df":1,"docs":{"46":{"tf":1.7320508075688772}}}}},"o":{"df":0,"docs":{},"s":{"df":0,"docs":{},"s":{"df":1,"docs":{"77":{"tf":1.0}}}}}},"m":{"a":{"df":0,"docs":{},"t":{"c":{"df":0,"docs":{},"h":{"df":1,"docs":{"47":{"tf":1.0}}}},"df":0,"docs":{},"h":{"df":0,"docs":{},"e":{"df":0,"docs":{},"m":{"a":{"df":0,"docs":{},"t":{"df":1,"docs":{"2":{"tf":1.0}}}},"df":0,"docs":{}}},"l":{"df":0,"docs":{},"i":{"b":{".":{"d":{"a":{"df":0,"docs":{},"t":{"a":{".":{"df":0,"docs":{},"n":{"a":{"df":0,"docs":{},"t":{".":{"b":{"a":{"df":0,"docs":{},"s":{"df":1,"docs":{"60":{"tf":1.0}}}},"df":0,"docs":{}},"df":0,"docs":{}},"df":0,"docs":{}}},"df":0,"docs":{}},"s":{"df":0,"docs":{},"e":{"df":0,"docs":{},"t":{"df":0,"docs":{},"l":{"df":0,"docs":{},"i":{"df":0,"docs":{},"k":{"df":0,"docs":{},"e":{".":{"b":{"a":{"df":0,"docs":{},"s":{"df":1,"docs":{"37":{"tf":1.0}}}},"df":0,"docs":{}},"df":0,"docs":{}},"df":0,"docs":{}}}}}}}}},"df":0,"docs":{}},"df":0,"docs":{}}},"df":0,"docs":{}},"df":0,"docs":{},"t":{"a":{"c":{"df":0,"docs":{},"t":{"df":0,"docs":{},"i":{"c":{".":{"b":{"df":0,"docs":{},"y":{"c":{"df":0,"docs":{},"o":{"df":0,"docs":{},"n":{"df":0,"docs":{},"t":{"df":0,"docs":{},"r":{"a":{"df":1,"docs":{"16":{"tf":1.0}}},"df":0,"docs":{}}}}}},"df":0,"docs":{}}},"c":{"a":{"df":0,"docs":{},"s":{"df":2,"docs":{"22":{"tf":1.0},"45":{"tf":1.0}}}},"df":0,"docs":{},"h":{"df":0,"docs":{},"o":{"df":0,"docs":{},"o":{"df":0,"docs":{},"s":{"df":1,"docs":{"24":{"tf":1.0}}}}}},"o":{"df":0,"docs":{},"n":{"df":0,"docs":{},"v":{"df":0,"docs":{},"e":{"df":0,"docs":{},"r":{"df":0,"docs":{},"t":{"df":1,"docs":{"31":{"tf":1.0}}}}}}}}},"df":0,"docs":{},"g":{"c":{"df":0,"docs":{},"o":{"df":0,"docs":{},"n":{"df":0,"docs":{},"g":{"df":0,"docs":{},"r":{"df":1,"docs":{"58":{"tf":1.0}}}}}}},"df":0,"docs":{}},"l":{"df":0,"docs":{},"e":{"df":0,"docs":{},"f":{"df":0,"docs":{},"t":{"df":0,"docs":{},"r":{"df":0,"docs":{},"i":{"df":0,"docs":{},"g":{"df":0,"docs":{},"h":{"df":0,"docs":{},"t":{"df":1,"docs":{"50":{"tf":1.0}}}}}}}}}},"i":{"b":{"df":0,"docs":{},"r":{"a":{"df":0,"docs":{},"r":{"df":0,"docs":{},"y":{"df":0,"docs":{},"s":{"df":0,"docs":{},"e":{"a":{"df":0,"docs":{},"r":{"c":{"df":0,"docs":{},"h":{"df":2,"docs":{"11":{"tf":1.0},"35":{"tf":1.0}}}},"df":0,"docs":{}}},"df":0,"docs":{}}}}}},"df":0,"docs":{}}},"df":0,"docs":{},"n":{"a":{"df":0,"docs":{},"r":{"df":0,"docs":{},"i":{"df":0,"docs":{},"t":{"df":0,"docs":{},"h":{"df":2,"docs":{"51":{"tf":1.0},"53":{"tf":1.0}}}}}}},"df":0,"docs":{}}}},"n":{"df":0,"docs":{},"t":{"df":0,"docs":{},"h":{"df":0,"docs":{},"r":{"df":0,"docs":{},"e":{"df":0,"docs":{},"w":{"df":0,"docs":{},"r":{"df":0,"docs":{},"i":{"df":0,"docs":{},"t":{"df":1,"docs":{"64":{"tf":1.0}}}}}}}}}}},"p":{"df":0,"docs":{},"u":{"df":0,"docs":{},"s":{"df":0,"docs":{},"h":{"df":0,"docs":{},"n":{"df":0,"docs":{},"e":{"df":0,"docs":{},"g":{"df":1,"docs":{"54":{"tf":1.0}}}}}}}}},"r":{"df":1,"docs":{"62":{"tf":1.0}},"e":{"df":0,"docs":{},"l":{"a":{"df":0,"docs":{},"t":{"df":0,"docs":{},"i":{"df":0,"docs":{},"o":{"df":0,"docs":{},"n":{".":{"df":0,"docs":{},"r":{"df":0,"docs":{},"f":{"df":0,"docs":{},"l":{"df":2,"docs":{"60":{"tf":1.0},"61":{"tf":1.4142135623730951}}}}}},"df":0,"docs":{}}}}}},"df":0,"docs":{}}}},"s":{"a":{"df":0,"docs":{},"y":{"df":1,"docs":{"65":{"tf":1.0}}}},"df":0,"docs":{},"o":{"df":0,"docs":{},"l":{"df":0,"docs":{},"v":{"df":0,"docs":{},"e":{"b":{"df":0,"docs":{},"y":{"df":0,"docs":{},"e":{"df":0,"docs":{},"l":{"df":0,"docs":{},"i":{"df":0,"docs":{},"m":{"df":1,"docs":{"5":{"tf":1.0}}}}}}}},"df":0,"docs":{}}}}}},"t":{"a":{"df":0,"docs":{},"u":{"df":0,"docs":{},"t":{"df":0,"docs":{},"o":{"df":1,"docs":{"75":{"tf":1.0}}}}}},"df":0,"docs":{}},"w":{"df":0,"docs":{},"l":{"df":0,"docs":{},"o":{"df":0,"docs":{},"g":{"df":1,"docs":{"77":{"tf":1.0}}}}}}},"df":0,"docs":{}},"df":0,"docs":{}}}},"df":0,"docs":{}},"df":0,"docs":{}}},"4":{"df":2,"docs":{"2":{"tf":1.0},"50":{"tf":1.0}}},"df":0,"docs":{}},"df":0,"docs":{}}}}}},"df":1,"docs":{"47":{"tf":1.7320508075688772}},"o":{"df":0,"docs":{},"n":{"df":0,"docs":{},"o":{"df":0,"docs":{},"i":{"d":{"df":0,"docs":{},"h":{"df":0,"docs":{},"o":{"df":0,"docs":{},"m":{".":{"df":0,"docs":{},"m":{"a":{"df":0,"docs":{},"p":{"_":{"df":0,"docs":{},"m":{"df":0,"docs":{},"u":{"df":0,"docs":{},"l":{"df":1,"docs":{"11":{"tf":1.0}}}}}},"df":0,"docs":{}}},"df":0,"docs":{}}},"df":0,"docs":{}}}}},"df":0,"docs":{}}}}},"u":{"df":0,"docs":{},"l":{"_":{"df":0,"docs":{},"i":{"df":0,"docs":{},"n":{"df":0,"docs":{},"v":{"_":{"df":0,"docs":{},"e":{"df":0,"docs":{},"q":{"_":{"df":0,"docs":{},"i":{"df":0,"docs":{},"f":{"df":0,"docs":{},"f":{"_":{"df":0,"docs":{},"e":{"df":0,"docs":{},"q":{"_":{"df":0,"docs":{},"m":{"df":0,"docs":{},"u":{"df":0,"docs":{},"l":{"df":1,"docs":{"64":{"tf":1.4142135623730951}}}}}},"df":0,"docs":{}}}},"df":0,"docs":{}}}}},"df":0,"docs":{}}}},"df":0,"docs":{}}}},"n":{"df":0,"docs":{},"e":{"df":0,"docs":{},"g":{"df":1,"docs":{"73":{"tf":1.0}}}}}},"df":0,"docs":{}}},"y":{"a":{"b":{"df":1,"docs":{"73":{"tf":2.23606797749979}}},"df":0,"docs":{}},"df":0,"docs":{},"e":{"df":0,"docs":{},"q":{".":{"df":0,"docs":{},"r":{"df":0,"docs":{},"e":{"df":0,"docs":{},"f":{"df":0,"docs":{},"l":{"df":1,"docs":{"60":{"tf":1.0}}}}}}},"df":1,"docs":{"60":{"tf":1.7320508075688772}}}}}},"n":{"a":{"df":0,"docs":{},"m":{"df":0,"docs":{},"e":{"df":11,"docs":{"23":{"tf":1.0},"26":{"tf":1.0},"37":{"tf":1.0},"48":{"tf":1.0},"51":{"tf":1.0},"53":{"tf":1.0},"54":{"tf":1.0},"58":{"tf":1.0},"60":{"tf":1.0},"75":{"tf":1.0},"77":{"tf":1.0}}}},"t":{".":{"d":{"df":0,"docs":{},"v":{"d":{"_":{"df":0,"docs":{},"i":{"df":0,"docs":{},"f":{"df":0,"docs":{},"f":{"_":{"d":{"df":0,"docs":{},"i":{"df":0,"docs":{},"v":{"_":{"df":0,"docs":{},"m":{"df":0,"docs":{},"u":{"df":0,"docs":{},"l":{"_":{"df":0,"docs":{},"e":{"df":0,"docs":{},"q":{"df":1,"docs":{"74":{"tf":1.0}}}}},"df":0,"docs":{}}}}},"df":0,"docs":{}}}},"df":0,"docs":{}},"df":0,"docs":{}}}}},"df":0,"docs":{}},"df":0,"docs":{}}},"df":0,"docs":{},"l":{"df":0,"docs":{},"t":{".":{"b":{"a":{"df":0,"docs":{},"s":{"df":1,"docs":{"35":{"tf":1.0}}}},"df":0,"docs":{}},"df":0,"docs":{}},"df":0,"docs":{}}},"m":{"df":0,"docs":{},"u":{"df":0,"docs":{},"l":{"_":{"a":{"df":0,"docs":{},"s":{"df":0,"docs":{},"s":{"df":0,"docs":{},"o":{"c":{"df":1,"docs":{"63":{"tf":1.4142135623730951}}},"df":0,"docs":{}}}}},"df":0,"docs":{}},"df":0,"docs":{}}}},"s":{"df":0,"docs":{},"t":{"df":0,"docs":{},"r":{"df":0,"docs":{},"o":{"df":0,"docs":{},"n":{"df":0,"docs":{},"g":{"_":{"df":0,"docs":{},"i":{"df":0,"docs":{},"n":{"d":{"df":0,"docs":{},"u":{"c":{"df":0,"docs":{},"t":{"df":0,"docs":{},"i":{"df":0,"docs":{},"o":{"df":0,"docs":{},"n":{"_":{"df":0,"docs":{},"o":{"df":0,"docs":{},"n":{"df":1,"docs":{"47":{"tf":1.0}}}}},"df":0,"docs":{}}}}}},"df":0,"docs":{}}},"df":0,"docs":{}}}},"df":0,"docs":{}}}}}}}},"df":15,"docs":{"12":{"tf":1.0},"28":{"tf":1.0},"29":{"tf":1.0},"31":{"tf":1.4142135623730951},"36":{"tf":1.0},"38":{"tf":1.4142135623730951},"44":{"tf":2.8284271247461903},"45":{"tf":1.0},"47":{"tf":1.4142135623730951},"48":{"tf":1.0},"53":{"tf":1.0},"60":{"tf":1.0},"63":{"tf":1.0},"72":{"tf":1.0},"77":{"tf":1.4142135623730951}}}},"df":8,"docs":{"44":{"tf":3.872983346207417},"45":{"tf":1.7320508075688772},"46":{"tf":2.0},"47":{"tf":3.3166247903554},"48":{"tf":1.7320508075688772},"59":{"tf":3.7416573867739413},"60":{"tf":2.449489742783178},"72":{"tf":2.23606797749979}},"e":{"df":0,"docs":{},"e":{"d":{"df":25,"docs":{"11":{"tf":1.0},"16":{"tf":1.0},"18":{"tf":1.0},"22":{"tf":1.0},"23":{"tf":1.0},"24":{"tf":1.0},"3":{"tf":1.0},"31":{"tf":1.0},"35":{"tf":1.0},"37":{"tf":1.0},"39":{"tf":1.0},"45":{"tf":1.0},"5":{"tf":1.0},"50":{"tf":1.0},"51":{"tf":1.0},"53":{"tf":1.0},"54":{"tf":1.0},"58":{"tf":1.0},"59":{"tf":1.0},"60":{"tf":1.0},"62":{"tf":1.0},"64":{"tf":1.0},"65":{"tf":1.0},"75":{"tf":1.0},"77":{"tf":1.0}}},"df":0,"docs":{}},"g":{"a":{"df":0,"docs":{},"t":{"df":1,"docs":{"54":{"tf":1.0}}}},"df":0,"docs":{}}},"l":{"df":0,"docs":{},"i":{"df":0,"docs":{},"n":{"a":{"df":0,"docs":{},"r":{"df":0,"docs":{},"i":{"df":0,"docs":{},"t":{"df":0,"docs":{},"h":{"df":1,"docs":{"53":{"tf":1.7320508075688772}}}}}}},"df":0,"docs":{}}}},"o":{"df":0,"docs":{},"n":{"c":{"df":0,"docs":{},"o":{"df":0,"docs":{},"m":{"df":0,"docs":{},"p":{"df":0,"docs":{},"u":{"df":0,"docs":{},"t":{"df":1,"docs":{"25":{"tf":1.0}}}}}}}},"df":1,"docs":{"53":{"tf":1.0}},"e":{"df":0,"docs":{},"m":{"df":0,"docs":{},"p":{"df":0,"docs":{},"t":{"df":0,"docs":{},"i":{"df":1,"docs":{"25":{"tf":1.0}}}}}}}}},"t":{"df":0,"docs":{},"h":{"_":{"df":0,"docs":{},"r":{"df":0,"docs":{},"e":{"df":0,"docs":{},"w":{"df":0,"docs":{},"r":{"df":0,"docs":{},"i":{"df":0,"docs":{},"t":{"df":2,"docs":{"59":{"tf":1.0},"64":{"tf":1.4142135623730951}}}}}}}}},"df":0,"docs":{}}}},"o":{"b":{"df":0,"docs":{},"t":{"a":{"df":0,"docs":{},"i":{"df":0,"docs":{},"n":{"df":1,"docs":{"59":{"tf":1.0}}}}},"df":0,"docs":{}}},"df":0,"docs":{},"n":{"df":0,"docs":{},"e":{"_":{"df":0,"docs":{},"m":{"df":0,"docs":{},"u":{"df":0,"docs":{},"l":{"df":1,"docs":{"64":{"tf":1.4142135623730951}}}}}},"df":0,"docs":{}}},"p":{"df":0,"docs":{},"e":{"df":0,"docs":{},"n":{"df":1,"docs":{"68":{"tf":1.0}}}},"t":{"df":0,"docs":{},"i":{"df":0,"docs":{},"o":{"df":0,"docs":{},"n":{"df":1,"docs":{"1":{"tf":1.0}}}}}}},"r":{".":{"df":0,"docs":{},"i":{"df":0,"docs":{},"n":{"df":0,"docs":{},"l":{"df":1,"docs":{"50":{"tf":1.4142135623730951}}},"r":{"df":1,"docs":{"50":{"tf":1.0}}}}}},"df":0,"docs":{}}},"p":{"(":{"0":{"df":1,"docs":{"47":{"tf":1.0}}},"df":0,"docs":{},"x":{"df":2,"docs":{"24":{"tf":1.4142135623730951},"48":{"tf":1.0}}}},"df":43,"docs":{"13":{"tf":1.7320508075688772},"15":{"tf":3.3166247903554},"16":{"tf":2.6457513110645907},"17":{"tf":2.8284271247461903},"18":{"tf":1.4142135623730951},"20":{"tf":2.449489742783178},"21":{"tf":1.7320508075688772},"22":{"tf":1.4142135623730951},"23":{"tf":3.0},"25":{"tf":2.449489742783178},"27":{"tf":3.0},"28":{"tf":1.0},"29":{"tf":2.6457513110645907},"33":{"tf":2.449489742783178},"35":{"tf":1.4142135623730951},"36":{"tf":1.7320508075688772},"39":{"tf":1.7320508075688772},"40":{"tf":3.0},"42":{"tf":2.23606797749979},"43":{"tf":1.4142135623730951},"44":{"tf":2.0},"46":{"tf":2.23606797749979},"47":{"tf":2.449489742783178},"48":{"tf":4.242640687119285},"49":{"tf":3.3166247903554},"5":{"tf":2.23606797749979},"50":{"tf":2.449489742783178},"54":{"tf":3.4641016151377544},"55":{"tf":2.0},"56":{"tf":2.23606797749979},"57":{"tf":2.6457513110645907},"59":{"tf":1.0},"6":{"tf":3.7416573867739413},"63":{"tf":1.7320508075688772},"65":{"tf":1.4142135623730951},"67":{"tf":2.23606797749979},"68":{"tf":1.4142135623730951},"7":{"tf":2.6457513110645907},"73":{"tf":1.7320508075688772},"74":{"tf":1.0},"75":{"tf":3.0},"76":{"tf":1.0},"9":{"tf":2.0}},"h":{"df":0,"docs":{},"r":{"a":{"df":0,"docs":{},"s":{"df":0,"docs":{},"e":{"b":{"df":0,"docs":{},"o":{"df":0,"docs":{},"o":{"df":0,"docs":{},"k":{"df":1,"docs":{"2":{"tf":1.0}}}}}},"df":0,"docs":{}}}},"df":0,"docs":{}}},"o":{"df":0,"docs":{},"s":{"df":0,"docs":{},"i":{"df":0,"docs":{},"t":{"df":2,"docs":{"44":{"tf":1.0},"45":{"tf":1.0}}}}}},"r":{"df":0,"docs":{},"o":{"df":0,"docs":{},"p":{"df":7,"docs":{"15":{"tf":1.0},"23":{"tf":1.0},"25":{"tf":1.0},"46":{"tf":1.0},"47":{"tf":1.0},"48":{"tf":1.0},"60":{"tf":1.0}}},"v":{"df":0,"docs":{},"e":{"df":2,"docs":{"19":{"tf":1.0},"30":{"tf":1.0}}}}}},"u":{"df":0,"docs":{},"s":{"df":0,"docs":{},"h":{"_":{"df":0,"docs":{},"n":{"df":0,"docs":{},"e":{"df":0,"docs":{},"g":{"df":1,"docs":{"54":{"tf":2.0}}}}}},"df":1,"docs":{"54":{"tf":1.0}}}}},"y":{"df":1,"docs":{"25":{"tf":1.4142135623730951}}}},"q":{"(":{"df":0,"docs":{},"i":{"df":1,"docs":{"48":{"tf":1.0}}}},"df":32,"docs":{"13":{"tf":1.0},"16":{"tf":2.23606797749979},"17":{"tf":2.0},"18":{"tf":1.4142135623730951},"20":{"tf":2.449489742783178},"21":{"tf":1.7320508075688772},"22":{"tf":1.4142135623730951},"23":{"tf":3.0},"27":{"tf":2.8284271247461903},"28":{"tf":1.0},"29":{"tf":1.0},"33":{"tf":1.4142135623730951},"35":{"tf":1.4142135623730951},"40":{"tf":2.6457513110645907},"42":{"tf":2.23606797749979},"44":{"tf":2.0},"48":{"tf":3.872983346207417},"49":{"tf":3.0},"5":{"tf":2.23606797749979},"50":{"tf":2.0},"54":{"tf":3.1622776601683795},"55":{"tf":1.4142135623730951},"56":{"tf":2.0},"57":{"tf":2.8284271247461903},"6":{"tf":3.4641016151377544},"63":{"tf":1.4142135623730951},"65":{"tf":1.4142135623730951},"67":{"tf":1.7320508075688772},"73":{"tf":1.7320508075688772},"74":{"tf":2.6457513110645907},"75":{"tf":2.23606797749979},"9":{"tf":2.0}}},"r":{"c":{"a":{"df":0,"docs":{},"s":{"df":0,"docs":{},"e":{"df":1,"docs":{"23":{"tf":2.0}}}}},"df":0,"docs":{}},"df":13,"docs":{"17":{"tf":2.449489742783178},"18":{"tf":1.4142135623730951},"20":{"tf":1.7320508075688772},"21":{"tf":1.7320508075688772},"22":{"tf":1.7320508075688772},"23":{"tf":2.0},"35":{"tf":1.4142135623730951},"40":{"tf":2.23606797749979},"48":{"tf":2.6457513110645907},"5":{"tf":1.4142135623730951},"57":{"tf":2.8284271247461903},"65":{"tf":1.4142135623730951},"75":{"tf":1.4142135623730951}},"e":{"c":{"df":0,"docs":{},"u":{"df":0,"docs":{},"r":{"df":0,"docs":{},"s":{"df":1,"docs":{"23":{"tf":1.0}}}}}},"df":0,"docs":{},"f":{"df":0,"docs":{},"i":{"df":0,"docs":{},"n":{"df":3,"docs":{"55":{"tf":1.7320508075688772},"56":{"tf":2.0},"57":{"tf":1.7320508075688772}}}},"l":{"df":2,"docs":{"60":{"tf":2.0},"61":{"tf":1.0}},"e":{"df":0,"docs":{},"x":{"df":1,"docs":{"60":{"tf":1.0}}}}}},"l":{"a":{"df":0,"docs":{},"t":{"df":1,"docs":{"58":{"tf":1.0}}}},"df":1,"docs":{"58":{"tf":2.23606797749979}}},"p":{"df":0,"docs":{},"e":{"a":{"df":0,"docs":{},"t":{"df":1,"docs":{"5":{"tf":1.4142135623730951}}}},"df":0,"docs":{}},"l":{"a":{"c":{"df":2,"docs":{"59":{"tf":2.0},"73":{"tf":1.0}}},"df":0,"docs":{}},"df":0,"docs":{}}}},"f":{"df":0,"docs":{},"l":{"df":5,"docs":{"51":{"tf":1.0},"60":{"tf":2.0},"61":{"tf":2.0},"74":{"tf":1.4142135623730951},"76":{"tf":1.0}}}},"i":{"df":0,"docs":{},"g":{"df":0,"docs":{},"h":{"df":0,"docs":{},"t":{"df":3,"docs":{"20":{"tf":1.0},"27":{"tf":1.0},"50":{"tf":1.7320508075688772}}}}},"n":{"df":0,"docs":{},"g":{"df":4,"docs":{"38":{"tf":1.0},"43":{"tf":1.0},"59":{"tf":2.0},"62":{"tf":2.23606797749979}}}}},"w":{"df":11,"docs":{"28":{"tf":1.0},"3":{"tf":1.0},"31":{"tf":1.0},"4":{"tf":1.0},"43":{"tf":1.0},"48":{"tf":1.0},"59":{"tf":1.4142135623730951},"63":{"tf":3.4641016151377544},"64":{"tf":1.0},"65":{"tf":1.0},"69":{"tf":1.0}}}},"s":{"a":{"df":0,"docs":{},"y":{"df":0,"docs":{},"s":{".":{"df":0,"docs":{},"n":{"df":0,"docs":{},"o":{"_":{"df":0,"docs":{},"v":{"df":0,"docs":{},"e":{"df":0,"docs":{},"r":{"df":0,"docs":{},"i":{"df":0,"docs":{},"f":{"df":0,"docs":{},"y":{"_":{"df":0,"docs":{},"i":{"df":0,"docs":{},"n":{"_":{"c":{"df":0,"docs":{},"i":{"df":1,"docs":{"66":{"tf":1.0}}}},"df":0,"docs":{}},"df":0,"docs":{}}}},"df":0,"docs":{}}}}}}}},"df":0,"docs":{}}},"v":{"df":0,"docs":{},"e":{"df":0,"docs":{},"r":{"df":0,"docs":{},"i":{"df":0,"docs":{},"f":{"df":0,"docs":{},"i":{"df":1,"docs":{"66":{"tf":1.0}}}}}}}}},"df":0,"docs":{}}}},"df":2,"docs":{"37":{"tf":2.449489742783178},"65":{"tf":1.4142135623730951}},"e":{"df":0,"docs":{},"t":{"_":{"df":0,"docs":{},"o":{"df":0,"docs":{},"p":{"df":0,"docs":{},"t":{"df":1,"docs":{"1":{"tf":1.0}}}}}},"df":1,"docs":{"37":{"tf":1.0}}}},"h":{"df":0,"docs":{},"o":{"df":0,"docs":{},"w":{"_":{"df":0,"docs":{},"t":{"df":0,"docs":{},"e":{"df":0,"docs":{},"r":{"df":0,"docs":{},"m":{"df":1,"docs":{"62":{"tf":1.4142135623730951}}}}}}},"df":15,"docs":{"16":{"tf":1.0},"26":{"tf":1.4142135623730951},"31":{"tf":1.0},"46":{"tf":1.4142135623730951},"48":{"tf":1.4142135623730951},"49":{"tf":1.0},"5":{"tf":1.7320508075688772},"54":{"tf":1.4142135623730951},"55":{"tf":1.0},"56":{"tf":1.0},"57":{"tf":2.6457513110645907},"6":{"tf":1.0},"67":{"tf":2.0},"73":{"tf":1.7320508075688772},"77":{"tf":1.4142135623730951}}}}},"i":{"df":0,"docs":{},"m":{"df":0,"docs":{},"p":{"_":{"a":{"df":0,"docs":{},"l":{"df":4,"docs":{"28":{"tf":1.0},"4":{"tf":1.0},"65":{"tf":1.0},"70":{"tf":1.4142135623730951}}}},"df":0,"docs":{}},"df":11,"docs":{"26":{"tf":1.4142135623730951},"3":{"tf":1.0},"44":{"tf":1.4142135623730951},"45":{"tf":1.4142135623730951},"62":{"tf":1.0},"65":{"tf":1.0},"68":{"tf":2.8284271247461903},"69":{"tf":1.4142135623730951},"70":{"tf":1.0},"71":{"tf":1.0},"73":{"tf":2.449489742783178}}}}},"o":{"df":0,"docs":{},"r":{"df":0,"docs":{},"r":{"df":0,"docs":{},"i":{"df":4,"docs":{"12":{"tf":2.0},"46":{"tf":1.4142135623730951},"47":{"tf":1.4142135623730951},"72":{"tf":2.0}}},"y":{"a":{"df":0,"docs":{},"x":{"df":1,"docs":{"12":{"tf":1.4142135623730951}}}},"df":0,"docs":{}}}}},"p":{"df":0,"docs":{},"l":{"df":0,"docs":{},"i":{"df":0,"docs":{},"t":{"df":1,"docs":{"73":{"tf":2.23606797749979}}}}}},"t":{"d":{".":{"df":0,"docs":{},"t":{"a":{"c":{"df":0,"docs":{},"t":{"df":0,"docs":{},"i":{"c":{".":{"df":0,"docs":{},"e":{"df":0,"docs":{},"x":{"df":0,"docs":{},"t":{"df":1,"docs":{"37":{"tf":1.0}}}}},"g":{"df":0,"docs":{},"u":{"a":{"df":0,"docs":{},"r":{"d":{"df":0,"docs":{},"e":{"df":0,"docs":{},"x":{"df":0,"docs":{},"p":{"df":0,"docs":{},"r":{"df":1,"docs":{"39":{"tf":1.0}}}}}}},"df":0,"docs":{}}},"df":0,"docs":{}}},"r":{"c":{"a":{"df":0,"docs":{},"s":{"df":1,"docs":{"23":{"tf":1.0}}}},"df":0,"docs":{}},"df":0,"docs":{},"e":{"df":0,"docs":{},"p":{"df":0,"docs":{},"l":{"a":{"c":{"df":1,"docs":{"59":{"tf":1.0}}},"df":0,"docs":{}},"df":0,"docs":{}}}}},"s":{"df":0,"docs":{},"h":{"df":0,"docs":{},"o":{"df":0,"docs":{},"w":{"df":0,"docs":{},"t":{"df":0,"docs":{},"e":{"df":0,"docs":{},"r":{"df":0,"docs":{},"m":{"df":1,"docs":{"18":{"tf":1.0}}}}}}}}}}},"df":0,"docs":{}},"df":0,"docs":{}}}},"df":0,"docs":{}},"df":0,"docs":{}}},"df":0,"docs":{}},"df":0,"docs":{}},"u":{"c":{"c":{"df":2,"docs":{"44":{"tf":2.6457513110645907},"46":{"tf":1.0}}},"df":0,"docs":{}},"df":0,"docs":{},"f":{"df":0,"docs":{},"f":{"df":0,"docs":{},"i":{"c":{"df":1,"docs":{"74":{"tf":2.6457513110645907}}},"df":0,"docs":{}}}}}},"t":{"a":{"c":{"df":0,"docs":{},"t":{"df":0,"docs":{},"i":{"c":{"df":1,"docs":{"2":{"tf":1.0}}},"df":0,"docs":{}}}},"df":0,"docs":{},"u":{"df":0,"docs":{},"t":{"df":0,"docs":{},"o":{"df":1,"docs":{"75":{"tf":2.449489742783178}},"l":{"df":0,"docs":{},"o":{"df":0,"docs":{},"g":{"df":1,"docs":{"75":{"tf":1.0}}}}}}}}},"df":2,"docs":{"12":{"tf":1.7320508075688772},"37":{"tf":2.449489742783178}},"h":{"df":0,"docs":{},"e":{"df":0,"docs":{},"o":{"df":0,"docs":{},"r":{"df":0,"docs":{},"e":{"df":0,"docs":{},"m":{"df":4,"docs":{"12":{"tf":1.0},"19":{"tf":1.0},"30":{"tf":1.0},"72":{"tf":1.0}}}},"i":{"df":1,"docs":{"2":{"tf":1.0}}}}}}},"r":{"df":0,"docs":{},"i":{"df":7,"docs":{"18":{"tf":1.0},"31":{"tf":1.0},"35":{"tf":1.4142135623730951},"51":{"tf":1.0},"53":{"tf":1.0},"65":{"tf":1.7320508075688772},"75":{"tf":1.4142135623730951}},"v":{"df":0,"docs":{},"i":{"a":{"df":0,"docs":{},"l":{"df":1,"docs":{"76":{"tf":2.449489742783178}}}},"df":0,"docs":{}}}},"u":{"df":0,"docs":{},"e":{"df":2,"docs":{"1":{"tf":1.0},"66":{"tf":1.4142135623730951}}}}},"y":{"df":0,"docs":{},"p":{"df":0,"docs":{},"e":{"df":5,"docs":{"2":{"tf":1.0},"37":{"tf":1.0},"60":{"tf":1.0},"61":{"tf":1.0},"68":{"tf":1.7320508075688772}}}}}},"u":{"df":2,"docs":{"60":{"tf":1.0},"68":{"tf":1.7320508075688772}},"n":{"df":0,"docs":{},"f":{"df":0,"docs":{},"o":{"df":0,"docs":{},"l":{"d":{"df":1,"docs":{"73":{"tf":1.0}}},"df":0,"docs":{}}}},"i":{"df":0,"docs":{},"v":{"df":0,"docs":{},"e":{"df":0,"docs":{},"r":{"df":0,"docs":{},"s":{"df":1,"docs":{"68":{"tf":1.0}}}}}}}},"s":{"df":2,"docs":{"24":{"tf":1.4142135623730951},"47":{"tf":1.0}}}},"v":{"a":{"df":0,"docs":{},"r":{"df":0,"docs":{},"i":{"a":{"b":{"df":0,"docs":{},"l":{"df":7,"docs":{"23":{"tf":1.0},"25":{"tf":1.0},"37":{"tf":1.4142135623730951},"47":{"tf":1.0},"61":{"tf":1.0},"64":{"tf":1.0},"68":{"tf":1.0}}}},"df":0,"docs":{}},"df":0,"docs":{}}}},"df":1,"docs":{"68":{"tf":1.7320508075688772}}},"w":{"a":{"df":0,"docs":{},"r":{"df":0,"docs":{},"n":{"df":1,"docs":{"1":{"tf":1.0}},"i":{"df":0,"docs":{},"n":{"df":0,"docs":{},"g":{"a":{"df":0,"docs":{},"s":{"df":0,"docs":{},"e":{"df":0,"docs":{},"r":{"df":0,"docs":{},"r":{"df":0,"docs":{},"o":{"df":0,"docs":{},"r":{"df":1,"docs":{"1":{"tf":1.0}}}}}}}}},"df":0,"docs":{}}}}}}},"df":0,"docs":{},"i":{"df":0,"docs":{},"t":{"df":0,"docs":{},"h":{"df":0,"docs":{},"o":{"df":0,"docs":{},"u":{"df":0,"docs":{},"t":{"df":1,"docs":{"77":{"tf":1.0}}}}}}}},"l":{"df":0,"docs":{},"o":{"df":0,"docs":{},"g":{"df":1,"docs":{"77":{"tf":1.7320508075688772}}}}}},"x":{")":{".":{"df":0,"docs":{},"p":{"df":0,"docs":{},"r":{"df":0,"docs":{},"o":{"df":0,"docs":{},"p":{"df":0,"docs":{},"e":{"df":0,"docs":{},"r":{"df":0,"docs":{},"t":{"df":0,"docs":{},"i":{"df":1,"docs":{"25":{"tf":1.0}}}}}}}}}},"v":{"a":{"df":0,"docs":{},"l":{"df":1,"docs":{"25":{"tf":1.0}}}},"df":0,"docs":{}}},"df":0,"docs":{}},"`":{"df":0,"docs":{},"が":{"df":0,"docs":{},"偶":{"df":0,"docs":{},"数":{"df":0,"docs":{},"の":{"df":0,"docs":{},"と":{"df":0,"docs":{},"き":{"`":{"3":{"df":1,"docs":{"43":{"tf":1.0}}},"df":0,"docs":{}},"df":0,"docs":{}}}}}}}},"df":24,"docs":{"12":{"tf":3.4641016151377544},"24":{"tf":3.1622776601683795},"25":{"tf":4.358898943540674},"26":{"tf":3.4641016151377544},"28":{"tf":2.6457513110645907},"29":{"tf":1.7320508075688772},"3":{"tf":1.0},"35":{"tf":1.7320508075688772},"36":{"tf":3.3166247903554},"37":{"tf":2.6457513110645907},"38":{"tf":3.872983346207417},"4":{"tf":1.0},"43":{"tf":3.4641016151377544},"48":{"tf":2.449489742783178},"51":{"tf":2.8284271247461903},"52":{"tf":1.4142135623730951},"54":{"tf":3.1622776601683795},"58":{"tf":2.23606797749979},"61":{"tf":1.7320508075688772},"62":{"tf":2.449489742783178},"65":{"tf":2.8284271247461903},"66":{"tf":1.4142135623730951},"72":{"tf":1.7320508075688772},"73":{"tf":5.196152422706632}}},"y":{"df":14,"docs":{"12":{"tf":3.4641016151377544},"24":{"tf":4.0},"25":{"tf":3.3166247903554},"3":{"tf":1.4142135623730951},"4":{"tf":1.4142135623730951},"43":{"tf":2.449489742783178},"48":{"tf":3.3166247903554},"51":{"tf":1.4142135623730951},"52":{"tf":1.4142135623730951},"54":{"tf":2.0},"62":{"tf":2.449489742783178},"65":{"tf":2.6457513110645907},"66":{"tf":2.0},"72":{"tf":1.7320508075688772}}},"z":{"df":6,"docs":{"3":{"tf":1.0},"4":{"tf":1.0},"43":{"tf":1.4142135623730951},"51":{"tf":1.4142135623730951},"65":{"tf":1.0},"72":{"tf":1.7320508075688772}},"e":{"df":0,"docs":{},"r":{"df":0,"docs":{},"o":{"df":2,"docs":{"44":{"tf":1.7320508075688772},"46":{"tf":1.0}}}}}}}},"breadcrumbs":{"root":{"0":{"df":15,"docs":{"12":{"tf":1.0},"26":{"tf":1.4142135623730951},"28":{"tf":1.7320508075688772},"31":{"tf":1.4142135623730951},"44":{"tf":2.0},"45":{"tf":1.0},"46":{"tf":1.4142135623730951},"47":{"tf":1.0},"51":{"tf":1.4142135623730951},"54":{"tf":1.4142135623730951},"58":{"tf":1.0},"61":{"tf":1.0},"72":{"tf":1.0},"73":{"tf":3.3166247903554},"74":{"tf":1.0}}},"1":{"0":{"0":{"df":1,"docs":{"62":{"tf":1.0}}},"df":0,"docs":{}},"2":{"df":1,"docs":{"51":{"tf":1.0}}},"3":{"df":2,"docs":{"61":{"tf":1.0},"74":{"tf":1.7320508075688772}}},"df":16,"docs":{"12":{"tf":1.7320508075688772},"26":{"tf":1.0},"28":{"tf":2.449489742783178},"35":{"tf":1.0},"36":{"tf":1.0},"44":{"tf":2.0},"46":{"tf":1.4142135623730951},"47":{"tf":1.0},"48":{"tf":2.8284271247461903},"52":{"tf":1.0},"54":{"tf":1.7320508075688772},"59":{"tf":1.0},"61":{"tf":1.4142135623730951},"64":{"tf":1.7320508075688772},"73":{"tf":1.4142135623730951},"76":{"tf":1.4142135623730951}}},"2":{"df":19,"docs":{"12":{"tf":3.0},"26":{"tf":3.1622776601683795},"29":{"tf":1.4142135623730951},"36":{"tf":1.0},"37":{"tf":1.0},"38":{"tf":1.4142135623730951},"43":{"tf":1.7320508075688772},"51":{"tf":1.4142135623730951},"52":{"tf":1.4142135623730951},"53":{"tf":1.4142135623730951},"58":{"tf":1.7320508075688772},"59":{"tf":2.6457513110645907},"61":{"tf":1.4142135623730951},"62":{"tf":2.8284271247461903},"64":{"tf":1.0},"72":{"tf":1.0},"73":{"tf":3.872983346207417},"74":{"tf":1.7320508075688772},"76":{"tf":1.0}},"回":{"df":0,"docs":{},"出":{"df":0,"docs":{},"現":{"df":0,"docs":{},"す":{"df":0,"docs":{},"る":{"df":0,"docs":{},"が":{"df":0,"docs":{},"，":{"2":{"df":1,"docs":{"64":{"tf":1.0}}},"df":0,"docs":{}}}}}}}}},"3":{"df":8,"docs":{"12":{"tf":1.0},"29":{"tf":1.0},"36":{"tf":1.0},"43":{"tf":1.4142135623730951},"51":{"tf":1.0},"61":{"tf":1.0},"74":{"tf":1.7320508075688772},"75":{"tf":1.0}}},"4":{"df":2,"docs":{"51":{"tf":1.4142135623730951},"59":{"tf":1.4142135623730951}},"│":{"0":{",":{"1":{",":{"2":{",":{"3":{"df":1,"docs":{"12":{"tf":1.0}}},"df":0,"docs":{}},"df":0,"docs":{}},"df":0,"docs":{}},"df":0,"docs":{}},"df":0,"docs":{}},"df":0,"docs":{}},"df":0,"docs":{}}},"5":{"df":1,"docs":{"59":{"tf":2.449489742783178}}},"7":{"0":{"df":2,"docs":{"61":{"tf":1.4142135623730951},"74":{"tf":2.449489742783178}}},"df":1,"docs":{"36":{"tf":1.0}}},"_":{"df":9,"docs":{"12":{"tf":1.0},"13":{"tf":1.0},"26":{"tf":1.0},"42":{"tf":1.0},"5":{"tf":1.0},"55":{"tf":1.0},"56":{"tf":1.4142135623730951},"57":{"tf":1.7320508075688772},"59":{"tf":1.7320508075688772}}},"a":{"b":{"df":0,"docs":{},"e":{"df":0,"docs":{},"l":{"df":1,"docs":{"77":{"tf":1.4142135623730951}}}}},"d":{"d":{"_":{"df":0,"docs":{},"z":{"df":0,"docs":{},"e":{"df":0,"docs":{},"r":{"df":0,"docs":{},"o":{"df":1,"docs":{"26":{"tf":1.4142135623730951}}}}}}},"df":0,"docs":{}},"df":0,"docs":{}},"df":0,"docs":{},"e":{"df":0,"docs":{},"s":{"df":0,"docs":{},"o":{"df":0,"docs":{},"p":{"df":6,"docs":{"3":{"tf":2.449489742783178},"37":{"tf":1.0},"4":{"tf":2.449489742783178},"65":{"tf":1.4142135623730951},"75":{"tf":1.4142135623730951},"76":{"tf":1.0}}}}}},"p":{"df":0,"docs":{},"p":{"df":0,"docs":{},"l":{"df":0,"docs":{},"i":{"df":16,"docs":{"10":{"tf":1.7320508075688772},"11":{"tf":2.23606797749979},"12":{"tf":2.23606797749979},"22":{"tf":1.4142135623730951},"23":{"tf":1.4142135623730951},"35":{"tf":1.4142135623730951},"4":{"tf":1.0},"5":{"tf":1.0},"50":{"tf":1.0},"56":{"tf":2.0},"6":{"tf":2.6457513110645907},"65":{"tf":2.0},"7":{"tf":1.7320508075688772},"74":{"tf":1.4142135623730951},"8":{"tf":1.4142135623730951},"9":{"tf":2.0}}},"y":{"_":{"a":{"df":0,"docs":{},"s":{"df":0,"docs":{},"s":{"df":0,"docs":{},"u":{"df":0,"docs":{},"m":{"df":0,"docs":{},"p":{"df":0,"docs":{},"t":{"df":2,"docs":{"10":{"tf":1.7320508075688772},"5":{"tf":2.8284271247461903}}}}}}}}},"df":0,"docs":{}},"df":0,"docs":{}}}}},"r":{"df":0,"docs":{},"i":{"df":0,"docs":{},"t":{"df":0,"docs":{},"h":{"df":0,"docs":{},"m":{"df":0,"docs":{},"e":{"df":0,"docs":{},"t":{"df":2,"docs":{"51":{"tf":1.0},"53":{"tf":1.0}}}}}}}}},"s":{"df":0,"docs":{},"s":{"df":0,"docs":{},"o":{"c":{"df":1,"docs":{"68":{"tf":1.4142135623730951}}},"df":0,"docs":{}},"u":{"df":0,"docs":{},"m":{"df":0,"docs":{},"p":{"df":0,"docs":{},"t":{"df":7,"docs":{"13":{"tf":2.23606797749979},"14":{"tf":1.4142135623730951},"15":{"tf":1.0},"34":{"tf":1.7320508075688772},"42":{"tf":1.0},"48":{"tf":1.0},"50":{"tf":1.4142135623730951}}}}}}}},"t":{"df":0,"docs":{},"t":{"df":0,"docs":{},"r":{"df":0,"docs":{},"i":{"b":{"df":0,"docs":{},"u":{"df":0,"docs":{},"t":{"df":2,"docs":{"60":{"tf":1.4142135623730951},"68":{"tf":1.0}}}}},"df":0,"docs":{}}}}}},"b":{"`":{"df":0,"docs":{},"と":{"`":{"df":0,"docs":{},"g":{"df":1,"docs":{"68":{"tf":1.0}}}},"df":0,"docs":{}}},"df":10,"docs":{"11":{"tf":2.0},"31":{"tf":2.0},"37":{"tf":2.449489742783178},"53":{"tf":1.7320508075688772},"58":{"tf":2.0},"63":{"tf":2.449489742783178},"64":{"tf":3.3166247903554},"68":{"tf":4.0},"73":{"tf":1.4142135623730951},"77":{"tf":4.123105625617661}},"o":{"df":0,"docs":{},"o":{"df":0,"docs":{},"l":{"df":1,"docs":{"66":{"tf":1.4142135623730951}}}}},"s":{"df":1,"docs":{"26":{"tf":1.7320508075688772}}},"y":{"_":{"c":{"a":{"df":0,"docs":{},"s":{"df":1,"docs":{"15":{"tf":2.449489742783178}}}},"df":0,"docs":{},"o":{"df":0,"docs":{},"n":{"df":0,"docs":{},"t":{"df":0,"docs":{},"r":{"a":{"df":1,"docs":{"16":{"tf":2.449489742783178}}},"df":0,"docs":{}}}}}},"df":0,"docs":{}},"df":0,"docs":{}}},"c":{"`":{"df":0,"docs":{},"の":{"df":0,"docs":{},"合":{"df":0,"docs":{},"成":{"df":0,"docs":{},"を":{"`":{"df":0,"docs":{},"f":{"df":1,"docs":{"68":{"tf":1.0}}}},"df":0,"docs":{}}}}}},"a":{"df":0,"docs":{},"l":{"c":{"df":2,"docs":{"19":{"tf":2.0},"59":{"tf":1.0}}},"df":0,"docs":{}},"s":{"df":0,"docs":{},"e":{"df":7,"docs":{"15":{"tf":1.4142135623730951},"20":{"tf":3.1622776601683795},"21":{"tf":2.8284271247461903},"22":{"tf":2.23606797749979},"23":{"tf":1.7320508075688772},"46":{"tf":1.4142135623730951},"73":{"tf":1.4142135623730951}}}},"t":{"df":0,"docs":{},"e":{"df":0,"docs":{},"g":{"df":0,"docs":{},"o":{"df":0,"docs":{},"r":{"df":0,"docs":{},"i":{"df":1,"docs":{"68":{"tf":1.4142135623730951}}},"y":{".":{"c":{"df":0,"docs":{},"o":{"df":0,"docs":{},"m":{"df":0,"docs":{},"p":{"df":1,"docs":{"68":{"tf":1.0}}}}}},"df":0,"docs":{},"h":{"df":0,"docs":{},"o":{"df":0,"docs":{},"g":{"df":1,"docs":{"68":{"tf":1.0}}}}},"{":{"df":0,"docs":{},"u":{"df":1,"docs":{"68":{"tf":1.0}}}}},"df":0,"docs":{}}}}}}}},"df":5,"docs":{"31":{"tf":2.0},"58":{"tf":1.4142135623730951},"63":{"tf":1.7320508075688772},"64":{"tf":1.4142135623730951},"68":{"tf":4.58257569495584}},"h":{"df":0,"docs":{},"o":{"df":0,"docs":{},"o":{"df":0,"docs":{},"s":{"df":2,"docs":{"24":{"tf":2.23606797749979},"25":{"tf":1.4142135623730951}}}}}},"i":{"df":1,"docs":{"66":{"tf":1.0}}},"l":{"a":{"df":0,"docs":{},"s":{"df":0,"docs":{},"s":{"df":1,"docs":{"68":{"tf":1.0}},"i":{"c":{"a":{"df":0,"docs":{},"l":{".":{"c":{"df":0,"docs":{},"h":{"df":0,"docs":{},"o":{"df":0,"docs":{},"i":{"c":{"df":1,"docs":{"25":{"tf":1.4142135623730951}}},"df":0,"docs":{}}}}},"df":0,"docs":{}},"df":0,"docs":{}}},"df":0,"docs":{}},"df":0,"docs":{}}}}},"df":0,"docs":{}},"o":{"df":0,"docs":{},"m":{"df":0,"docs":{},"p":{"_":{"a":{"df":0,"docs":{},"p":{"df":0,"docs":{},"p":{"df":0,"docs":{},"l":{"df":0,"docs":{},"i":{"df":2,"docs":{"4":{"tf":1.0},"65":{"tf":1.0}}}}}}},"df":0,"docs":{},"i":{"d":{"df":1,"docs":{"68":{"tf":1.4142135623730951}}},"df":0,"docs":{}}},"df":1,"docs":{"68":{"tf":2.6457513110645907}}}},"n":{"df":0,"docs":{},"g":{"df":0,"docs":{},"r":{"df":1,"docs":{"26":{"tf":3.0}},"u":{"df":0,"docs":{},"e":{"df":0,"docs":{},"n":{"c":{"df":1,"docs":{"26":{"tf":1.0}}},"df":0,"docs":{}}}}}},"s":{"df":0,"docs":{},"t":{"df":0,"docs":{},"r":{"df":0,"docs":{},"u":{"c":{"df":0,"docs":{},"t":{"df":0,"docs":{},"o":{"df":0,"docs":{},"r":{"df":4,"docs":{"27":{"tf":2.23606797749979},"28":{"tf":1.7320508075688772},"57":{"tf":2.8284271247461903},"67":{"tf":1.0}}}}}},"df":0,"docs":{}}}}},"t":{"df":0,"docs":{},"r":{"a":{"d":{"df":0,"docs":{},"i":{"c":{"df":0,"docs":{},"t":{"df":5,"docs":{"15":{"tf":1.0},"16":{"tf":1.0},"29":{"tf":2.6457513110645907},"49":{"tf":1.0},"76":{"tf":1.0}}}},"df":0,"docs":{}}},"df":0,"docs":{}},"df":0,"docs":{}}},"v":{"df":1,"docs":{"30":{"tf":2.0}},"e":{"df":0,"docs":{},"r":{"df":0,"docs":{},"t":{"df":1,"docs":{"31":{"tf":2.23606797749979}}}}}}}}},"d":{"df":3,"docs":{"58":{"tf":1.4142135623730951},"63":{"tf":1.7320508075688772},"68":{"tf":2.23606797749979}},"e":{"df":0,"docs":{},"f":{"df":4,"docs":{"38":{"tf":1.4142135623730951},"44":{"tf":1.0},"72":{"tf":1.0},"73":{"tf":1.0}}}},"o":{"df":0,"docs":{},"n":{"df":0,"docs":{},"e":{"df":4,"docs":{"12":{"tf":1.4142135623730951},"32":{"tf":2.0},"35":{"tf":1.0},"5":{"tf":1.0}}}}},"s":{"df":0,"docs":{},"i":{"df":0,"docs":{},"m":{"df":0,"docs":{},"p":{"df":2,"docs":{"38":{"tf":1.0},"71":{"tf":1.7320508075688772}}}}}}},"df":0,"docs":{},"e":{"df":2,"docs":{"63":{"tf":1.7320508075688772},"68":{"tf":1.4142135623730951}},"v":{"df":0,"docs":{},"e":{"df":0,"docs":{},"n":{"df":1,"docs":{"59":{"tf":1.7320508075688772}}}}},"x":{"a":{"c":{"df":0,"docs":{},"t":{"df":30,"docs":{"11":{"tf":1.0},"14":{"tf":1.7320508075688772},"17":{"tf":1.0},"18":{"tf":1.0},"20":{"tf":1.4142135623730951},"21":{"tf":1.4142135623730951},"23":{"tf":1.0},"24":{"tf":1.0},"25":{"tf":1.0},"26":{"tf":1.0},"27":{"tf":1.7320508075688772},"31":{"tf":1.4142135623730951},"33":{"tf":2.6457513110645907},"34":{"tf":1.7320508075688772},"35":{"tf":3.3166247903554},"39":{"tf":1.0},"40":{"tf":1.4142135623730951},"48":{"tf":1.0},"5":{"tf":1.0},"54":{"tf":1.0},"55":{"tf":1.4142135623730951},"57":{"tf":2.449489742783178},"6":{"tf":1.7320508075688772},"64":{"tf":1.0},"65":{"tf":2.23606797749979},"67":{"tf":1.4142135623730951},"7":{"tf":1.0},"74":{"tf":1.0},"75":{"tf":1.4142135623730951},"9":{"tf":1.7320508075688772}}}},"df":0,"docs":{},"m":{"df":0,"docs":{},"p":{"df":0,"docs":{},"l":{"df":61,"docs":{"11":{"tf":1.0},"13":{"tf":1.0},"15":{"tf":1.0},"16":{"tf":1.0},"17":{"tf":1.4142135623730951},"18":{"tf":1.0},"20":{"tf":1.0},"21":{"tf":1.0},"22":{"tf":1.0},"23":{"tf":1.4142135623730951},"24":{"tf":1.0},"25":{"tf":1.0},"26":{"tf":1.4142135623730951},"27":{"tf":1.4142135623730951},"28":{"tf":1.0},"29":{"tf":2.0},"3":{"tf":1.0},"31":{"tf":1.0},"33":{"tf":1.4142135623730951},"35":{"tf":1.4142135623730951},"36":{"tf":1.0},"37":{"tf":1.0},"38":{"tf":1.0},"39":{"tf":1.0},"4":{"tf":1.0},"40":{"tf":1.0},"42":{"tf":1.0},"43":{"tf":1.0},"44":{"tf":1.0},"45":{"tf":1.0},"46":{"tf":1.0},"47":{"tf":1.0},"48":{"tf":1.4142135623730951},"49":{"tf":1.0},"5":{"tf":1.4142135623730951},"50":{"tf":1.4142135623730951},"51":{"tf":1.4142135623730951},"52":{"tf":1.0},"53":{"tf":1.0},"54":{"tf":1.4142135623730951},"55":{"tf":1.0},"56":{"tf":1.0},"57":{"tf":1.4142135623730951},"58":{"tf":1.4142135623730951},"59":{"tf":1.0},"6":{"tf":1.4142135623730951},"60":{"tf":1.4142135623730951},"61":{"tf":1.7320508075688772},"62":{"tf":1.4142135623730951},"63":{"tf":1.0},"64":{"tf":1.0},"65":{"tf":1.4142135623730951},"67":{"tf":1.0},"68":{"tf":1.0},"7":{"tf":1.0},"73":{"tf":1.0},"74":{"tf":1.0},"75":{"tf":2.0},"76":{"tf":1.4142135623730951},"77":{"tf":1.0},"9":{"tf":1.0}}}}}},"df":0,"docs":{},"i":{"df":0,"docs":{},"s":{"df":0,"docs":{},"t":{"df":5,"docs":{"25":{"tf":1.0},"36":{"tf":2.449489742783178},"43":{"tf":1.0},"54":{"tf":1.0},"59":{"tf":1.0}}}}},"p":{"df":0,"docs":{},"l":{"df":0,"docs":{},"o":{"d":{"df":1,"docs":{"12":{"tf":1.4142135623730951}}},"df":0,"docs":{},"s":{"df":0,"docs":{},"i":{"df":0,"docs":{},"o":{"df":0,"docs":{},"n":{")":{"df":0,"docs":{},"と":{"df":0,"docs":{},"呼":{"df":0,"docs":{},"び":{"df":0,"docs":{},"ま":{"df":0,"docs":{},"す":{"df":0,"docs":{},"が":{"df":0,"docs":{},"，":{"c":{"df":0,"docs":{},"o":{"df":0,"docs":{},"n":{"df":0,"docs":{},"t":{"df":0,"docs":{},"r":{"a":{"d":{"df":0,"docs":{},"i":{"c":{"df":0,"docs":{},"t":{"df":1,"docs":{"29":{"tf":1.0}}}},"df":0,"docs":{}}},"df":0,"docs":{}},"df":0,"docs":{}}}}}},"df":0,"docs":{}}}}}}}}},"df":0,"docs":{}}}}}}}},"t":{"df":1,"docs":{"37":{"tf":2.449489742783178}},"e":{"df":0,"docs":{},"n":{"df":0,"docs":{},"s":{"df":0,"docs":{},"i":{"df":0,"docs":{},"o":{"df":0,"docs":{},"n":{"df":1,"docs":{"37":{"tf":1.0}}}}}}}}}}},"f":{"a":{"c":{"df":2,"docs":{"44":{"tf":2.6457513110645907},"45":{"tf":1.7320508075688772}}},"df":0,"docs":{},"l":{"df":0,"docs":{},"s":{"df":7,"docs":{"16":{"tf":1.4142135623730951},"29":{"tf":1.4142135623730951},"49":{"tf":2.0},"5":{"tf":1.0},"52":{"tf":1.0},"7":{"tf":1.7320508075688772},"76":{"tf":1.0}}}}},"df":12,"docs":{"11":{"tf":2.23606797749979},"24":{"tf":2.8284271247461903},"25":{"tf":3.0},"26":{"tf":3.7416573867739413},"3":{"tf":2.23606797749979},"31":{"tf":1.7320508075688772},"37":{"tf":1.7320508075688772},"38":{"tf":2.449489742783178},"4":{"tf":1.7320508075688772},"63":{"tf":1.7320508075688772},"65":{"tf":2.23606797749979},"68":{"tf":3.605551275463989}},"e":{"df":0,"docs":{},"r":{"df":0,"docs":{},"m":{"a":{"df":0,"docs":{},"t":{"df":1,"docs":{"72":{"tf":1.0}},"l":{"a":{"df":0,"docs":{},"s":{"df":0,"docs":{},"t":{"df":0,"docs":{},"t":{"df":0,"docs":{},"h":{"df":0,"docs":{},"e":{"df":0,"docs":{},"o":{"df":0,"docs":{},"r":{"df":0,"docs":{},"e":{"df":0,"docs":{},"m":{"df":1,"docs":{"72":{"tf":1.4142135623730951}}}}}}}}}}}},"df":0,"docs":{}}}},"df":0,"docs":{}}}},"l":{"df":0,"docs":{},"t":{"df":1,"docs":{"72":{"tf":1.0}}}},"u":{"df":0,"docs":{},"n":{"df":4,"docs":{"17":{"tf":1.0},"18":{"tf":1.0},"25":{"tf":1.4142135623730951},"38":{"tf":1.4142135623730951}},"e":{"df":0,"docs":{},"x":{"df":0,"docs":{},"t":{"df":1,"docs":{"38":{"tf":2.23606797749979}}}}}}}},"g":{"df":10,"docs":{"11":{"tf":1.7320508075688772},"24":{"tf":2.8284271247461903},"26":{"tf":2.23606797749979},"3":{"tf":1.7320508075688772},"37":{"tf":1.7320508075688772},"38":{"tf":2.449489742783178},"4":{"tf":1.4142135623730951},"64":{"tf":1.7320508075688772},"65":{"tf":1.7320508075688772},"68":{"tf":2.6457513110645907}},"e":{"_":{"df":0,"docs":{},"i":{"df":0,"docs":{},"f":{"df":0,"docs":{},"f":{"_":{"df":0,"docs":{},"l":{"df":1,"docs":{"73":{"tf":1.4142135623730951}}}},"df":0,"docs":{}}}}},"df":0,"docs":{},"n":{"df":0,"docs":{},"e":{"df":0,"docs":{},"r":{"a":{"df":0,"docs":{},"r":{"df":1,"docs":{"77":{"tf":1.0}}}},"df":1,"docs":{"46":{"tf":1.0}}}}}},"o":{"a":{"df":0,"docs":{},"l":{"df":1,"docs":{"27":{"tf":1.0}}}},"df":0,"docs":{}},"r":{"df":0,"docs":{},"o":{"df":0,"docs":{},"u":{"df":0,"docs":{},"p":{"df":2,"docs":{"11":{"tf":1.4142135623730951},"64":{"tf":1.0}}}}}},"u":{"a":{"df":0,"docs":{},"r":{"d":{"_":{"df":0,"docs":{},"h":{"df":0,"docs":{},"y":{"df":0,"docs":{},"p":{"df":8,"docs":{"15":{"tf":1.4142135623730951},"24":{"tf":1.4142135623730951},"39":{"tf":2.23606797749979},"46":{"tf":1.7320508075688772},"47":{"tf":1.0},"59":{"tf":1.4142135623730951},"73":{"tf":1.4142135623730951},"77":{"tf":1.7320508075688772}}}}}},"df":0,"docs":{}},"df":0,"docs":{}}},"df":0,"docs":{}}},"h":{".":{"df":0,"docs":{},"l":{"df":0,"docs":{},"e":{"df":0,"docs":{},"f":{"df":0,"docs":{},"t":{"df":1,"docs":{"27":{"tf":1.4142135623730951}}}}}},"r":{"df":0,"docs":{},"i":{"df":0,"docs":{},"g":{"df":0,"docs":{},"h":{"df":0,"docs":{},"t":{"df":1,"docs":{"27":{"tf":1.0}}}}}}}},"1":{"df":4,"docs":{"51":{"tf":1.0},"52":{"tf":1.0},"58":{"tf":2.0},"63":{"tf":1.4142135623730951}}},"2":{"df":4,"docs":{"51":{"tf":1.0},"52":{"tf":1.0},"58":{"tf":1.4142135623730951},"63":{"tf":1.4142135623730951}}},"a":{"b":{"df":1,"docs":{"63":{"tf":1.7320508075688772}}},"df":0,"docs":{}},"c":{"df":1,"docs":{"31":{"tf":1.4142135623730951}}},"df":31,"docs":{"11":{"tf":1.4142135623730951},"12":{"tf":1.0},"15":{"tf":1.0},"16":{"tf":2.0},"17":{"tf":1.0},"20":{"tf":2.23606797749979},"21":{"tf":1.7320508075688772},"22":{"tf":1.4142135623730951},"23":{"tf":2.449489742783178},"24":{"tf":1.4142135623730951},"25":{"tf":1.7320508075688772},"26":{"tf":2.0},"27":{"tf":1.4142135623730951},"29":{"tf":1.7320508075688772},"31":{"tf":3.0},"40":{"tf":1.4142135623730951},"46":{"tf":1.7320508075688772},"48":{"tf":1.4142135623730951},"49":{"tf":1.7320508075688772},"53":{"tf":1.0},"54":{"tf":1.4142135623730951},"56":{"tf":1.7320508075688772},"59":{"tf":1.7320508075688772},"6":{"tf":2.8284271247461903},"63":{"tf":2.449489742783178},"68":{"tf":3.1622776601683795},"73":{"tf":3.1622776601683795},"75":{"tf":1.4142135623730951},"76":{"tf":1.0},"77":{"tf":2.23606797749979},"9":{"tf":1.4142135623730951}},"e":{"a":{"d":{"df":1,"docs":{"5":{"tf":1.4142135623730951}}},"df":0,"docs":{}},"df":0,"docs":{},"l":{"df":0,"docs":{},"p":{"df":1,"docs":{"1":{"tf":1.0}}}}},"f":{"df":2,"docs":{"24":{"tf":2.0},"26":{"tf":1.4142135623730951}}},"g":{"df":1,"docs":{"24":{"tf":1.7320508075688772}},"f":{"df":0,"docs":{},"i":{"df":0,"docs":{},"n":{"df":0,"docs":{},"j":{"df":3,"docs":{"3":{"tf":1.0},"4":{"tf":1.4142135623730951},"65":{"tf":1.4142135623730951}}}}}}},"k":{"df":1,"docs":{"59":{"tf":2.6457513110645907}}},"n":{"df":2,"docs":{"59":{"tf":1.4142135623730951},"7":{"tf":2.0}},"e":{"_":{"df":0,"docs":{},"s":{"df":0,"docs":{},"t":{"df":1,"docs":{"25":{"tf":1.4142135623730951}}}}},"df":0,"docs":{}},"n":{"df":0,"docs":{},"p":{"df":1,"docs":{"15":{"tf":1.0}}}},"p":{"df":1,"docs":{"29":{"tf":1.0}}},"q":{"df":2,"docs":{"16":{"tf":1.4142135623730951},"49":{"tf":1.4142135623730951}}}},"o":{"df":0,"docs":{},"g":{"df":0,"docs":{},"e":{"df":1,"docs":{"68":{"tf":1.0}}}},"m":{"df":1,"docs":{"68":{"tf":4.0}}}},"p":{"df":27,"docs":{"13":{"tf":1.0},"15":{"tf":1.7320508075688772},"16":{"tf":1.0},"17":{"tf":2.0},"18":{"tf":2.0},"20":{"tf":1.4142135623730951},"21":{"tf":1.4142135623730951},"22":{"tf":1.4142135623730951},"23":{"tf":2.23606797749979},"27":{"tf":1.4142135623730951},"29":{"tf":1.0},"33":{"tf":2.8284271247461903},"39":{"tf":1.7320508075688772},"40":{"tf":1.7320508075688772},"42":{"tf":1.0},"48":{"tf":1.7320508075688772},"49":{"tf":2.0},"5":{"tf":1.4142135623730951},"50":{"tf":1.4142135623730951},"55":{"tf":1.4142135623730951},"56":{"tf":1.4142135623730951},"57":{"tf":2.0},"6":{"tf":2.23606797749979},"65":{"tf":1.4142135623730951},"67":{"tf":1.4142135623730951},"7":{"tf":1.4142135623730951},"9":{"tf":1.4142135623730951}},"q":{"df":10,"docs":{"17":{"tf":2.0},"18":{"tf":1.7320508075688772},"35":{"tf":1.4142135623730951},"40":{"tf":1.7320508075688772},"42":{"tf":1.4142135623730951},"48":{"tf":1.7320508075688772},"5":{"tf":1.7320508075688772},"56":{"tf":1.4142135623730951},"63":{"tf":2.0},"65":{"tf":1.4142135623730951}}},"r":{"df":4,"docs":{"20":{"tf":1.4142135623730951},"21":{"tf":1.4142135623730951},"22":{"tf":1.4142135623730951},"23":{"tf":1.4142135623730951}}}},"q":{"df":15,"docs":{"20":{"tf":1.4142135623730951},"21":{"tf":1.4142135623730951},"22":{"tf":1.4142135623730951},"23":{"tf":2.23606797749979},"27":{"tf":1.4142135623730951},"33":{"tf":1.7320508075688772},"35":{"tf":1.4142135623730951},"40":{"tf":1.7320508075688772},"42":{"tf":1.0},"48":{"tf":1.7320508075688772},"49":{"tf":1.4142135623730951},"5":{"tf":1.0},"55":{"tf":1.4142135623730951},"57":{"tf":2.0},"67":{"tf":1.4142135623730951}},"n":{"df":1,"docs":{"5":{"tf":1.4142135623730951}}},"r":{"df":11,"docs":{"17":{"tf":2.0},"18":{"tf":1.7320508075688772},"20":{"tf":1.4142135623730951},"21":{"tf":1.4142135623730951},"22":{"tf":1.4142135623730951},"23":{"tf":1.4142135623730951},"35":{"tf":1.4142135623730951},"40":{"tf":1.7320508075688772},"48":{"tf":1.7320508075688772},"5":{"tf":1.0},"65":{"tf":1.4142135623730951}}}},"r":{"df":2,"docs":{"57":{"tf":2.0},"65":{"tf":1.4142135623730951}}},"x":{"df":3,"docs":{"28":{"tf":1.4142135623730951},"43":{"tf":2.0},"73":{"tf":1.7320508075688772}}},"y":{"df":1,"docs":{"43":{"tf":1.4142135623730951}},"p":{"df":1,"docs":{"48":{"tf":1.0}}}}},"i":{"d":{"_":{"c":{"df":0,"docs":{},"o":{"df":0,"docs":{},"m":{"df":0,"docs":{},"p":{"df":1,"docs":{"68":{"tf":1.4142135623730951}}}}}},"df":0,"docs":{}},"df":2,"docs":{"51":{"tf":1.7320508075688772},"68":{"tf":2.449489742783178}}},"df":0,"docs":{},"f":{"df":0,"docs":{},"f":{".":{"df":0,"docs":{},"m":{"df":0,"docs":{},"p":{"df":0,"docs":{},"r":{"df":1,"docs":{"74":{"tf":1.0}}}}}},"df":0,"docs":{}}},"h":{"df":4,"docs":{"44":{"tf":1.0},"45":{"tf":1.7320508075688772},"46":{"tf":1.4142135623730951},"47":{"tf":1.4142135623730951}}},"m":{"df":0,"docs":{},"p":{"df":0,"docs":{},"o":{"df":0,"docs":{},"r":{"df":0,"docs":{},"t":{"df":26,"docs":{"11":{"tf":1.0},"16":{"tf":1.0},"18":{"tf":1.0},"22":{"tf":1.0},"23":{"tf":1.0},"24":{"tf":1.0},"3":{"tf":1.0},"31":{"tf":1.0},"35":{"tf":1.0},"37":{"tf":1.0},"39":{"tf":1.0},"45":{"tf":1.0},"5":{"tf":1.0},"50":{"tf":1.0},"51":{"tf":1.0},"53":{"tf":1.0},"54":{"tf":1.0},"58":{"tf":1.0},"59":{"tf":1.0},"60":{"tf":1.7320508075688772},"61":{"tf":1.0},"62":{"tf":1.0},"64":{"tf":1.0},"65":{"tf":1.0},"75":{"tf":1.0},"77":{"tf":1.0}}}}}}},"n":{"d":{"df":0,"docs":{},"u":{"c":{"df":0,"docs":{},"t":{"df":5,"docs":{"44":{"tf":2.6457513110645907},"45":{"tf":2.23606797749979},"46":{"tf":1.7320508075688772},"47":{"tf":1.4142135623730951},"60":{"tf":1.0}}}},"df":0,"docs":{}}},"df":0,"docs":{},"f":{"df":0,"docs":{},"i":{"df":0,"docs":{},"x":{"df":0,"docs":{},"r":{":":{"8":{"0":{"df":1,"docs":{"68":{"tf":1.0}}},"df":0,"docs":{}},"df":0,"docs":{}},"df":0,"docs":{}}}},"o":{"df":0,"docs":{},"v":{"df":0,"docs":{},"i":{"df":0,"docs":{},"e":{"df":0,"docs":{},"w":{"df":1,"docs":{"65":{"tf":1.0}}}}}}}},"j":{"df":0,"docs":{},"e":{"c":{"df":0,"docs":{},"t":{"df":3,"docs":{"3":{"tf":1.7320508075688772},"4":{"tf":1.7320508075688772},"65":{"tf":1.7320508075688772}}}},"df":0,"docs":{}}},"l":{"df":4,"docs":{"15":{"tf":1.0},"20":{"tf":1.7320508075688772},"21":{"tf":1.4142135623730951},"73":{"tf":1.0}}},"r":{"df":4,"docs":{"15":{"tf":1.0},"20":{"tf":1.7320508075688772},"21":{"tf":1.4142135623730951},"73":{"tf":1.0}}},"s":{"df":0,"docs":{},"e":{"df":0,"docs":{},"r":{"df":0,"docs":{},"t":{"df":1,"docs":{"20":{"tf":1.4142135623730951}}}}}},"t":{"df":5,"docs":{"26":{"tf":2.0},"54":{"tf":1.4142135623730951},"58":{"tf":1.4142135623730951},"59":{"tf":1.0},"73":{"tf":1.7320508075688772}},"r":{"df":0,"docs":{},"o":{"d":{"df":0,"docs":{},"u":{"c":{"df":1,"docs":{"48":{"tf":1.0}}},"df":0,"docs":{}}},"df":20,"docs":{"15":{"tf":1.0},"16":{"tf":1.0},"17":{"tf":1.0},"18":{"tf":1.0},"20":{"tf":1.0},"21":{"tf":1.0},"22":{"tf":1.0},"23":{"tf":1.4142135623730951},"25":{"tf":1.0},"28":{"tf":1.0},"3":{"tf":1.0},"37":{"tf":1.0},"4":{"tf":1.0},"40":{"tf":1.0},"48":{"tf":2.8284271247461903},"49":{"tf":2.0},"5":{"tf":1.0},"54":{"tf":1.0},"59":{"tf":1.0},"65":{"tf":1.0}}}}}},"t":{"df":0,"docs":{},"e":{"_":{"df":0,"docs":{},"f":{"a":{"df":0,"docs":{},"l":{"df":0,"docs":{},"s":{"df":1,"docs":{"73":{"tf":1.0}}}}},"df":0,"docs":{}},"t":{"df":0,"docs":{},"r":{"df":0,"docs":{},"u":{"df":1,"docs":{"73":{"tf":1.0}}}}}},"df":0,"docs":{}}}},"k":{"df":3,"docs":{"45":{"tf":1.4142135623730951},"47":{"tf":1.7320508075688772},"59":{"tf":3.3166247903554}}},"l":{".":{"df":0,"docs":{},"l":{"df":0,"docs":{},"e":{"df":0,"docs":{},"n":{"df":0,"docs":{},"g":{"df":0,"docs":{},"t":{"df":0,"docs":{},"h":{"df":1,"docs":{"46":{"tf":1.0}}}}}}}}},"df":1,"docs":{"46":{"tf":3.1622776601683795}},"e":{"a":{"df":0,"docs":{},"n":{".":{"df":0,"docs":{},"m":{"df":0,"docs":{},"v":{"a":{"df":0,"docs":{},"r":{"df":0,"docs":{},"i":{"d":{".":{"df":0,"docs":{},"r":{"df":0,"docs":{},"e":{"df":0,"docs":{},"f":{"df":0,"docs":{},"l":{"df":1,"docs":{"61":{"tf":1.0}}}}},"f":{"df":0,"docs":{},"l":{"df":1,"docs":{"61":{"tf":1.0}}}}}},"df":0,"docs":{}},"df":0,"docs":{}}}},"df":0,"docs":{}}}},"4":{"df":5,"docs":{"0":{"tf":1.7320508075688772},"1":{"tf":1.0},"19":{"tf":1.0},"2":{"tf":1.0},"30":{"tf":1.0}}},"df":8,"docs":{"0":{"tf":1.0},"17":{"tf":1.0},"2":{"tf":2.0},"44":{"tf":1.0},"49":{"tf":1.0},"7":{"tf":1.0},"73":{"tf":1.0},"77":{"tf":1.0}}}},"df":0,"docs":{},"f":{"df":0,"docs":{},"t":{"df":3,"docs":{"20":{"tf":1.0},"27":{"tf":1.0},"50":{"tf":2.449489742783178}}}}},"i":{"df":0,"docs":{},"n":{"a":{"df":0,"docs":{},"r":{"df":0,"docs":{},"i":{"df":0,"docs":{},"t":{"df":0,"docs":{},"h":{"df":5,"docs":{"51":{"tf":3.3166247903554},"52":{"tf":1.7320508075688772},"53":{"tf":1.7320508075688772},"54":{"tf":1.0},"73":{"tf":1.4142135623730951}}}}}}},"df":0,"docs":{},"e":{"a":{"df":0,"docs":{},"r":{"df":2,"docs":{"51":{"tf":1.0},"53":{"tf":1.0}}}},"df":0,"docs":{}}},"s":{"df":0,"docs":{},"t":{".":{"df":0,"docs":{},"l":{"df":0,"docs":{},"e":{"df":0,"docs":{},"n":{"df":0,"docs":{},"g":{"df":0,"docs":{},"t":{"df":0,"docs":{},"h":{"df":1,"docs":{"46":{"tf":1.7320508075688772}}}}}}}}},"df":1,"docs":{"46":{"tf":1.7320508075688772}}}}},"o":{"df":0,"docs":{},"s":{"df":0,"docs":{},"s":{"df":1,"docs":{"77":{"tf":1.0}}}}}},"m":{"a":{"df":0,"docs":{},"t":{"c":{"df":0,"docs":{},"h":{"df":1,"docs":{"47":{"tf":1.0}}}},"df":0,"docs":{},"h":{"df":0,"docs":{},"e":{"df":0,"docs":{},"m":{"a":{"df":0,"docs":{},"t":{"df":1,"docs":{"2":{"tf":1.0}}}},"df":0,"docs":{}}},"l":{"df":0,"docs":{},"i":{"b":{".":{"d":{"a":{"df":0,"docs":{},"t":{"a":{".":{"df":0,"docs":{},"n":{"a":{"df":0,"docs":{},"t":{".":{"b":{"a":{"df":0,"docs":{},"s":{"df":1,"docs":{"60":{"tf":1.0}}}},"df":0,"docs":{}},"df":0,"docs":{}},"df":0,"docs":{}}},"df":0,"docs":{}},"s":{"df":0,"docs":{},"e":{"df":0,"docs":{},"t":{"df":0,"docs":{},"l":{"df":0,"docs":{},"i":{"df":0,"docs":{},"k":{"df":0,"docs":{},"e":{".":{"b":{"a":{"df":0,"docs":{},"s":{"df":1,"docs":{"37":{"tf":1.0}}}},"df":0,"docs":{}},"df":0,"docs":{}},"df":0,"docs":{}}}}}}}}},"df":0,"docs":{}},"df":0,"docs":{}}},"df":0,"docs":{}},"df":0,"docs":{},"t":{"a":{"c":{"df":0,"docs":{},"t":{"df":0,"docs":{},"i":{"c":{".":{"b":{"df":0,"docs":{},"y":{"c":{"df":0,"docs":{},"o":{"df":0,"docs":{},"n":{"df":0,"docs":{},"t":{"df":0,"docs":{},"r":{"a":{"df":1,"docs":{"16":{"tf":1.0}}},"df":0,"docs":{}}}}}},"df":0,"docs":{}}},"c":{"a":{"df":0,"docs":{},"s":{"df":2,"docs":{"22":{"tf":1.0},"45":{"tf":1.0}}}},"df":0,"docs":{},"h":{"df":0,"docs":{},"o":{"df":0,"docs":{},"o":{"df":0,"docs":{},"s":{"df":1,"docs":{"24":{"tf":1.0}}}}}},"o":{"df":0,"docs":{},"n":{"df":0,"docs":{},"v":{"df":0,"docs":{},"e":{"df":0,"docs":{},"r":{"df":0,"docs":{},"t":{"df":1,"docs":{"31":{"tf":1.0}}}}}}}}},"df":0,"docs":{},"g":{"c":{"df":0,"docs":{},"o":{"df":0,"docs":{},"n":{"df":0,"docs":{},"g":{"df":0,"docs":{},"r":{"df":1,"docs":{"58":{"tf":1.0}}}}}}},"df":0,"docs":{}},"l":{"df":0,"docs":{},"e":{"df":0,"docs":{},"f":{"df":0,"docs":{},"t":{"df":0,"docs":{},"r":{"df":0,"docs":{},"i":{"df":0,"docs":{},"g":{"df":0,"docs":{},"h":{"df":0,"docs":{},"t":{"df":1,"docs":{"50":{"tf":1.0}}}}}}}}}},"i":{"b":{"df":0,"docs":{},"r":{"a":{"df":0,"docs":{},"r":{"df":0,"docs":{},"y":{"df":0,"docs":{},"s":{"df":0,"docs":{},"e":{"a":{"df":0,"docs":{},"r":{"c":{"df":0,"docs":{},"h":{"df":2,"docs":{"11":{"tf":1.0},"35":{"tf":1.0}}}},"df":0,"docs":{}}},"df":0,"docs":{}}}}}},"df":0,"docs":{}}},"df":0,"docs":{},"n":{"a":{"df":0,"docs":{},"r":{"df":0,"docs":{},"i":{"df":0,"docs":{},"t":{"df":0,"docs":{},"h":{"df":2,"docs":{"51":{"tf":1.0},"53":{"tf":1.0}}}}}}},"df":0,"docs":{}}}},"n":{"df":0,"docs":{},"t":{"df":0,"docs":{},"h":{"df":0,"docs":{},"r":{"df":0,"docs":{},"e":{"df":0,"docs":{},"w":{"df":0,"docs":{},"r":{"df":0,"docs":{},"i":{"df":0,"docs":{},"t":{"df":1,"docs":{"64":{"tf":1.0}}}}}}}}}}},"p":{"df":0,"docs":{},"u":{"df":0,"docs":{},"s":{"df":0,"docs":{},"h":{"df":0,"docs":{},"n":{"df":0,"docs":{},"e":{"df":0,"docs":{},"g":{"df":1,"docs":{"54":{"tf":1.0}}}}}}}}},"r":{"df":1,"docs":{"62":{"tf":1.0}},"e":{"df":0,"docs":{},"l":{"a":{"df":0,"docs":{},"t":{"df":0,"docs":{},"i":{"df":0,"docs":{},"o":{"df":0,"docs":{},"n":{".":{"df":0,"docs":{},"r":{"df":0,"docs":{},"f":{"df":0,"docs":{},"l":{"df":2,"docs":{"60":{"tf":1.0},"61":{"tf":1.4142135623730951}}}}}},"df":0,"docs":{}}}}}},"df":0,"docs":{}}}},"s":{"a":{"df":0,"docs":{},"y":{"df":1,"docs":{"65":{"tf":1.0}}}},"df":0,"docs":{},"o":{"df":0,"docs":{},"l":{"df":0,"docs":{},"v":{"df":0,"docs":{},"e":{"b":{"df":0,"docs":{},"y":{"df":0,"docs":{},"e":{"df":0,"docs":{},"l":{"df":0,"docs":{},"i":{"df":0,"docs":{},"m":{"df":1,"docs":{"5":{"tf":1.0}}}}}}}},"df":0,"docs":{}}}}}},"t":{"a":{"df":0,"docs":{},"u":{"df":0,"docs":{},"t":{"df":0,"docs":{},"o":{"df":1,"docs":{"75":{"tf":1.0}}}}}},"df":0,"docs":{}},"w":{"df":0,"docs":{},"l":{"df":0,"docs":{},"o":{"df":0,"docs":{},"g":{"df":1,"docs":{"77":{"tf":1.0}}}}}}},"df":0,"docs":{}},"df":0,"docs":{}}}},"df":0,"docs":{}},"df":0,"docs":{}}},"4":{"df":2,"docs":{"2":{"tf":1.0},"50":{"tf":1.0}}},"df":0,"docs":{}},"df":0,"docs":{}}}}}},"df":1,"docs":{"47":{"tf":1.7320508075688772}},"o":{"df":0,"docs":{},"n":{"df":0,"docs":{},"o":{"df":0,"docs":{},"i":{"d":{"df":0,"docs":{},"h":{"df":0,"docs":{},"o":{"df":0,"docs":{},"m":{".":{"df":0,"docs":{},"m":{"a":{"df":0,"docs":{},"p":{"_":{"df":0,"docs":{},"m":{"df":0,"docs":{},"u":{"df":0,"docs":{},"l":{"df":1,"docs":{"11":{"tf":1.0}}}}}},"df":0,"docs":{}}},"df":0,"docs":{}}},"df":0,"docs":{}}}}},"df":0,"docs":{}}}}},"u":{"df":0,"docs":{},"l":{"_":{"df":0,"docs":{},"i":{"df":0,"docs":{},"n":{"df":0,"docs":{},"v":{"_":{"df":0,"docs":{},"e":{"df":0,"docs":{},"q":{"_":{"df":0,"docs":{},"i":{"df":0,"docs":{},"f":{"df":0,"docs":{},"f":{"_":{"df":0,"docs":{},"e":{"df":0,"docs":{},"q":{"_":{"df":0,"docs":{},"m":{"df":0,"docs":{},"u":{"df":0,"docs":{},"l":{"df":1,"docs":{"64":{"tf":1.4142135623730951}}}}}},"df":0,"docs":{}}}},"df":0,"docs":{}}}}},"df":0,"docs":{}}}},"df":0,"docs":{}}}},"n":{"df":0,"docs":{},"e":{"df":0,"docs":{},"g":{"df":1,"docs":{"73":{"tf":1.0}}}}}},"df":0,"docs":{}}},"y":{"a":{"b":{"df":1,"docs":{"73":{"tf":2.23606797749979}}},"df":0,"docs":{}},"df":0,"docs":{},"e":{"df":0,"docs":{},"q":{".":{"df":0,"docs":{},"r":{"df":0,"docs":{},"e":{"df":0,"docs":{},"f":{"df":0,"docs":{},"l":{"df":1,"docs":{"60":{"tf":1.0}}}}}}},"df":1,"docs":{"60":{"tf":1.7320508075688772}}}}}},"n":{"a":{"df":0,"docs":{},"m":{"df":0,"docs":{},"e":{"df":11,"docs":{"23":{"tf":1.0},"26":{"tf":1.0},"37":{"tf":1.0},"48":{"tf":1.0},"51":{"tf":1.0},"53":{"tf":1.0},"54":{"tf":1.0},"58":{"tf":1.0},"60":{"tf":1.0},"75":{"tf":1.0},"77":{"tf":1.0}}}},"t":{".":{"d":{"df":0,"docs":{},"v":{"d":{"_":{"df":0,"docs":{},"i":{"df":0,"docs":{},"f":{"df":0,"docs":{},"f":{"_":{"d":{"df":0,"docs":{},"i":{"df":0,"docs":{},"v":{"_":{"df":0,"docs":{},"m":{"df":0,"docs":{},"u":{"df":0,"docs":{},"l":{"_":{"df":0,"docs":{},"e":{"df":0,"docs":{},"q":{"df":1,"docs":{"74":{"tf":1.0}}}}},"df":0,"docs":{}}}}},"df":0,"docs":{}}}},"df":0,"docs":{}},"df":0,"docs":{}}}}},"df":0,"docs":{}},"df":0,"docs":{}}},"df":0,"docs":{},"l":{"df":0,"docs":{},"t":{".":{"b":{"a":{"df":0,"docs":{},"s":{"df":1,"docs":{"35":{"tf":1.0}}}},"df":0,"docs":{}},"df":0,"docs":{}},"df":0,"docs":{}}},"m":{"df":0,"docs":{},"u":{"df":0,"docs":{},"l":{"_":{"a":{"df":0,"docs":{},"s":{"df":0,"docs":{},"s":{"df":0,"docs":{},"o":{"c":{"df":1,"docs":{"63":{"tf":1.4142135623730951}}},"df":0,"docs":{}}}}},"df":0,"docs":{}},"df":0,"docs":{}}}},"s":{"df":0,"docs":{},"t":{"df":0,"docs":{},"r":{"df":0,"docs":{},"o":{"df":0,"docs":{},"n":{"df":0,"docs":{},"g":{"_":{"df":0,"docs":{},"i":{"df":0,"docs":{},"n":{"d":{"df":0,"docs":{},"u":{"c":{"df":0,"docs":{},"t":{"df":0,"docs":{},"i":{"df":0,"docs":{},"o":{"df":0,"docs":{},"n":{"_":{"df":0,"docs":{},"o":{"df":0,"docs":{},"n":{"df":1,"docs":{"47":{"tf":1.0}}}}},"df":0,"docs":{}}}}}},"df":0,"docs":{}}},"df":0,"docs":{}}}},"df":0,"docs":{}}}}}}}},"df":15,"docs":{"12":{"tf":1.0},"28":{"tf":1.0},"29":{"tf":1.0},"31":{"tf":1.4142135623730951},"36":{"tf":1.0},"38":{"tf":1.4142135623730951},"44":{"tf":2.8284271247461903},"45":{"tf":1.0},"47":{"tf":1.4142135623730951},"48":{"tf":1.0},"53":{"tf":1.0},"60":{"tf":1.0},"63":{"tf":1.0},"72":{"tf":1.0},"77":{"tf":1.4142135623730951}}}},"df":8,"docs":{"44":{"tf":3.872983346207417},"45":{"tf":1.7320508075688772},"46":{"tf":2.0},"47":{"tf":3.3166247903554},"48":{"tf":1.7320508075688772},"59":{"tf":3.7416573867739413},"60":{"tf":2.449489742783178},"72":{"tf":2.23606797749979}},"e":{"df":0,"docs":{},"e":{"d":{"df":25,"docs":{"11":{"tf":1.0},"16":{"tf":1.0},"18":{"tf":1.0},"22":{"tf":1.0},"23":{"tf":1.0},"24":{"tf":1.0},"3":{"tf":1.0},"31":{"tf":1.0},"35":{"tf":1.0},"37":{"tf":1.0},"39":{"tf":1.0},"45":{"tf":1.0},"5":{"tf":1.0},"50":{"tf":1.0},"51":{"tf":1.0},"53":{"tf":1.0},"54":{"tf":1.0},"58":{"tf":1.0},"59":{"tf":1.0},"60":{"tf":1.0},"62":{"tf":1.0},"64":{"tf":1.0},"65":{"tf":1.0},"75":{"tf":1.0},"77":{"tf":1.0}}},"df":0,"docs":{}},"g":{"a":{"df":0,"docs":{},"t":{"df":1,"docs":{"54":{"tf":1.0}}}},"df":0,"docs":{}}},"l":{"df":0,"docs":{},"i":{"df":0,"docs":{},"n":{"a":{"df":0,"docs":{},"r":{"df":0,"docs":{},"i":{"df":0,"docs":{},"t":{"df":0,"docs":{},"h":{"df":1,"docs":{"53":{"tf":2.23606797749979}}}}}}},"df":0,"docs":{}}}},"o":{"df":0,"docs":{},"n":{"c":{"df":0,"docs":{},"o":{"df":0,"docs":{},"m":{"df":0,"docs":{},"p":{"df":0,"docs":{},"u":{"df":0,"docs":{},"t":{"df":1,"docs":{"25":{"tf":1.0}}}}}}}},"df":1,"docs":{"53":{"tf":1.0}},"e":{"df":0,"docs":{},"m":{"df":0,"docs":{},"p":{"df":0,"docs":{},"t":{"df":0,"docs":{},"i":{"df":1,"docs":{"25":{"tf":1.0}}}}}}}}},"t":{"df":0,"docs":{},"h":{"_":{"df":0,"docs":{},"r":{"df":0,"docs":{},"e":{"df":0,"docs":{},"w":{"df":0,"docs":{},"r":{"df":0,"docs":{},"i":{"df":0,"docs":{},"t":{"df":2,"docs":{"59":{"tf":1.0},"64":{"tf":1.7320508075688772}}}}}}}}},"df":0,"docs":{}}}},"o":{"b":{"df":0,"docs":{},"t":{"a":{"df":0,"docs":{},"i":{"df":0,"docs":{},"n":{"df":1,"docs":{"59":{"tf":1.0}}}}},"df":0,"docs":{}}},"df":0,"docs":{},"n":{"df":0,"docs":{},"e":{"_":{"df":0,"docs":{},"m":{"df":0,"docs":{},"u":{"df":0,"docs":{},"l":{"df":1,"docs":{"64":{"tf":1.4142135623730951}}}}}},"df":0,"docs":{}}},"p":{"df":0,"docs":{},"e":{"df":0,"docs":{},"n":{"df":1,"docs":{"68":{"tf":1.0}}}},"t":{"df":0,"docs":{},"i":{"df":0,"docs":{},"o":{"df":0,"docs":{},"n":{"df":1,"docs":{"1":{"tf":1.0}}}}}}},"r":{".":{"df":0,"docs":{},"i":{"df":0,"docs":{},"n":{"df":0,"docs":{},"l":{"df":1,"docs":{"50":{"tf":1.4142135623730951}}},"r":{"df":1,"docs":{"50":{"tf":1.0}}}}}},"df":0,"docs":{}}},"p":{"(":{"0":{"df":1,"docs":{"47":{"tf":1.0}}},"df":0,"docs":{},"x":{"df":2,"docs":{"24":{"tf":1.4142135623730951},"48":{"tf":1.0}}}},"df":43,"docs":{"13":{"tf":1.7320508075688772},"15":{"tf":3.3166247903554},"16":{"tf":2.6457513110645907},"17":{"tf":2.8284271247461903},"18":{"tf":1.4142135623730951},"20":{"tf":2.449489742783178},"21":{"tf":1.7320508075688772},"22":{"tf":1.4142135623730951},"23":{"tf":3.0},"25":{"tf":2.449489742783178},"27":{"tf":3.0},"28":{"tf":1.0},"29":{"tf":2.6457513110645907},"33":{"tf":2.449489742783178},"35":{"tf":1.4142135623730951},"36":{"tf":1.7320508075688772},"39":{"tf":1.7320508075688772},"40":{"tf":3.0},"42":{"tf":2.23606797749979},"43":{"tf":1.4142135623730951},"44":{"tf":2.0},"46":{"tf":2.23606797749979},"47":{"tf":2.449489742783178},"48":{"tf":4.242640687119285},"49":{"tf":3.3166247903554},"5":{"tf":2.23606797749979},"50":{"tf":2.449489742783178},"54":{"tf":3.4641016151377544},"55":{"tf":2.0},"56":{"tf":2.23606797749979},"57":{"tf":2.6457513110645907},"59":{"tf":1.0},"6":{"tf":3.7416573867739413},"63":{"tf":1.7320508075688772},"65":{"tf":1.4142135623730951},"67":{"tf":2.23606797749979},"68":{"tf":1.4142135623730951},"7":{"tf":2.6457513110645907},"73":{"tf":1.7320508075688772},"74":{"tf":1.0},"75":{"tf":3.0},"76":{"tf":1.0},"9":{"tf":2.0}},"h":{"df":0,"docs":{},"r":{"a":{"df":0,"docs":{},"s":{"df":0,"docs":{},"e":{"b":{"df":0,"docs":{},"o":{"df":0,"docs":{},"o":{"df":0,"docs":{},"k":{"df":1,"docs":{"2":{"tf":1.0}}}}}},"df":0,"docs":{}}}},"df":0,"docs":{}}},"o":{"df":0,"docs":{},"s":{"df":0,"docs":{},"i":{"df":0,"docs":{},"t":{"df":2,"docs":{"44":{"tf":1.0},"45":{"tf":1.0}}}}}},"r":{"df":0,"docs":{},"o":{"df":0,"docs":{},"p":{"df":7,"docs":{"15":{"tf":1.0},"23":{"tf":1.0},"25":{"tf":1.0},"46":{"tf":1.0},"47":{"tf":1.0},"48":{"tf":1.0},"60":{"tf":1.0}}},"v":{"df":0,"docs":{},"e":{"df":2,"docs":{"19":{"tf":1.0},"30":{"tf":1.0}}}}}},"u":{"df":0,"docs":{},"s":{"df":0,"docs":{},"h":{"_":{"df":0,"docs":{},"n":{"df":0,"docs":{},"e":{"df":0,"docs":{},"g":{"df":1,"docs":{"54":{"tf":2.449489742783178}}}}}},"df":1,"docs":{"54":{"tf":1.0}}}}},"y":{"df":1,"docs":{"25":{"tf":1.4142135623730951}}}},"q":{"(":{"df":0,"docs":{},"i":{"df":1,"docs":{"48":{"tf":1.0}}}},"df":32,"docs":{"13":{"tf":1.0},"16":{"tf":2.23606797749979},"17":{"tf":2.0},"18":{"tf":1.4142135623730951},"20":{"tf":2.449489742783178},"21":{"tf":1.7320508075688772},"22":{"tf":1.4142135623730951},"23":{"tf":3.0},"27":{"tf":2.8284271247461903},"28":{"tf":1.0},"29":{"tf":1.0},"33":{"tf":1.4142135623730951},"35":{"tf":1.4142135623730951},"40":{"tf":2.6457513110645907},"42":{"tf":2.23606797749979},"44":{"tf":2.0},"48":{"tf":3.872983346207417},"49":{"tf":3.0},"5":{"tf":2.23606797749979},"50":{"tf":2.0},"54":{"tf":3.1622776601683795},"55":{"tf":1.4142135623730951},"56":{"tf":2.0},"57":{"tf":2.8284271247461903},"6":{"tf":3.4641016151377544},"63":{"tf":1.4142135623730951},"65":{"tf":1.4142135623730951},"67":{"tf":1.7320508075688772},"73":{"tf":1.7320508075688772},"74":{"tf":2.6457513110645907},"75":{"tf":2.23606797749979},"9":{"tf":2.0}}},"r":{"c":{"a":{"df":0,"docs":{},"s":{"df":0,"docs":{},"e":{"df":1,"docs":{"23":{"tf":2.23606797749979}}}}},"df":0,"docs":{}},"df":13,"docs":{"17":{"tf":2.449489742783178},"18":{"tf":1.4142135623730951},"20":{"tf":1.7320508075688772},"21":{"tf":1.7320508075688772},"22":{"tf":1.7320508075688772},"23":{"tf":2.0},"35":{"tf":1.4142135623730951},"40":{"tf":2.23606797749979},"48":{"tf":2.6457513110645907},"5":{"tf":1.4142135623730951},"57":{"tf":2.8284271247461903},"65":{"tf":1.4142135623730951},"75":{"tf":1.4142135623730951}},"e":{"c":{"df":0,"docs":{},"u":{"df":0,"docs":{},"r":{"df":0,"docs":{},"s":{"df":1,"docs":{"23":{"tf":1.0}}}}}},"df":0,"docs":{},"f":{"df":0,"docs":{},"i":{"df":0,"docs":{},"n":{"df":3,"docs":{"55":{"tf":2.23606797749979},"56":{"tf":2.23606797749979},"57":{"tf":2.0}}}},"l":{"df":2,"docs":{"60":{"tf":2.0},"61":{"tf":1.0}},"e":{"df":0,"docs":{},"x":{"df":1,"docs":{"60":{"tf":1.0}}}}}},"l":{"a":{"df":0,"docs":{},"t":{"df":1,"docs":{"58":{"tf":1.0}}}},"df":1,"docs":{"58":{"tf":2.6457513110645907}}},"p":{"df":0,"docs":{},"e":{"a":{"df":0,"docs":{},"t":{"df":1,"docs":{"5":{"tf":1.4142135623730951}}}},"df":0,"docs":{}},"l":{"a":{"c":{"df":2,"docs":{"59":{"tf":2.449489742783178},"73":{"tf":1.0}}},"df":0,"docs":{}},"df":0,"docs":{}}}},"f":{"df":0,"docs":{},"l":{"df":5,"docs":{"51":{"tf":1.0},"60":{"tf":2.449489742783178},"61":{"tf":2.23606797749979},"74":{"tf":1.4142135623730951},"76":{"tf":1.0}}}},"i":{"df":0,"docs":{},"g":{"df":0,"docs":{},"h":{"df":0,"docs":{},"t":{"df":3,"docs":{"20":{"tf":1.0},"27":{"tf":1.0},"50":{"tf":2.23606797749979}}}}},"n":{"df":0,"docs":{},"g":{"df":4,"docs":{"38":{"tf":1.0},"43":{"tf":1.0},"59":{"tf":2.0},"62":{"tf":2.6457513110645907}}}}},"w":{"df":11,"docs":{"28":{"tf":1.0},"3":{"tf":1.0},"31":{"tf":1.0},"4":{"tf":1.0},"43":{"tf":1.0},"48":{"tf":1.0},"59":{"tf":1.4142135623730951},"63":{"tf":3.7416573867739413},"64":{"tf":1.4142135623730951},"65":{"tf":1.0},"69":{"tf":1.0}}}},"s":{"a":{"df":0,"docs":{},"y":{"df":0,"docs":{},"s":{".":{"df":0,"docs":{},"n":{"df":0,"docs":{},"o":{"_":{"df":0,"docs":{},"v":{"df":0,"docs":{},"e":{"df":0,"docs":{},"r":{"df":0,"docs":{},"i":{"df":0,"docs":{},"f":{"df":0,"docs":{},"y":{"_":{"df":0,"docs":{},"i":{"df":0,"docs":{},"n":{"_":{"c":{"df":0,"docs":{},"i":{"df":1,"docs":{"66":{"tf":1.0}}}},"df":0,"docs":{}},"df":0,"docs":{}}}},"df":0,"docs":{}}}}}}}},"df":0,"docs":{}}},"v":{"df":0,"docs":{},"e":{"df":0,"docs":{},"r":{"df":0,"docs":{},"i":{"df":0,"docs":{},"f":{"df":0,"docs":{},"i":{"df":1,"docs":{"66":{"tf":1.0}}}}}}}}},"df":0,"docs":{}}}},"df":2,"docs":{"37":{"tf":2.449489742783178},"65":{"tf":1.4142135623730951}},"e":{"df":0,"docs":{},"t":{"_":{"df":0,"docs":{},"o":{"df":0,"docs":{},"p":{"df":0,"docs":{},"t":{"df":1,"docs":{"1":{"tf":1.0}}}}}},"df":1,"docs":{"37":{"tf":1.0}}}},"h":{"df":0,"docs":{},"o":{"df":0,"docs":{},"w":{"_":{"df":0,"docs":{},"t":{"df":0,"docs":{},"e":{"df":0,"docs":{},"r":{"df":0,"docs":{},"m":{"df":1,"docs":{"62":{"tf":1.4142135623730951}}}}}}},"df":15,"docs":{"16":{"tf":1.0},"26":{"tf":1.4142135623730951},"31":{"tf":1.0},"46":{"tf":1.4142135623730951},"48":{"tf":1.4142135623730951},"49":{"tf":1.0},"5":{"tf":1.7320508075688772},"54":{"tf":1.4142135623730951},"55":{"tf":1.0},"56":{"tf":1.0},"57":{"tf":2.6457513110645907},"6":{"tf":1.0},"67":{"tf":2.449489742783178},"73":{"tf":1.7320508075688772},"77":{"tf":1.4142135623730951}}}}},"i":{"df":0,"docs":{},"m":{"df":0,"docs":{},"p":{"_":{"a":{"df":0,"docs":{},"l":{"df":4,"docs":{"28":{"tf":1.0},"4":{"tf":1.0},"65":{"tf":1.0},"70":{"tf":1.7320508075688772}}}},"df":0,"docs":{}},"df":11,"docs":{"26":{"tf":1.4142135623730951},"3":{"tf":1.0},"44":{"tf":1.4142135623730951},"45":{"tf":1.4142135623730951},"62":{"tf":1.0},"65":{"tf":1.0},"68":{"tf":3.1622776601683795},"69":{"tf":2.0},"70":{"tf":1.4142135623730951},"71":{"tf":1.4142135623730951},"73":{"tf":2.449489742783178}}}}},"o":{"df":0,"docs":{},"r":{"df":0,"docs":{},"r":{"df":0,"docs":{},"i":{"df":4,"docs":{"12":{"tf":2.0},"46":{"tf":1.4142135623730951},"47":{"tf":1.4142135623730951},"72":{"tf":2.449489742783178}}},"y":{"a":{"df":0,"docs":{},"x":{"df":1,"docs":{"12":{"tf":1.4142135623730951}}}},"df":0,"docs":{}}}}},"p":{"df":0,"docs":{},"l":{"df":0,"docs":{},"i":{"df":0,"docs":{},"t":{"df":1,"docs":{"73":{"tf":2.6457513110645907}}}}}},"t":{"d":{".":{"df":0,"docs":{},"t":{"a":{"c":{"df":0,"docs":{},"t":{"df":0,"docs":{},"i":{"c":{".":{"df":0,"docs":{},"e":{"df":0,"docs":{},"x":{"df":0,"docs":{},"t":{"df":1,"docs":{"37":{"tf":1.0}}}}},"g":{"df":0,"docs":{},"u":{"a":{"df":0,"docs":{},"r":{"d":{"df":0,"docs":{},"e":{"df":0,"docs":{},"x":{"df":0,"docs":{},"p":{"df":0,"docs":{},"r":{"df":1,"docs":{"39":{"tf":1.0}}}}}}},"df":0,"docs":{}}},"df":0,"docs":{}}},"r":{"c":{"a":{"df":0,"docs":{},"s":{"df":1,"docs":{"23":{"tf":1.0}}}},"df":0,"docs":{}},"df":0,"docs":{},"e":{"df":0,"docs":{},"p":{"df":0,"docs":{},"l":{"a":{"c":{"df":1,"docs":{"59":{"tf":1.0}}},"df":0,"docs":{}},"df":0,"docs":{}}}}},"s":{"df":0,"docs":{},"h":{"df":0,"docs":{},"o":{"df":0,"docs":{},"w":{"df":0,"docs":{},"t":{"df":0,"docs":{},"e":{"df":0,"docs":{},"r":{"df":0,"docs":{},"m":{"df":1,"docs":{"18":{"tf":1.0}}}}}}}}}}},"df":0,"docs":{}},"df":0,"docs":{}}}},"df":0,"docs":{}},"df":0,"docs":{}}},"df":0,"docs":{}},"df":0,"docs":{}},"u":{"c":{"c":{"df":2,"docs":{"44":{"tf":2.6457513110645907},"46":{"tf":1.0}}},"df":0,"docs":{}},"df":0,"docs":{},"f":{"df":0,"docs":{},"f":{"df":0,"docs":{},"i":{"c":{"df":1,"docs":{"74":{"tf":3.0}}},"df":0,"docs":{}}}}}},"t":{"a":{"c":{"df":0,"docs":{},"t":{"df":0,"docs":{},"i":{"c":{"df":1,"docs":{"2":{"tf":1.0}}},"df":0,"docs":{}}}},"df":0,"docs":{},"u":{"df":0,"docs":{},"t":{"df":0,"docs":{},"o":{"df":1,"docs":{"75":{"tf":2.8284271247461903}},"l":{"df":0,"docs":{},"o":{"df":0,"docs":{},"g":{"df":1,"docs":{"75":{"tf":1.0}}}}}}}}},"df":2,"docs":{"12":{"tf":1.7320508075688772},"37":{"tf":2.449489742783178}},"h":{"df":0,"docs":{},"e":{"df":0,"docs":{},"o":{"df":0,"docs":{},"r":{"df":0,"docs":{},"e":{"df":0,"docs":{},"m":{"df":4,"docs":{"12":{"tf":1.0},"19":{"tf":1.0},"30":{"tf":1.0},"72":{"tf":1.0}}}},"i":{"df":1,"docs":{"2":{"tf":1.0}}}}}}},"r":{"df":0,"docs":{},"i":{"df":7,"docs":{"18":{"tf":1.0},"31":{"tf":1.0},"35":{"tf":1.4142135623730951},"51":{"tf":1.0},"53":{"tf":1.0},"65":{"tf":1.7320508075688772},"75":{"tf":1.4142135623730951}},"v":{"df":0,"docs":{},"i":{"a":{"df":0,"docs":{},"l":{"df":1,"docs":{"76":{"tf":2.8284271247461903}}}},"df":0,"docs":{}}}},"u":{"df":0,"docs":{},"e":{"df":2,"docs":{"1":{"tf":1.0},"66":{"tf":1.4142135623730951}}}}},"y":{"df":0,"docs":{},"p":{"df":0,"docs":{},"e":{"df":5,"docs":{"2":{"tf":1.0},"37":{"tf":1.0},"60":{"tf":1.0},"61":{"tf":1.0},"68":{"tf":1.7320508075688772}}}}}},"u":{"df":2,"docs":{"60":{"tf":1.0},"68":{"tf":1.7320508075688772}},"n":{"df":0,"docs":{},"f":{"df":0,"docs":{},"o":{"df":0,"docs":{},"l":{"d":{"df":1,"docs":{"73":{"tf":1.0}}},"df":0,"docs":{}}}},"i":{"df":0,"docs":{},"v":{"df":0,"docs":{},"e":{"df":0,"docs":{},"r":{"df":0,"docs":{},"s":{"df":1,"docs":{"68":{"tf":1.0}}}}}}}},"s":{"df":2,"docs":{"24":{"tf":1.4142135623730951},"47":{"tf":1.0}}}},"v":{"a":{"df":0,"docs":{},"r":{"df":0,"docs":{},"i":{"a":{"b":{"df":0,"docs":{},"l":{"df":7,"docs":{"23":{"tf":1.0},"25":{"tf":1.0},"37":{"tf":1.4142135623730951},"47":{"tf":1.0},"61":{"tf":1.0},"64":{"tf":1.0},"68":{"tf":1.0}}}},"df":0,"docs":{}},"df":0,"docs":{}}}},"df":1,"docs":{"68":{"tf":1.7320508075688772}}},"w":{"a":{"df":0,"docs":{},"r":{"df":0,"docs":{},"n":{"df":1,"docs":{"1":{"tf":1.0}},"i":{"df":0,"docs":{},"n":{"df":0,"docs":{},"g":{"a":{"df":0,"docs":{},"s":{"df":0,"docs":{},"e":{"df":0,"docs":{},"r":{"df":0,"docs":{},"r":{"df":0,"docs":{},"o":{"df":0,"docs":{},"r":{"df":1,"docs":{"1":{"tf":1.0}}}}}}}}},"df":0,"docs":{}}}}}}},"df":0,"docs":{},"i":{"df":0,"docs":{},"t":{"df":0,"docs":{},"h":{"df":0,"docs":{},"o":{"df":0,"docs":{},"u":{"df":0,"docs":{},"t":{"df":1,"docs":{"77":{"tf":1.0}}}}}}}},"l":{"df":0,"docs":{},"o":{"df":0,"docs":{},"g":{"df":1,"docs":{"77":{"tf":2.23606797749979}}}}}},"x":{")":{".":{"df":0,"docs":{},"p":{"df":0,"docs":{},"r":{"df":0,"docs":{},"o":{"df":0,"docs":{},"p":{"df":0,"docs":{},"e":{"df":0,"docs":{},"r":{"df":0,"docs":{},"t":{"df":0,"docs":{},"i":{"df":1,"docs":{"25":{"tf":1.0}}}}}}}}}},"v":{"a":{"df":0,"docs":{},"l":{"df":1,"docs":{"25":{"tf":1.0}}}},"df":0,"docs":{}}},"df":0,"docs":{}},"`":{"df":0,"docs":{},"が":{"df":0,"docs":{},"偶":{"df":0,"docs":{},"数":{"df":0,"docs":{},"の":{"df":0,"docs":{},"と":{"df":0,"docs":{},"き":{"`":{"3":{"df":1,"docs":{"43":{"tf":1.0}}},"df":0,"docs":{}},"df":0,"docs":{}}}}}}}},"df":24,"docs":{"12":{"tf":3.4641016151377544},"24":{"tf":3.1622776601683795},"25":{"tf":4.358898943540674},"26":{"tf":3.4641016151377544},"28":{"tf":2.6457513110645907},"29":{"tf":1.7320508075688772},"3":{"tf":1.0},"35":{"tf":1.7320508075688772},"36":{"tf":3.3166247903554},"37":{"tf":2.6457513110645907},"38":{"tf":3.872983346207417},"4":{"tf":1.0},"43":{"tf":3.4641016151377544},"48":{"tf":2.449489742783178},"51":{"tf":2.8284271247461903},"52":{"tf":1.4142135623730951},"54":{"tf":3.1622776601683795},"58":{"tf":2.23606797749979},"61":{"tf":1.7320508075688772},"62":{"tf":2.449489742783178},"65":{"tf":2.8284271247461903},"66":{"tf":1.4142135623730951},"72":{"tf":1.7320508075688772},"73":{"tf":5.196152422706632}}},"y":{"df":14,"docs":{"12":{"tf":3.4641016151377544},"24":{"tf":4.0},"25":{"tf":3.3166247903554},"3":{"tf":1.4142135623730951},"4":{"tf":1.4142135623730951},"43":{"tf":2.449489742783178},"48":{"tf":3.3166247903554},"51":{"tf":1.4142135623730951},"52":{"tf":1.4142135623730951},"54":{"tf":2.0},"62":{"tf":2.449489742783178},"65":{"tf":2.6457513110645907},"66":{"tf":2.0},"72":{"tf":1.7320508075688772}}},"z":{"df":6,"docs":{"3":{"tf":1.0},"4":{"tf":1.0},"43":{"tf":1.4142135623730951},"51":{"tf":1.4142135623730951},"65":{"tf":1.0},"72":{"tf":1.7320508075688772}},"e":{"df":0,"docs":{},"r":{"df":0,"docs":{},"o":{"df":2,"docs":{"44":{"tf":1.7320508075688772},"46":{"tf":1.0}}}}}}}},"title":{"root":{"a":{"df":0,"docs":{},"e":{"df":0,"docs":{},"s":{"df":0,"docs":{},"o":{"df":0,"docs":{},"p":{"df":2,"docs":{"3":{"tf":1.0},"4":{"tf":1.0}}}}}},"p":{"df":0,"docs":{},"p":{"df":0,"docs":{},"l":{"df":0,"docs":{},"i":{"df":3,"docs":{"11":{"tf":1.0},"56":{"tf":1.0},"6":{"tf":1.0}}},"y":{"_":{"a":{"df":0,"docs":{},"s":{"df":0,"docs":{},"s":{"df":0,"docs":{},"u":{"df":0,"docs":{},"m":{"df":0,"docs":{},"p":{"df":0,"docs":{},"t":{"df":2,"docs":{"10":{"tf":1.0},"5":{"tf":1.0}}}}}}}}},"df":0,"docs":{}},"df":0,"docs":{}}}}},"s":{"df":0,"docs":{},"s":{"df":0,"docs":{},"u":{"df":0,"docs":{},"m":{"df":0,"docs":{},"p":{"df":0,"docs":{},"t":{"df":2,"docs":{"13":{"tf":1.0},"34":{"tf":1.0}}}}}}}}},"b":{"df":0,"docs":{},"y":{"_":{"c":{"a":{"df":0,"docs":{},"s":{"df":1,"docs":{"15":{"tf":1.0}}}},"df":0,"docs":{},"o":{"df":0,"docs":{},"n":{"df":0,"docs":{},"t":{"df":0,"docs":{},"r":{"a":{"df":1,"docs":{"16":{"tf":1.0}}},"df":0,"docs":{}}}}}},"df":0,"docs":{}},"df":0,"docs":{}}},"c":{"a":{"df":0,"docs":{},"l":{"c":{"df":1,"docs":{"19":{"tf":1.0}}},"df":0,"docs":{}},"s":{"df":0,"docs":{},"e":{"df":3,"docs":{"20":{"tf":1.0},"21":{"tf":1.0},"22":{"tf":1.0}}}}},"df":0,"docs":{},"h":{"df":0,"docs":{},"o":{"df":0,"docs":{},"o":{"df":0,"docs":{},"s":{"df":1,"docs":{"24":{"tf":1.0}}}}}},"o":{"df":0,"docs":{},"n":{"df":0,"docs":{},"g":{"df":0,"docs":{},"r":{"df":1,"docs":{"26":{"tf":1.0}}}},"s":{"df":0,"docs":{},"t":{"df":0,"docs":{},"r":{"df":0,"docs":{},"u":{"c":{"df":0,"docs":{},"t":{"df":0,"docs":{},"o":{"df":0,"docs":{},"r":{"df":2,"docs":{"27":{"tf":1.0},"57":{"tf":1.0}}}}}},"df":0,"docs":{}}}}},"t":{"df":0,"docs":{},"r":{"a":{"d":{"df":0,"docs":{},"i":{"c":{"df":0,"docs":{},"t":{"df":1,"docs":{"29":{"tf":1.0}}}},"df":0,"docs":{}}},"df":0,"docs":{}},"df":0,"docs":{}}},"v":{"df":1,"docs":{"30":{"tf":1.0}},"e":{"df":0,"docs":{},"r":{"df":0,"docs":{},"t":{"df":1,"docs":{"31":{"tf":1.0}}}}}}}}},"d":{"df":0,"docs":{},"o":{"df":0,"docs":{},"n":{"df":0,"docs":{},"e":{"df":1,"docs":{"32":{"tf":1.0}}}}},"s":{"df":0,"docs":{},"i":{"df":0,"docs":{},"m":{"df":0,"docs":{},"p":{"df":1,"docs":{"71":{"tf":1.0}}}}}}},"df":0,"docs":{},"e":{"df":0,"docs":{},"x":{"a":{"c":{"df":0,"docs":{},"t":{"df":4,"docs":{"14":{"tf":1.0},"33":{"tf":1.0},"35":{"tf":1.0},"9":{"tf":1.0}}}},"df":0,"docs":{}},"df":0,"docs":{},"i":{"df":0,"docs":{},"s":{"df":0,"docs":{},"t":{"df":1,"docs":{"36":{"tf":1.0}}}}},"t":{"df":1,"docs":{"37":{"tf":1.0}}}}},"f":{"df":0,"docs":{},"u":{"df":0,"docs":{},"n":{"df":0,"docs":{},"e":{"df":0,"docs":{},"x":{"df":0,"docs":{},"t":{"df":1,"docs":{"38":{"tf":1.0}}}}}}}},"g":{"df":0,"docs":{},"u":{"a":{"df":0,"docs":{},"r":{"d":{"_":{"df":0,"docs":{},"h":{"df":0,"docs":{},"y":{"df":0,"docs":{},"p":{"df":1,"docs":{"39":{"tf":1.0}}}}}},"df":0,"docs":{}},"df":0,"docs":{}}},"df":0,"docs":{}}},"i":{"df":0,"docs":{},"n":{"d":{"df":0,"docs":{},"u":{"c":{"df":0,"docs":{},"t":{"df":2,"docs":{"44":{"tf":1.0},"45":{"tf":1.0}}}},"df":0,"docs":{}}},"df":0,"docs":{},"t":{"df":0,"docs":{},"r":{"df":0,"docs":{},"o":{"df":1,"docs":{"48":{"tf":1.0}}}}}}},"l":{"df":0,"docs":{},"e":{"a":{"df":0,"docs":{},"n":{"4":{"df":1,"docs":{"0":{"tf":1.0}}},"df":0,"docs":{}}},"df":0,"docs":{},"f":{"df":0,"docs":{},"t":{"df":1,"docs":{"50":{"tf":1.0}}}}},"i":{"df":0,"docs":{},"n":{"a":{"df":0,"docs":{},"r":{"df":0,"docs":{},"i":{"df":0,"docs":{},"t":{"df":0,"docs":{},"h":{"df":1,"docs":{"51":{"tf":1.0}}}}}}},"df":0,"docs":{}}}},"n":{"df":0,"docs":{},"l":{"df":0,"docs":{},"i":{"df":0,"docs":{},"n":{"a":{"df":0,"docs":{},"r":{"df":0,"docs":{},"i":{"df":0,"docs":{},"t":{"df":0,"docs":{},"h":{"df":1,"docs":{"53":{"tf":1.0}}}}}}},"df":0,"docs":{}}}},"t":{"df":0,"docs":{},"h":{"_":{"df":0,"docs":{},"r":{"df":0,"docs":{},"e":{"df":0,"docs":{},"w":{"df":0,"docs":{},"r":{"df":0,"docs":{},"i":{"df":0,"docs":{},"t":{"df":1,"docs":{"64":{"tf":1.0}}}}}}}}},"df":0,"docs":{}}}},"p":{"df":0,"docs":{},"u":{"df":0,"docs":{},"s":{"df":0,"docs":{},"h":{"_":{"df":0,"docs":{},"n":{"df":0,"docs":{},"e":{"df":0,"docs":{},"g":{"df":1,"docs":{"54":{"tf":1.0}}}}}},"df":0,"docs":{}}}}},"r":{"c":{"a":{"df":0,"docs":{},"s":{"df":0,"docs":{},"e":{"df":1,"docs":{"23":{"tf":1.0}}}}},"df":0,"docs":{}},"df":0,"docs":{},"e":{"df":0,"docs":{},"f":{"df":0,"docs":{},"i":{"df":0,"docs":{},"n":{"df":1,"docs":{"55":{"tf":1.0}}}}},"l":{"df":1,"docs":{"58":{"tf":1.0}}},"p":{"df":0,"docs":{},"l":{"a":{"c":{"df":1,"docs":{"59":{"tf":1.0}}},"df":0,"docs":{}},"df":0,"docs":{}}}},"f":{"df":0,"docs":{},"l":{"df":1,"docs":{"60":{"tf":1.0}}}},"i":{"df":0,"docs":{},"g":{"df":0,"docs":{},"h":{"df":0,"docs":{},"t":{"df":1,"docs":{"50":{"tf":1.0}}}}},"n":{"df":0,"docs":{},"g":{"df":1,"docs":{"62":{"tf":1.0}}}}},"w":{"df":1,"docs":{"63":{"tf":1.0}}}},"s":{"df":0,"docs":{},"h":{"df":0,"docs":{},"o":{"df":0,"docs":{},"w":{"df":1,"docs":{"67":{"tf":1.0}}}}},"i":{"df":0,"docs":{},"m":{"df":0,"docs":{},"p":{"_":{"a":{"df":0,"docs":{},"l":{"df":1,"docs":{"70":{"tf":1.0}}}},"df":0,"docs":{}},"df":2,"docs":{"68":{"tf":1.0},"69":{"tf":1.0}}}}},"o":{"df":0,"docs":{},"r":{"df":0,"docs":{},"r":{"df":0,"docs":{},"i":{"df":1,"docs":{"72":{"tf":1.0}}}}}},"p":{"df":0,"docs":{},"l":{"df":0,"docs":{},"i":{"df":0,"docs":{},"t":{"df":1,"docs":{"73":{"tf":1.0}}}}}},"u":{"df":0,"docs":{},"f":{"df":0,"docs":{},"f":{"df":0,"docs":{},"i":{"c":{"df":1,"docs":{"74":{"tf":1.0}}},"df":0,"docs":{}}}}}},"t":{"a":{"df":0,"docs":{},"u":{"df":0,"docs":{},"t":{"df":0,"docs":{},"o":{"df":1,"docs":{"75":{"tf":1.0}}}}}},"df":0,"docs":{},"r":{"df":0,"docs":{},"i":{"df":0,"docs":{},"v":{"df":0,"docs":{},"i":{"a":{"df":0,"docs":{},"l":{"df":1,"docs":{"76":{"tf":1.0}}}},"df":0,"docs":{}}}}}},"w":{"df":0,"docs":{},"l":{"df":0,"docs":{},"o":{"df":0,"docs":{},"g":{"df":1,"docs":{"77":{"tf":1.0}}}}}}}}},"lang":"English","pipeline":["trimmer","stopWordFilter","stemmer"],"ref":"id","version":"0.9.5"},"results_options":{"limit_results":30,"teaser_word_count":30},"search_options":{"bool":"OR","expand":true,"fields":{"body":{"boost":1},"breadcrumbs":{"boost":1},"title":{"boost":2}}}}
\ No newline at end of file
+{"doc_urls":["index.html#lean4-タクティク逆引きリスト","index.html#オプションについて","index.html#リンク集","aesop.html#aesop","apply_assumption.html#apply_assumption","apply.html#apply","apply.html#否定--について","apply.html#よくあるエラー","apply.html#exact-との関連","apply.html#apply_assumption-との関連","apply_search.html#apply","assumption.html#assumption","assumption.html#exact-との関連","by_cases.html#by_cases","by_contra.html#by_contra","by.html#by","by.html#by-1","calc.html#calc","cases.html#cases","cases.html#case-を書かない","cases.html#cases-1","cases.html#rcases","choose.html#choose","choose.html#補足","congr.html#congr","constructor.html#constructor","constructor.html#同値を示す","contradiction.html#contradiction","conv.html#conv","convert.html#convert","done.html#done","exact.html#exact","exact.html#assumption-との関連","exact_search.html#exact","exists.html#exists","ext.html#ext","funext.html#funext","guard_hyp.html#guard_hyp","have.html#have","have.html#パターンマッチ","have.html#論理積-","have.html#存在-","induction.html#induction","induction.html#induction-1","induction.html#一般のについての帰納法","induction.html#強い帰納法","intro.html#intro","intro.html#否定--について","left_right.html#left-right","linarith.html#linarith","linarith.html#補足","nlinarith.html#nlinarith","push_neg.html#push_neg","refine.html#refine","refine.html#apply-との関連","refine.html#constructor-との関連","rel.html#rel","replace.html#replace","rfl.html#rfl","rfl.html#補足","ring.html#ring","rw.html#rw","rw.html#nth_rw","says.html#says","says.html#オプション","show.html#show","simp.html#simp","simp.html#simp-1","simp.html#simp_all","simp.html#dsimp","sorry.html#sorry","split.html#split","suffices.html#suffices","tauto.html#tauto","trivial.html#trivial","wlog.html#wlog"],"index":{"documentStore":{"docInfo":{"0":{"body":1,"breadcrumbs":2,"title":1},"1":{"body":6,"breadcrumbs":1,"title":0},"10":{"body":61,"breadcrumbs":3,"title":1},"11":{"body":9,"breadcrumbs":2,"title":1},"12":{"body":2,"breadcrumbs":2,"title":1},"13":{"body":30,"breadcrumbs":2,"title":1},"14":{"body":31,"breadcrumbs":2,"title":1},"15":{"body":37,"breadcrumbs":0,"title":0},"16":{"body":24,"breadcrumbs":0,"title":0},"17":{"body":4,"breadcrumbs":2,"title":1},"18":{"body":49,"breadcrumbs":2,"title":1},"19":{"body":33,"breadcrumbs":2,"title":1},"2":{"body":10,"breadcrumbs":1,"title":0},"20":{"body":26,"breadcrumbs":2,"title":1},"21":{"body":61,"breadcrumbs":2,"title":1},"22":{"body":64,"breadcrumbs":2,"title":1},"23":{"body":67,"breadcrumbs":1,"title":0},"24":{"body":75,"breadcrumbs":2,"title":1},"25":{"body":36,"breadcrumbs":2,"title":1},"26":{"body":27,"breadcrumbs":1,"title":0},"27":{"body":31,"breadcrumbs":2,"title":1},"28":{"body":4,"breadcrumbs":2,"title":1},"29":{"body":37,"breadcrumbs":2,"title":1},"3":{"body":75,"breadcrumbs":2,"title":1},"30":{"body":1,"breadcrumbs":2,"title":1},"31":{"body":25,"breadcrumbs":2,"title":1},"32":{"body":3,"breadcrumbs":2,"title":1},"33":{"body":37,"breadcrumbs":3,"title":1},"34":{"body":23,"breadcrumbs":2,"title":1},"35":{"body":48,"breadcrumbs":2,"title":1},"36":{"body":40,"breadcrumbs":2,"title":1},"37":{"body":13,"breadcrumbs":2,"title":1},"38":{"body":39,"breadcrumbs":0,"title":0},"39":{"body":0,"breadcrumbs":0,"title":0},"4":{"body":54,"breadcrumbs":2,"title":1},"40":{"body":17,"breadcrumbs":0,"title":0},"41":{"body":38,"breadcrumbs":0,"title":0},"42":{"body":67,"breadcrumbs":2,"title":1},"43":{"body":22,"breadcrumbs":2,"title":1},"44":{"body":51,"breadcrumbs":1,"title":0},"45":{"body":40,"breadcrumbs":1,"title":0},"46":{"body":101,"breadcrumbs":2,"title":1},"47":{"body":42,"breadcrumbs":1,"title":0},"48":{"body":29,"breadcrumbs":4,"title":2},"49":{"body":43,"breadcrumbs":2,"title":1},"5":{"body":49,"breadcrumbs":2,"title":1},"50":{"body":13,"breadcrumbs":1,"title":0},"51":{"body":21,"breadcrumbs":2,"title":1},"52":{"body":62,"breadcrumbs":2,"title":1},"53":{"body":17,"breadcrumbs":2,"title":1},"54":{"body":26,"breadcrumbs":2,"title":1},"55":{"body":62,"breadcrumbs":2,"title":1},"56":{"body":36,"breadcrumbs":2,"title":1},"57":{"body":81,"breadcrumbs":2,"title":1},"58":{"body":34,"breadcrumbs":2,"title":1},"59":{"body":27,"breadcrumbs":1,"title":0},"6":{"body":21,"breadcrumbs":1,"title":0},"60":{"body":33,"breadcrumbs":2,"title":1},"61":{"body":55,"breadcrumbs":2,"title":1},"62":{"body":34,"breadcrumbs":2,"title":1},"63":{"body":70,"breadcrumbs":0,"title":0},"64":{"body":13,"breadcrumbs":0,"title":0},"65":{"body":19,"breadcrumbs":2,"title":1},"66":{"body":142,"breadcrumbs":2,"title":1},"67":{"body":2,"breadcrumbs":2,"title":1},"68":{"body":2,"breadcrumbs":2,"title":1},"69":{"body":2,"breadcrumbs":2,"title":1},"7":{"body":1,"breadcrumbs":1,"title":0},"70":{"body":26,"breadcrumbs":2,"title":1},"71":{"body":115,"breadcrumbs":2,"title":1},"72":{"body":38,"breadcrumbs":2,"title":1},"73":{"body":39,"breadcrumbs":2,"title":1},"74":{"body":16,"breadcrumbs":2,"title":1},"75":{"body":42,"breadcrumbs":2,"title":1},"8":{"body":17,"breadcrumbs":2,"title":1},"9":{"body":3,"breadcrumbs":2,"title":1}},"docs":{"0":{"body":"「普段の数学を Lean でどうやって実現するんだろう」という疑問に答えるために，よく使うタクティクをユースケースから逆引きできるようにまとめたリストです． なお，タクティクの説明に付記している名前の由来についての説明は公式に説明があったものではなく，あくまで憶測であることをお断りしておきます．","breadcrumbs":"Lean4 タクティク逆引きリスト » Lean4 タクティク逆引きリスト","id":"0","title":"Lean4 タクティク逆引きリスト"},"1":{"body":"タクティクによっては，オプションを設定することで挙動を変更することができます．オプションの設定には，set_option を使用します．たとえば，set_option warningAsError true と書くと，warning(警告) がエラーとして扱われるようになります． 使用できるオプションの一覧は #help option または こちらのリスト で確認することができます．","breadcrumbs":"Lean4 タクティク逆引きリスト » オプションについて","id":"1","title":"オプションについて"},"10":{"body":"apply? は，カレントゴールを apply や refine で変形することができないか，ライブラリから検索して提案してくれるタクティクです． 複数の候補が提案されたときは，どれを選ぶとゴールが何に変わるのか表示されるので，その中から好ましいものを選ぶと良いでしょう． import Mathlib.Algebra.Group.Defs\nimport Mathlib.Algebra.Hom.Group.Defs\nimport Mathlib.Tactic.LibrarySearch -- apply? を使うのに必要 /-- 群準同型は積を保つ -/\nexample [Group G] [Group H] (f : G →* H) (a b : G) : f (a * b) = f a * f b := by -- `exact MonoidHom.map_mul f a b` を提案してくれる apply? /-! ## 補足 `apply?` はあくまで証明を書くときに補助として使うものです． `sorry` と同じように，清書した証明に残してはいけません． `sorry` と同じと言いましたが，実際 `apply?` は `sorryAx` を裏で使用します．\n-/ theorem T (x y : Nat) (_: x ≤ y) : 2 ^ x ≤ 2 ^ y := by apply? -- `apply?` しただけで `done` が通り，示せているように見える done -- 以下に示すように，裏で `sorryAx` が使われている /-- info: 'T' depends on axioms: [sorryAx] -/\n#guard_msgs in #print axioms T","breadcrumbs":"apply?: apply できるか検索 » apply?","id":"10","title":"apply?"},"11":{"body":"assumption は，現在のゴール ⊢ P がローカルコンテキストにあるとき，ゴールを閉じます． example (hP: P) (_: Q) : P := by assumption","breadcrumbs":"assumption: 仮定からゴールを閉じる » assumption","id":"11","title":"assumption"},"12":{"body":"assumption による証明は，どの仮定を使うか明示すれば exact で書き直すことができます．","breadcrumbs":"assumption: 仮定からゴールを閉じる » exact との関連","id":"12","title":"exact との関連"},"13":{"body":"by_cases は排中律を使って場合分けをするタクティクです． by_cases h: P とすると，P が成り立つときと成り立たないときのゴールがそれぞれ生成されます． example (P: Prop) : ¬¬P → P := by intro hnnP -- `P` が成り立つかどうかで場合分けする by_cases hP: P case inl => -- `P` が成り立つとき guard_hyp hP : P assumption case inr => -- `¬ P` が成り立つとき guard_hyp hP : ¬P contradiction","breadcrumbs":"by_cases: 排中律 » by_cases","id":"13","title":"by_cases"},"14":{"body":"needs: import Mathlib.Tactic.ByContra by_contra は，背理法を使いたいときに役立つタクティクです． ゴールが ⊢ P であるときに by_contra h を実行すると，h : ¬ P がローカルコンテキストに追加されて，同時にゴールが ⊢ False になります． example (h: ¬Q → ¬P) : P → Q := by -- `P` であると仮定する intro hP -- `¬Q` であると仮定して矛盾を導きたい by_contra hnQ show False -- `¬ Q → ¬ P` と `¬Q` から `¬P` が導かれる have := h hnQ -- これは仮定に矛盾 contradiction","breadcrumbs":"by_contra: 背理法 » by_contra","id":"14","title":"by_contra"},"15":{"body":"Lean においては，命題は型で，証明はその項です．命題 P の証明を構成するとは項 h : P を構成するということです．by は，証明の構成をタクティクで行いたいときに使います． -- `P → R` というのは `P` の証明を与えられたときに `R` の証明を返す関数の型\n-- したがって，その証明は関数となる\nexample (hPQ : P → Q) (hQR : Q → R) : P → R := fun hP ↦ hQR (hPQ hP) -- 同じ命題をタクティクで示した例\nexample (hPQ : P → Q) (hQR : Q → R) : P → R := by intro hP exact hQR (hPQ hP)","breadcrumbs":"by: タクティクモードに入る » by","id":"15","title":"by"},"16":{"body":"needs: import Std.Tactic.ShowTerm by? を使うとタクティクモードで構成した証明を直接構成した証明に変換してくれます． example (hPQ : P → Q) (hQR : Q → R) : P → R := by? -- `Try this: fun hP => hQR (hPQ hP)` と提案してくれる intro hP exact hQR (hPQ hP)","breadcrumbs":"by: タクティクモードに入る » by?","id":"16","title":"by?"},"17":{"body":"calc は計算モードに入るためのタクティクです．詳細については Theorem Proving in Lean4 をご参照ください．","breadcrumbs":"calc: 計算モードに入る » calc","id":"17","title":"calc"},"18":{"body":"cases は場合分けを行います．ローカルコンテキストに h: P ∨ Q があるときに cases h とすると，仮定に P を付け加えたゴール inl と，仮定に Q を付け加えたゴール inr を生成します．それぞれ，insert left と insert right の略ではないかと思います． example : P ∨ Q → (P → R) → (Q → R) → R := by -- `h: P ∨ Q` intro h hPR hQR -- `case inl` と `case inr` の２つのゴールを生成する cases h -- `P` が成り立つ場合 case inl hP => exact hPR hP -- `Q` が成り立つ場合 case inr hQ => exact hQR hQ","breadcrumbs":"cases: 論理和∨を使う » cases","id":"18","title":"cases"},"19":{"body":"上記の例では case を場合分けの枝ごとに書いていますが，下の例のように case を書かずに済ませることもできます． example : P ∨ Q → (P → R) → (Q → R) → R := by -- `h: P ∨ Q` intro h hPR hQR -- `case inl` と `case inr` の２つのゴールを生成する cases h with | inl hP => exact hPR hP | inr hQ => exact hQR hQ","breadcrumbs":"cases: 論理和∨を使う » case を書かない","id":"19","title":"case を書かない"},"2":{"body":"Mathematics in type Theory 日本語訳 このリストでは「命題は型，証明はその項」という型理論を基礎として数学を実装する際の事実は既知としています．こういった話に全く馴染みがない方は，まずこちらの記事を読まれると良いと思います． mathlib4-all-tactics 全タクティクの網羅的なリスト． 数学系のためのLean勉強会 Lean で数学をどのように実装するのか，実際に実装する過程を追うことで学べる教材です．いくつかコード例を拝借させていただきました． Lean phrasebook 英語ですが，数学でのよくある推論ステップが，Lean にどのように翻訳されるかがよくまとめられたリストです．","breadcrumbs":"Lean4 タクティク逆引きリスト » リンク集","id":"2","title":"リンク集"},"20":{"body":"needs: import Mathlib.Tactic.Cases cases' を使用すると分解した仮定に簡潔に名前をつけることができます． example : P ∨ Q → (P → R) → (Q → R) → R := by intro h hPR hQR -- 場合分けをする cases' h with hP hQ · apply hPR hP · apply hQR hQ","breadcrumbs":"cases: 論理和∨を使う » cases'","id":"20","title":"cases'"},"21":{"body":"needs: import Std.Tactic.RCases named after: 再帰的(recursive) cases rcases は cases をパターンに従って再帰的に適用します．論理和∨以外にも使うことができます． variable (P Q R : Prop) example : P ∨ Q → (P → R) → (Q → R) → R := by intro h hPR hQR -- 場合分けをする rcases h with hP | hQ · apply hPR hP · apply hQR hQ example : P ∧ Q → Q ∧ P := by -- `h: P ∧ Q` と仮定する intro h -- `h: P ∧ Q` を `hP: P` と `hQ: Q` に分解する rcases h with ⟨hP, hQ⟩ -- `Q ∧ P` を証明する exact ⟨hQ, hP⟩","breadcrumbs":"cases: 論理和∨を使う » rcases","id":"21","title":"rcases"},"22":{"body":"needs: import Mathlib.Tactic.Choose h : ∀ x, ∃ y, P(x, y) が成り立っているときに，choose f hf using h は写像 f: X → Y と f が満たす性質 hf : ∀ x, P(x, f x) のペアを作ります． example (f : X → Y) (hf : ∀ y, ∃ x, f x = y) : ∃ g : Y → X, ∀ y, f (g y) = y := by -- 写像 `g : Y → X` を構成する choose g hg using hf -- `g` が満たす条件がローカルコンテキストに追加される guard_hyp g: Y → X guard_hyp hg: ∀ (y : Y), f (g y) = y exact ⟨g, hg⟩","breadcrumbs":"choose: 選択関数を得る » choose","id":"22","title":"choose"},"23":{"body":"choose が自動で示してくれることは選択原理 Classical.choice を使って手動で示すことができます．たとえば次のようになります． variable (P : X → Y → Prop) noncomputable example (h : ∀ x, ∃ y, P x y) : ∃ f : X → Y, ∀ x, P x (f x) := by -- `f` を作る let f' : (x : X) → {y // P x y} := fun x ↦ have hne_st : Nonempty {y // P x y} := let ⟨y, py⟩ := h x; ⟨⟨y, py⟩⟩ Classical.choice hne_st let f : X → Y := fun x ↦ (f' x).val -- 上記で作った関数が条件を満たすことを示す have h₁ : ∀ x, P x (f x) := by intro x exact (f' x).property exists f","breadcrumbs":"choose: 選択関数を得る » 補足","id":"23","title":"補足"},"24":{"body":"named after: 合同(congruence) congr は，⊢ f as = f bs という形のゴールがあったときに，ゴールを ⊢ as = bs に変えます．再帰的に適用されるので，⊢ g (f as) = g (f bs) という形のゴールでも同じ結果になります． example (f : Int → X) (h : x = 0) : f (2 + x) = f 2 := by congr show 2 + x = 2 simp only [h, add_zero] congr が適用される再帰の深さを引数として渡すことができます．これは，主に単に congr とするだけだと「行き過ぎ」になるときに調整する目的で使用されます． example (f : Int → Int) (g : Int → X) (h : x = 0) (hf : ∀ x, f x = f (- x)) : g (f (2 + x)) = g (f (- 2)) := by -- 仮に `congr` とすると -- ゴールが `⊢ 2 + x = -2` になってしまう congr 1 show f (2 + x) = f (-2) simp only [h, add_zero] exact hf _","breadcrumbs":"congr: ゴールの差異に注目する » congr","id":"24","title":"congr"},"25":{"body":"ゴールが ⊢ P ∧ Q であるとき，constructor を実行すると，ゴールが２つのゴール ⊢ P と ⊢ Q に分割されます． example (hP: P) (hQ: Q) : P ∧ Q := by -- goal が `left` と `right` に分割される constructor · -- `P` を示す exact hP · -- `Q` を示す exact hQ なお h: P ∧ Q から P や Q の証明を得るのは，それぞれ h.left と h.right で可能です． example (h: P ∧ Q) : P := by exact h.left","breadcrumbs":"constructor: 論理積∧を示す » constructor","id":"25","title":"constructor"},"26":{"body":"constructor はゴールが ⊢ P ↔ Q であるときにも使用できます． example (x : Nat) : x = 0 ↔ x + 1 = 1 := by constructor · -- `x = 0 → x + 1 = 1` を示す intro hx rw [hx] · -- `x + 1 = 1 → x = 0` を示す simp_all","breadcrumbs":"constructor: 論理積∧を示す » 同値を示す","id":"26","title":"同値を示す"},"27":{"body":"矛盾からはどんな命題でも証明することができます．これを爆発律(principle of explosion)と呼びますが，contradiction は，この爆発律を使ってゴールを閉じるタクティクです． ローカルコンテキストに P と ¬ P が同時にあるなど，矛盾した状況にあるときにゴールを閉じます． -- `False`\nexample (h : False) : P := by contradiction -- 明らかに偽な等式\nexample (h : 2 + 2 = 3) : P := by contradiction -- 明らかに偽な等式\nexample (x : Nat) (h : x ≠ x) : P := by contradiction -- 矛盾する仮定\nexample (hP : P) (hnP : ¬ P) : Q := by contradiction","breadcrumbs":"contradiction: 爆発律 » contradiction","id":"27","title":"contradiction"},"28":{"body":"conv は変換モードに入るためのタクティクです．詳細については Theorem Proving in Lean4 をご参照ください．","breadcrumbs":"conv: 変換モードに入る » conv","id":"28","title":"conv"},"29":{"body":"needs: import Mathlib.Tactic.Convert ローカルコンテキストに現在のゴールに近いけれども等しくはない h があるとき，exact h としても失敗します．しかし convert h は成功する可能性があり，成功した場合は h とゴールの差分を新たなゴールとします． example (f : Nat → Nat) (h : f (a + b) = 0) (hc: a + b = c) : f (c) = 0 := by -- `h` はゴールと等しくないので失敗する try exact [h] -- `h` とゴールの差分を新たなゴールにする convert h -- ゴールが `⊢ c = a + b` に変わっている show c = a + b rw [hc]","breadcrumbs":"convert: 惜しい補題を使う » convert","id":"29","title":"convert"},"3":{"body":"aesop は，intro や simp を使用してルーチンな証明を自動で行う，強力なタクティクです． aesop? を使うことにより，中身を見ることも可能です． import Aesop -- `aesop` を使用するため\nimport Mathlib.Init.Function -- `Injective` を使用するため\nimport Mathlib.Tactic.Says -- `says` を使用するため -- CI 環境で `says` のチェックをしない\nset_option says.no_verify_in_CI true -- 以下 `X` `Y` `Z`を集合とする\nvariable {X Y Z : Type} open Function /-! ## aesop -/ -- 合成 `g ∘ f` が単射なら，`f` も単射\nexample {f : X → Y} {g : Y → Z} (hgfinj : Injective (g ∘ f)) : Injective f := by rw [Injective] show ∀ ⦃a₁ a₂ : X⦄, f a₁ = f a₂ → a₁ = a₂ -- 示すべきことがまだまだあるように見えるが，一発で証明が終わる aesop /-! ## aesop? aesop が成功するとき，aesop? に置き換えると， ゴールを達成するのにどんなタクティクを使用したか教えてくれる．\n-/ example {f : X → Y} {g : Y → Z} (hgfinj : Injective (g ∘ f)) : Injective f := by rw [Injective] -- `aesop?` は `says` 以下に続く一連のタクティクを示す aesop? says intro a₁ a₂ a apply hgfinj simp_all only [comp_apply]","breadcrumbs":"aesop: ルーチン自動化 » aesop","id":"3","title":"aesop"},"30":{"body":"done は，証明終了の合図です．証明すべきゴールが残っていない時に成功し，それ以外の時にはエラーになります．QED のようなものです．","breadcrumbs":"done: 証明終了を宣言 » done","id":"30","title":"done"},"31":{"body":"ゴールが P で，ローカルコンテキストに hP: P があるときに，exact hP はゴールを閉じます． example (hP: P) : P := by exact hP hP がゴールの証明になっていないときには，失敗してエラーになります． exact ⟨ hP, hQ ⟩ のようにすると，論理積∧の形をした命題を証明することができます． example (hP: P) (hQ: Q) : P ∧ Q := by exact ⟨ hP, hQ ⟩","breadcrumbs":"exact: 証明を直接構成 » exact","id":"31","title":"exact"},"32":{"body":"exact は常にどの命題を使うか明示する必要がありますが，「ゴールを exact で閉じることができるような命題をローカルコンテキストから自動で探す」 assumption というタクティクもあります．","breadcrumbs":"exact: 証明を直接構成 » assumption との関連","id":"32","title":"assumption との関連"},"33":{"body":"exact? は，カレントゴールを exact で閉じることができないか，ライブラリから検索して提案してくれるタクティクです．閉じることができなければ，エラーになります． import Mathlib.Tactic.LibrarySearch -- `exact?` を使うのに必要 variable (P Q : Prop) -- `exact?` はライブラリ検索を行う\nexample : x < x + 1 := by -- `Try this: exact Nat.lt.base x` と出力される exact? -- ローカルコンテキストにある仮定を自動で使ってゴールを導いてくれる\nexample (hPQ : P → Q) (hQR : Q → R) (hQ : P) : R := by -- `Try this: exact hQR (hPQ hQ)` と出力される exact? -- 証明は `exact?` だけで終わっている done","breadcrumbs":"exact?: exact できるか検索 » exact?","id":"33","title":"exact?"},"34":{"body":"exists は，「～という x が存在する」という命題を示すために，「この x を使え」と指示するコマンドです． ゴールが ⊢ ∃ x, P x のとき，x: X がローカルコンテキストにあれば，exists x によりゴールが P x に変わります．同時に，P x が自明な場合は証明が終了します． example : ∃ x : Nat, 3 * x + 1 = 7 := by exists 2","breadcrumbs":"exists: 存在∃を示す » exists","id":"34","title":"exists"},"35":{"body":"needs: import Std.Tactic.Ext named after: 外延性(extensionality) ext は，外延性を使うタクティクです．外延性とは，「同じものから作られているものは同じである」という主張のことです．たとえば 集合 A, B ⊂ α について A = B は x ∈ A ↔ x ∈ B と同じ 2つの写像 f g : A → B があるとき f = g は ∀ a ∈ A, f a = g a と同じ といったことを指します． @[ext] で登録されたルールを使用するため，集合の等式 A = B を示すときは Mathlib.Data.SetLike.Basic も必要です． variable {α : Type} -- `s` と `t` は `α` の部分集合\nvariable (s t : Set α) example : s ∩ t = t ∩ s := by -- `x ∈ α` を取る．` x ∈ s ∩ t ↔ x ∈ t ∩ s` を証明すればよい ext x aesop なお A ⊂ B を示すために元を取るのは intro x で可能です．","breadcrumbs":"ext: 外延性を使う » ext","id":"35","title":"ext"},"36":{"body":"関数 f と g が等しいことを示す際に，引数 x をとって f x = g x を示そうとすることがありますが，funext はそれを行うタクティクです. def f := fun (x : Nat) ↦ x + x def g := fun (x : Nat) ↦ 2 * x example : f = g := by -- 引数 `x` を取る funext x -- `f x` と `g x` を展開する dsimp [f, g] -- `x + x` と `2 * x` が等しいことを証明する ring","breadcrumbs":"funext: 関数等式を示す » funext","id":"36","title":"funext"},"37":{"body":"needs: import Std.Tactic.GuardExpr guard_hyp は，ローカルコンテキストにある命題を確認するタクティクです．指定した仮定が存在すれば成功し，そうでなければ失敗します． example (hP : P) : P := by -- 現在ローカルコンテキストにある命題を確認できる guard_hyp hP : P exact hP 通常の証明で使うことはあまりないかもしれません．このタクティクリストでは，ローカルコンテキストの変化を説明するために使用することがあります．","breadcrumbs":"guard_hyp: 仮定や補題を確認 » guard_hyp","id":"37","title":"guard_hyp"},"38":{"body":"have は，証明の途中でわかることをローカルコンテキストに追加するコマンドです． have h: P := ... で P という命題の証明を構成し，その証明に h という名前を付けることができます． example (hPQ: P → Q) (hQR: Q → R) : P → R := by -- 示したいことが `P → R` なので，`P` だと仮定する intro hP -- 仮定 `hPQ : P → Q` と `hP : P` から `Q` が導かれる have hQ : Q := by exact hPQ hP -- 仮定 `hQR : Q → R` と `hQ : Q` から `R` が導かれる exact hQR hQ 名前を省略して have : P := ... とすると，自動的に this という名前になります．","breadcrumbs":"have: 補題を用意する » have","id":"38","title":"have"},"39":{"body":"補題を示すだけでなく，ある特定の形をした主張を分解するのにも have は使うことができます．","breadcrumbs":"have: 補題を用意する » パターンマッチ","id":"39","title":"パターンマッチ"},"4":{"body":"needs: import Mathlib.Tactic.SolveByElim apply_assumption は，ゴールが ⊢ head であるときに，... → ∀ _, ... → head という形の命題をローカルコンテキストから探し，それを用いてゴールを書き換えます． import Mathlib.Tactic.SolveByElim variable (P Q R : Prop) /-! ## apply_assumption -/ example (hPQ : P → Q) : ¬ Q → ¬ P := by intro hQn hP -- 矛盾を示したい show False -- 自動で `hQn` を適用 apply_assumption show Q -- 自動で `hPQ` を適用 apply_assumption show P -- 自動で `hP` を適用 apply_assumption -- 証明終わり done /-! ## repeat apply_assumption タクティクを繰り返すことを指示するタクティク `repeat` と組み合わせると， 「ローカルコンテキストにある仮定を適切に選んで apply, exact することを繰り返し， ゴールを閉じる」ことができます．\n-/ example (hPQ : P → Q) (hQR : Q → R) (hQ : P) : R := by repeat apply_assumption","breadcrumbs":"apply_assumption: 仮定から後方推論 » apply_assumption","id":"4","title":"apply_assumption"},"40":{"body":"次のように，P ∧ Q という命題から P と Q を取り出すことができます． example (hPQ: P ∧ Q) : P := by -- `P ∧ Q` という仮定を分解する -- `hQ: Q` は不要なのでアンダースコアに置き換える have ⟨ hP, _ ⟩ := hPQ assumption","breadcrumbs":"have: 補題を用意する » 論理積 ∧","id":"40","title":"論理積 ∧"},"41":{"body":"次のように，∃ x: X, P x という命題から，条件を満たす x を取り出すことができます．x: X と hx: P x がローカルコンテキストに追加されます． -- `x`が偶数のとき`3 * x`も偶数\nexample (x : ℕ) (hx : ∃ y, x = 2 * y) : ∃ z, 3 * x = 2 * z := by -- `hx` で存在が主張されている `y` と， -- `x = 2 * y` という命題を得る have ⟨y, hy⟩ := hx exists 3 * y rw [hy] ring","breadcrumbs":"have: 補題を用意する » 存在 ∃","id":"41","title":"存在 ∃"},"42":{"body":"induction は，帰納法のためのタクティクです． 自然数を例に説明します．Lean では自然数は次のように帰納的に定義されています. inductive Nat | zero : Nat | succ (n : Nat) : Nat succ は後者関数と呼ばれる関数で，n + 1 := succ n です． n : Nat についてゴール P n ⊢ Q n があったとします．このとき induction n を行うと，コンストラクタ zero と succ のそれぞれに対して，対応するゴールを生成します．つまり P 0 ⊢ Q 0 (P (succ a)) (P a → Q a) ⊢ Q (succ a) の２つのゴールです． -- 階乗関数\ndef fac : Nat → Nat | 0 => 1 | n + 1 => (n + 1) * fac n example (n : Nat) : 0 < fac n := by -- `n` についての帰納法で示す induction n with | zero => -- `fac` の定義から従う simp [fac] | succ n ih => -- `fac` の定義から従う simp [fac] positivity","breadcrumbs":"induction: 帰納法 » induction","id":"42","title":"induction"},"43":{"body":"needs: import Mathlib.Tactic.Cases induction' というタクティクもあります．こちらは箇条書きによる，より簡潔な書き方が可能です． example (n : Nat) : 0 < fac n := by -- `ih` は帰納法の仮定 -- `k` は `ih` に登場する変数 induction' n with k ih · simp [fac] · simp [fac] positivity","breadcrumbs":"induction: 帰納法 » induction'","id":"43","title":"induction'"},"44":{"body":"また，induction' では「リストの長さに対する帰納法」のようなより複雑な帰納法を行うことができます． example (l : List α) (P : List α → Prop) : P l := by -- リストの長さに対する帰納法 induction' h : l.length generalizing l case zero => -- リストの長さが 0 のとき guard_hyp h: List.length l = 0 show P l sorry case succ n IH => -- リストの長さが `n + 1` のとき guard_hyp h: List.length l = n + 1 -- 帰納法の仮定が使える guard_hyp IH: ∀ (l : List α), List.length l = n → P l show P l sorry","breadcrumbs":"induction: 帰納法 » 一般の～についての帰納法","id":"44","title":"一般の～についての帰納法"},"45":{"body":"時には，より強い帰納法が必要なこともあります．強い帰納法とは，たとえば P(0) を示す (∀ k < n, P (k)) → P (n) を示す したがって ∀ n, P (n) である という形式で表されるような帰納法のことです．これは超限帰納法の特別な場合です．これを使用するには，Nat.strong_induction_on を使って次のようにします． variable (P : Nat → Prop) example (n : Nat) : P n := by -- `n` についての強い帰納法で示す induction' n using Nat.strong_induction_on with n ih -- 仮定が追加される guard_hyp ih : ∀ (m : ℕ), m < n → P m match n with | 0 => sorry | k + 1 => sorry","breadcrumbs":"induction: 帰納法 » 強い帰納法","id":"45","title":"強い帰納法"},"46":{"body":"named after: 導入(introduce) intro は数学で慣習的に行われる P → Q を示すときに最初に P を仮定する ∀ x ∈ A, P(x) を示すときに最初に x ∈ A が与えられたと仮定する といった導入を実行します． 具体的には，intro は ゴールが ⊢ P → Q という形であるときに P をローカルコンテキストに追加して，ゴールを ⊢ Q に変える ゴールが ⊢ ∀ x, P x という形であるときに x をローカルコンテキストに追加してゴールを ⊢ P x に変える といった挙動をします． example (hPQ: P → Q) (hQR: Q → R) : P → R := by -- 示したいことが `P → R` なので，`P` だと仮定する intro hP -- `R` を示したい show R -- 仮定 `hPQ : P → Q` と `hP : P` から `Q` が導かれる have hQ : Q := hPQ hP -- 仮定 `hQR : Q → R` と `hQ : Q` から `R` が導かれる exact hQR hQ もう一つ使用例を挙げておきます： example (P Q : Nat → Prop) (h : ∀ n, P n ↔ Q n) : ∀ y, P (y + 1) → Q (y + 1) := by -- 任意の `y` について示すので，`intro` で `y` を導入する -- そして `P (y + 1) → Q(y + 1)` を示したいので，`P (y + 1)` を仮定する intro y hyP -- `Q (y + 1)` を示せば良い show Q (y + 1) -- 同値を使ってゴールを書き換える rw [← h] -- 仮定 `P (y + 1)` より従う assumption","breadcrumbs":"intro: 含意→や全称∀を示す » intro","id":"46","title":"intro"},"47":{"body":"Lean では否定 ¬ P は P → False として定義されているので，ゴールが ¬ P のときに intro すると P が仮定に追加されて，ゴールが False に変わります． False は矛盾を導けば証明できます． example (h: P → Q) : ¬Q → ¬P := by -- 示したいことが `¬Q → ¬P` なので，`¬Q` だと仮定する -- そうするとゴールが `¬P` になるので， -- さらに `intro` を行って仮定 `hP : P` を導入する intro hnQ hP -- 矛盾を示したい show False -- `hP : P` と `h : P → Q` から `Q` が導かれる have hQ : Q := h hP -- `hQ : Q` と `hnQ : ¬Q` から矛盾が導かれる contradiction","breadcrumbs":"intro: 含意→や全称∀を示す » 否定 ¬ について","id":"47","title":"否定 ¬ について"},"48":{"body":"needs: import Mathlib.Tactic.LeftRight ゴールが ⊢ P ∨ Q であるとき，left はゴールを ⊢ P に，right はゴールを ⊢ Q に変えます． example (hP: P) : P ∨ Q := by left assumption left, right を使わずに Mathlib4 なしで同じことをするには，Or.inl または Or.inr を使用します． example (hP: P) : P ∨ Q := by apply Or.inl assumption","breadcrumbs":"left, right: 論理和∨を示す » left, right","id":"48","title":"left, right"},"49":{"body":"needs: import Mathlib.Tactic.Linarith named after: 線形算術(linear arithmetic) linarith は線形な(不)等式を導くことができます． example (h1 : 2 * x < 3 * y) (h2 : -4 * x + 2 * z < 0): 12 * y - 4 * z ≥ 0 := by linarith linarith はローカルコンテキストを読み取ってくれるので，linarith が通らないとき補題を追加してあげると通るようになることがあります． example : id x ≤ x := by -- `linarith` で示すことはできない try linarith have : id x = x := rfl -- `id x = x` だと教えてあげると `linarith` で示せる linarith","breadcrumbs":"linarith: 線形(不)等式を示す » linarith","id":"49","title":"linarith"},"5":{"body":"apply は含意 → をゴールに適用するタクティクです． ゴールが ⊢ Q で，ローカルコンテキストに h: P → Q があるときに，apply h を実行するとゴールが ⊢ P に書き換わります． -- `P → Q` かつ `P` ならば `Q`\nexample (h: P → Q) (hP: P) : Q := by apply h -- ゴールが `P` に変わっている show P exact hP 注意点として，h: P → Q は P の証明を受け取って Q の証明を返す関数でもあるので，上記の例は apply を使わずに exact h hP で閉じることもできます． -- `P → Q` かつ `P` ならば `Q`\nexample (h: P → Q) (hP: P) : Q := by exact h hP","breadcrumbs":"apply: 含意→を使う » apply","id":"5","title":"apply"},"50":{"body":"もう少し詳細に書くと，linarith は「ロールコンテキストにある線形な(不)等式系に矛盾があるか調べる」タクティクなので，次のような使い方もできます． example (h1: x = 2 * y) (h2 : - x + 2 * y = 1) : False := by linarith","breadcrumbs":"linarith: 線形(不)等式を示す » 補足","id":"50","title":"補足"},"51":{"body":"needs: import Mathlib.Tactic.Linarith named after: non-linear(非線形) arithmetic(算術) nlinarith は非線形な式も扱えるように linarith にいくつか前処理を追加したものです． example (a b: Nat) (h : a ≤ b) : a ^ 2 ≤ b ^ 2 := by -- `linarith` では示すことができない try linarith nlinarith","breadcrumbs":"nlinarith: 非線形な(不)等式を示す » nlinarith","id":"51","title":"nlinarith"},"52":{"body":"needs: import Mathlib.Tactic.PushNeg named after: 押し込む(push) 否定(negation) push_neg はドモルガン則を使って，否定を式の中に押し込みます．たとえば ¬ (P ∧ Q) は P → ¬ Q に， ¬ ∀ x, P x は ∃ x, ¬ P x に という調子で変形します． [1] example (h: P → Q) : ¬ (P ∧ ¬ Q) := by -- ドモルガン則を適用して，`¬` を内側に押し込む push_neg -- `¬` を内側に押し込んだ結果，`¬ P ∨ Q` が得られる -- これは `P → Q` と同値 show P → Q exact h example : ¬ ∃ x : Int , ∀ y : Int, (x + y = 0) := by -- ドモルガン則を適用して，`¬` を内側に押し込む push_neg -- `¬` を内側に押し込んだ結果，ゴールが変わる show ∀ x, ∃ y, ¬ (x + y = 0) intro x exists (- x + 1) linarith [1] モードによって ¬ (P ∧ Q) を P → ¬ Q としたり，¬ P ∨ ¬ Q としたりします．","breadcrumbs":"push_neg: ドモルガン » push_neg","id":"52","title":"push_neg"},"53":{"body":"refine は exact と同様に機能しますが，プレースホルダを受け入れて新しいゴールを生成するという違いがあります． example (hP: P) (hQ: Q) : P ∧ Q := by -- 穴埋め形式で証明を作ることができる refine ⟨?_, hQ⟩ -- ゴールが `⊢ P` になる show P exact hP","breadcrumbs":"refine: 一般の後方推論 » refine","id":"53","title":"refine"},"54":{"body":"h : P → Q という命題があって，ゴールが ⊢ Q であるとき refine h ?_ は apply h と同様に機能するので，refine で apply を代用することができます． example (hPQ : P → Q) (hP : P) : Q := by refine hPQ ?_ -- ゴールが `⊢ P` になる show P refine hP","breadcrumbs":"refine: 一般の後方推論 » apply との関連","id":"54","title":"apply との関連"},"55":{"body":"refine は constructor の代わりに使うこともできます．実際 refine は constructor よりも柔軟で，⊢ P ∧ Q ∧ R のような形のゴールは constructor よりも簡潔に分割できます． example (hP: P) (hQ: Q) (hR : R) : P ∧ Q ∧ R := by -- ゴールを３つに分割する refine ⟨?_, ?_, ?_⟩ · show P exact hP · show Q exact hQ · show R exact hR -- `constructor` を使った場合\n-- 一度に２つのゴールに分割することしかできない\nexample (hP: P) (hQ: Q) (hR : R) : P ∧ Q ∧ R := by constructor · show P exact hP · show Q ∧ R constructor · show Q exact hQ · show R exact hR","breadcrumbs":"refine: 一般の後方推論 » constructor との関連","id":"55","title":"constructor との関連"},"56":{"body":"needs: import Mathlib.Tactic.GCongr named after: 関係(relation) rel は，不等式を代入して適用し，不等式を示します． example (h1 : a ≤ b) (h2 : c ≤ d) : a + c ≤ b + d := by rel [h1, h2] rel は，たとえば整数 x: Int に対して 0 ≤ x ^ 2 であることを自動的に適用するなど, 多少の推論を行います． example (x: Int) (h1 : a ≤ b) : x ^ 2 * a ≤ x ^ 2 * b := by rel [h1]","breadcrumbs":"rel: 不等式を使う » rel","id":"56","title":"rel"},"57":{"body":"needs: import Std.Tactic.Replace replace は have と同じく補題を入手するためのタクティクですが，have とは異なりローカルコンテキストにすでにある命題を置き換えることができます． have を使った場合，ローカルコンテキストにすでに h : P がある状態で，再び h という名前で別の命題を示すと，古い方の h はアクセス不能になって † が付いた状態になってしまいます． replace であれば，古い方が新しい方に置き換えられ，† の付いた命題は出現しません． example : ∀ (n : Int), Even (5 * n) → Even n := by intro n hn -- `Even (5 * n)` という仮定を分解 obtain ⟨ k, hk ⟩ := hn -- 以下がローカルコンテキストに追加される guard_hyp hk: 5 * n = k + k -- `k + k` という形が使いづらいので，`2 * k` に置き換える replace hk : 5 * n = 2 * k := by rw [hk] ring -- `hk` の内容が変化している guard_hyp hk: 5 * n = 2 * k -- 計算をする have := by calc n _ = 5 * n - 4 * n := by ring _ = 2 * k - 4 * n := by rw [hk] _ = 2 * (k - 2 * n) := by ring exists k - 2 * n nth_rw 1 [this] ring","breadcrumbs":"replace: 補題の入れ替え » replace","id":"57","title":"replace"},"58":{"body":"needs: import Mathlib.Tactic.Relation.Rfl named after: 反射律(reflexivity) rfl は，refl attribute の付けられた定理を用いて関係の反射性を示すタクティクです． inductive MyEq {α : Type u} : α → α → Prop | refl (a : α) : MyEq a a attribute [refl] MyEq.refl example (n : ℕ) : MyEq n n := by rfl @[refl] で登録された定理を用いるので，追加でライブラリを import することにより示すことができる命題が増えます． -- `import Mathlib.Data.Nat.Basic` が必要\nexample (n : Nat) : n ≤ n := by rfl","breadcrumbs":"rfl: 関係の反射性を示す » rfl","id":"58","title":"rfl"},"59":{"body":"実は Mathlib.Tactic.Relation.Rfl を import するかどうかにより，内部で呼び出されるタクティクが変わります． Mathlib.Tactic.Relation.Rfl ありなら Lean.MVarId.rfl が， なしなら Lean.MVarId.refl が それぞれ参照されます．後者は @[refl] が付けられた一般の関係の反射性にアクセスできず，等号 = の反射性しか使うことができません． 後者の場合 rfl は，単に定義から等しいものが等しいことを示すタクティクになります． variable (α : Type) example : 1 + 1 = 2 := by rfl example (x : α) : x = x := by rfl example : (2 ^ 70 + 3 ^ 70) % 13 = 0 := by rfl","breadcrumbs":"rfl: 関係の反射性を示す » 補足","id":"59","title":"補足"},"6":{"body":"また，Lean では否定 ¬ P は P → False として実装されているため，ゴールが ⊢ False であるときに hn: ¬P に対して apply hn とするとゴールが ⊢ P に書き換わります． -- 矛盾\nexample (hn: ¬ P) (hP: P) : False := by -- ゴールが `P` に変わる apply hn exact hP","breadcrumbs":"apply: 含意→を使う » 否定 ¬ について","id":"6","title":"否定 ¬ について"},"60":{"body":"needs: import Mathlib.Tactic.Ring ring は，可換環の等式を示します． example : (x + y) ^ 2 = x ^ 2 + 2 * x * y + y ^ 2 := by ring simp 等と異なり，ring? タクティクは用意されていませんが，show_term で具体的にどんなルールが適用されたのかを知ることができます．ただし，その出力結果は非常に長く読みづらいものであることがしばしばです．例えば， example : (x + y) ^ 2 = x ^ 2 + 2 * x * y + y ^ 2 := by show_term ring の出力をここに掲載すると100行を超えてしまいます．","breadcrumbs":"ring: 環の等式を示す » ring","id":"60","title":"ring"},"61":{"body":"rw は rewrite（書き換え）を行うタクティクです．等式や同値をもとに書き換えを行います． hab: a = b や hPQ : P ↔ Q がローカルコンテキストにあるとき， rw [hab] はゴールの中の a をすべて b に置き換え， rw [hPQ] はゴールの中の P をすべて Q に置き換えます． 順番は重要で，b を a に置き換えたいときなどは rw [← hab] のように ← をつけます． h1, h2, ... について続けて置き換えを行いたいときは，rw [h1, h2, ...] のようにします． ゴールではなく，ローカルコンテキストにある h: P を書き換えたいときには at をつけて rw [hPQ] at h とします．すべての箇所で置き換えたいときは rw [hPQ] at * とします． example (a b c d e f : Nat) (h : a * b = c * d) (h' : e = f) : a * (b * e) = c * (d * f) := by rw [h'] -- 結合法則を使う rw [← Nat.mul_assoc] rw [h] -- 結合法則を使う rw [Nat.mul_assoc]","breadcrumbs":"rw: 同値変形 » rw","id":"61","title":"rw"},"62":{"body":"needs: import Mathlib.Tactic.NthRewrite rw はマッチした項をすべて置き換えてしまいます．特定の項だけを書き換えたいとき，nth_rw が使用できます．対象の式中に現れる順番を1始まりで指定することで，項を指定します．指定された順番が式中の対象の項の数よりも多い場合はエラーになります． -- `G` は群\nvariable [Group G] example (a b : G) : a * b⁻¹ = 1 ↔ a = b := by -- `one_mul: 1 * b = b` を使って `b` を `1 * b` に書き換える -- `b` は2回出現するが，2番目だけ置き換える nth_rw 2 [← one_mul b] -- `mul_inv_eq_iff_eq_mul: a * b⁻¹ = c ↔ a = c * b` を使う exact mul_inv_eq_iff_eq_mul","breadcrumbs":"rw: 同値変形 » nth_rw","id":"62","title":"nth_rw"},"63":{"body":"needs: import Mathlib.Tactic.Says exact? や apply? は証明を書いている過程で使用することを想定したタクティクです．Try this: という提案をクリックして採用したら，exact? や apply? は提案内容で上書きされて，最終的な証明には残りません． では，証明のある部分が apply? などにより提案された内容であることを明示したい場合はどうしたら良いでしょうか？says タクティクはまさにその問題を解決するタクティクです． example (hPQ : P → Q) (hQR : Q → R) (hRS : R → S) (hP : P) : S := by -- `exact?` は実行されない exact? says exact hRS (hQR (hPQ hP)) また，simp? や aesop? などに対しても使用することができ，やはりドキュメントとして役に立ちます． -- 合成 `g ∘ f` が単射なら，`f` も単射\nexample {f : X → Y} {g : Y → Z} (hgfinj : Injective (g ∘ f)) : Injective f := by rw [Injective] aesop? says intro a₁ a₂ a apply hgfinj simp_all only [comp_apply] より詳細には，検索タクティク X があり，その提案内容が Try this: Y だったとき，X says とすると says は Try this: Y の代わりに Try this: X says Y という提案を infoview 上で出します．それをクリックすると，X says の内容が X says Y で置換されます．そして，X says Y が実行されるときには X は飛ばされます．","breadcrumbs":"says: タクティク提案の痕跡を残す » says","id":"63","title":"says"},"64":{"body":"says.verify : Bool : true にすると，X says Y の Y のところに，実際には提案されていないタクティクを入れたときにエラーになります． says.no_verify_in_CI : Bool : true にすると，CI 環境で X says Y の Y の部分が実際に提案されている内容と一致するかのチェックが走らなくなります．","breadcrumbs":"says: タクティク提案の痕跡を残す » オプション","id":"64","title":"オプション"},"65":{"body":"show P は, ゴールの中に ⊢ P があるときにそれをメインのゴールにします． たとえば，証明中にこれから示すべきことを明示し，コードを読みやすくする目的で使うことができます． example (hP: P) (hQ: Q) : P ∧ Q := by constructor · show P exact hP · show Q exact hQ","breadcrumbs":"show: 示すべきことを宣言 » show","id":"65","title":"show"},"66":{"body":"simp は，ターゲットを決められた規則に基づいて自動で簡約（simplify）するタクティクです．カスタマイズすることが可能で，簡約に使ってほしい命題を登録することができます． universe u v -- 圏の公理\nclass Category (C : Type u) where -- 射 Hom : C → C → Type v -- 射の合成 comp : ∀ {a b c : C}, Hom a b → Hom b c → Hom a c -- 恒等射. `id a` が `a` 上の恒等射を意味する id : ∀ (a : C), Hom a a -- 恒等射の性質 id_comp : ∀ {a b : C} (f : Hom a b), comp (id a) f = f comp_id : ∀ {a b : C} (f : Hom a b), comp f (id b) = f -- 射の結合律 assoc : ∀ {a b c d : C} (f : Hom a b) (g : Hom b c) (h : Hom c d), comp (comp f g) h = comp f (comp g h) -- `f : Hom a b`と`g : Hom b c`の合成を`f ≫ g`と書く\ninfixr:80 \" ≫ \" => Category.comp -- `Category.hoge` ではなく `hoge` で呼び出せるようにする\nopen Category -- 公理の等式が `simp` で使えるようにする\nattribute [simp] id_comp comp_id assoc -- 変数の定義\nvariable {C : Type u} [Category.{u, v} C] {a b c d e : C} example (f : Hom a b) (g : Hom b c) (h : Hom c d) (i : Hom d e) : (f ≫ (id b ≫ g)) ≫ (h ≫ i) = f ≫ (g ≫ ((id c ≫ h) ≫ i)) := by -- 上で `simp` で使えるようにした等式を使って自動で簡約する simp 既知の h: P という証明を使って簡約させたいときは，明示的に simp [h] と指定することで可能です． 何も指定しなければゴールを簡約しますが，ローカルコンテキストにある h: P を簡約させたければ simp at h と指定することで可能です．","breadcrumbs":"simp: 簡約 » simp","id":"66","title":"simp"},"67":{"body":"simp は自動的に証明を行ってくれますが，何が使われたのか知りたいときもあります．simp? は簡約に何が使われたのかを示してくれるので，rw などを用いて明示的に書き直すことができます．","breadcrumbs":"simp: 簡約 » simp?","id":"67","title":"simp?"},"68":{"body":"simp_all は simp [*] at * の強化版で，ローカルコンテキストとゴールをこれ以上簡約できなくなるまですべて簡約します．","breadcrumbs":"simp: 簡約 » simp_all","id":"68","title":"simp_all"},"69":{"body":"dsimp は，定義上(definitionally)等しいもの同士しか簡約しないという制約付きの simp です．","breadcrumbs":"simp: 簡約 » dsimp","id":"69","title":"dsimp"},"7":{"body":"apply には引数が必須なのですが，省略しても近くにエラーが出ません．一般に，構文的に間違った証明を書いた場合には，エラーがわかりやすい場所に出てくれる保証はありません．","breadcrumbs":"apply: 含意→を使う » よくあるエラー","id":"7","title":"よくあるエラー"},"70":{"body":"証明の細部を埋める前にコンパイルが通るようにしたいとき，証明で埋めるべき箇所に sorry と書くとコンパイルが通るようになります．ただし，sorry を使用しているという旨の警告が出ます． -- Fermat の最終定理\ndef FermatLastTheorem := ∀ x y z n : Nat, n > 2 ∧ x * y * z ≠ 0 → x ^ n + y ^ n ≠ z ^ n theorem flt : FermatLastTheorem := sorry","breadcrumbs":"sorry: 証明したことにする » sorry","id":"70","title":"sorry"},"71":{"body":"ゴールにある if ... then ... else 式を扱うのに有用なタクティクです． if 式を扱う必要が生じるのは，典型的には Lean で定義したアルゴリズムや関数に関して，何か性質を証明しようとしたときです． ゴールが ⊢ Q (if P then a else b) であったときに，split を使用すると2つのサブゴールが生成されます．具体的には 1つはローカルコンテキストに † : P が追加され，ゴールが ⊢ Q (a) 1つはローカルコンテキストに † : ¬ P が追加され，ゴールが ⊢ Q (b) というサブゴールです．split によって追加される仮定は名前がついているとは限りません．名前がついていなかった場合，case などで名前を付けることができます． -- if 式を使って関数を定義する\ndef myabs (x : Int) : Int := if x ≥ 0 then x else - x example (x : Int) : myabs (2 * x) = 2 * myabs x := by -- `myabs` の定義を展開する unfold myabs -- ゴールの中に if 式があって複雑 show (if 2 * x ≥ 0 then 2 * x else -(2 * x)) = 2 * if x ≥ 0 then x else -x -- `split` タクティクでケース分割する split case inl h => -- `2 * x ≥ 0` の場合 guard_hyp h: 2 * x ≥ 0 -- 左辺にあった if 式が消えた show 2 * x = 2 * if x ≥ 0 then x else -x replace h : x ≥ 0 := by linarith [h] -- `simp` で if を消すことができる simp? [h] says simp only [ge_iff_le, h, ite_true] case inr h => -- `2 * x < 0` の場合 guard_hyp h: ¬2 * x ≥ 0 -- 左辺にあった if 式が消えた show -(2 * x) = 2 * if x ≥ 0 then x else -x -- if 式を消すための補題を準備する have hx : ¬ x ≥ 0 := by linarith [h] -- `simp` で簡約 simp? [h, hx] says simp only [ge_iff_le, hx, ite_false, mul_neg]","breadcrumbs":"split: if 式を含む命題を示す » split","id":"71","title":"split"},"72":{"body":"suffices は，数学でよくある「～を示せば十分である」という推論を行うタクティクです． ゴールが ⊢ P であるときに suffices Q from を実行すると， suffices Q from のブロック内では，仮定に this: Q が追加され， suffices Q from 以降では，ゴールが ⊢ Q に書き換えられます． apply と似ていますが，apply と違って「十分条件になっていること」の証明が明らかでないときにも使うことができます． example : 13 ∣ (2 ^ 70 + 3 ^ 70) := by -- 余りがゼロであることを示せば十分 suffices (2 ^ 70 + 3 ^ 70) % 13 = 0 from by exact Iff.mpr (Nat.dvd_iff_div_mul_eq (2 ^ 70 + 3 ^ 70) 13) rfl rfl suffices Q from ... という形式の場合は，証明を直接構成することが必要です．suffices Q from by ... とすると，タクティクによって証明を構成するモードになります．","breadcrumbs":"suffices: 十分条件に帰着 » suffices","id":"72","title":"suffices"},"73":{"body":"needs: import Mathlib.Tactic.Tauto named after: トートロジー(tautology) tauto は， トートロジー(恒真式)であることに基づいてゴールを閉じるタクティクです． ゴールを閉じることができなければエラーになります． -- 含意の導入\nexample (h : P) : Q → P := by tauto -- フレーゲの3段論法\nexample : (P → (Q → R)) → ((P → Q) → (P → R)) := by tauto -- 排中律\nexample : P ∨ ¬ P := by -- `aesop` では示すことができない try aesop tauto -- 対偶\nexample (h : P → Q) : ¬ Q → ¬ P := by -- `exact?` では示すことができない try exact? tauto","breadcrumbs":"tauto: トートロジーを示す » tauto","id":"73","title":"tauto"},"74":{"body":"trivial は明らかなことを示します． trivial は，rfl や contradiction などのタクティクを実行して，現在のゴールを閉じようとします． -- 定義から明らかな等式\nexample : 1 + 1 = 2 := by trivial -- 矛盾があるので, どんな命題でも証明できる\nexample (h: False) : P := by trivial 普段の数学でいう「自明」な命題は trivial では示せないことがほとんどだと思います． aesop を試してみてください．","breadcrumbs":"trivial: 自明 » trivial","id":"74","title":"trivial"},"75":{"body":"needs: import Mathlib.Tactic.WLOG named after: 一般性を失わずに(without loss of generarity) wlog は，数学でよく使われる「一般性を失うことなく～と仮定してよい」というフレーズの Lean での対応物です． example (a b : Nat) : a + b = b + a := by -- `a ≤ b` だと仮定しても一般性を失わない wlog h : a ≤ b with H -- `a ≤ b` なら成り立つと仮定して，そうでないときにも成り立つことを示す · show a + b = b + a guard_hyp H : ∀ (a b : Nat), a ≤ b → a + b = b + a guard_hyp h : ¬a ≤ b abel -- `a ≤ b` であるときに成り立つことを示す · show a + b = b + a guard_hyp h: a ≤ b abel","breadcrumbs":"wlog: 一般性を失わずに特殊化 » wlog","id":"75","title":"wlog"},"8":{"body":"exact の代わりに apply を使うことができます． -- `P → Q` かつ `P` ならば `Q`\nexample (h: P → Q) (hP: P) : Q := by apply h apply hP","breadcrumbs":"apply: 含意→を使う » exact との関連","id":"8","title":"exact との関連"},"9":{"body":"apply は常にどの命題を使うか明示する必要がありますが，「ゴールに apply が適用できるような命題をローカルコンテキストから自動で探す」 apply_assumption というタクティクもあります．","breadcrumbs":"apply: 含意→を使う » apply_assumption との関連","id":"9","title":"apply_assumption との関連"}},"length":76,"save":true},"fields":["title","body","breadcrumbs"],"index":{"body":{"root":{"0":{"df":14,"docs":{"24":{"tf":1.4142135623730951},"26":{"tf":1.7320508075688772},"29":{"tf":1.4142135623730951},"42":{"tf":2.0},"43":{"tf":1.0},"44":{"tf":1.4142135623730951},"45":{"tf":1.0},"49":{"tf":1.4142135623730951},"52":{"tf":1.4142135623730951},"56":{"tf":1.0},"59":{"tf":1.0},"70":{"tf":1.0},"71":{"tf":3.3166247903554},"72":{"tf":1.0}}},"1":{"0":{"0":{"df":1,"docs":{"60":{"tf":1.0}}},"df":0,"docs":{}},"2":{"df":1,"docs":{"49":{"tf":1.0}}},"3":{"df":2,"docs":{"59":{"tf":1.0},"72":{"tf":1.7320508075688772}}},"df":15,"docs":{"24":{"tf":1.0},"26":{"tf":2.449489742783178},"33":{"tf":1.0},"34":{"tf":1.0},"42":{"tf":2.0},"44":{"tf":1.4142135623730951},"45":{"tf":1.0},"46":{"tf":2.8284271247461903},"50":{"tf":1.0},"52":{"tf":1.7320508075688772},"57":{"tf":1.0},"59":{"tf":1.4142135623730951},"62":{"tf":1.7320508075688772},"71":{"tf":1.4142135623730951},"74":{"tf":1.4142135623730951}}},"2":{"df":19,"docs":{"10":{"tf":1.4142135623730951},"24":{"tf":3.1622776601683795},"27":{"tf":1.4142135623730951},"34":{"tf":1.0},"35":{"tf":1.0},"36":{"tf":1.4142135623730951},"41":{"tf":1.7320508075688772},"49":{"tf":1.4142135623730951},"50":{"tf":1.4142135623730951},"51":{"tf":1.4142135623730951},"56":{"tf":1.7320508075688772},"57":{"tf":2.6457513110645907},"59":{"tf":1.4142135623730951},"60":{"tf":2.8284271247461903},"62":{"tf":1.0},"70":{"tf":1.0},"71":{"tf":3.872983346207417},"72":{"tf":1.7320508075688772},"74":{"tf":1.0}},"回":{"df":0,"docs":{},"出":{"df":0,"docs":{},"現":{"df":0,"docs":{},"す":{"df":0,"docs":{},"る":{"df":0,"docs":{},"が":{"df":0,"docs":{},"，":{"2":{"df":1,"docs":{"62":{"tf":1.0}}},"df":0,"docs":{}}}}}}}}},"3":{"df":7,"docs":{"27":{"tf":1.0},"34":{"tf":1.0},"41":{"tf":1.4142135623730951},"49":{"tf":1.0},"59":{"tf":1.0},"72":{"tf":1.7320508075688772},"73":{"tf":1.0}}},"4":{"df":2,"docs":{"49":{"tf":1.4142135623730951},"57":{"tf":1.4142135623730951}}},"5":{"df":1,"docs":{"57":{"tf":2.449489742783178}}},"7":{"0":{"df":2,"docs":{"59":{"tf":1.4142135623730951},"72":{"tf":2.449489742783178}}},"df":1,"docs":{"34":{"tf":1.0}}},"_":{"df":9,"docs":{"10":{"tf":1.0},"11":{"tf":1.0},"24":{"tf":1.0},"4":{"tf":1.0},"40":{"tf":1.0},"53":{"tf":1.0},"54":{"tf":1.4142135623730951},"55":{"tf":1.7320508075688772},"57":{"tf":1.7320508075688772}}},"a":{"b":{"df":0,"docs":{},"e":{"df":0,"docs":{},"l":{"df":1,"docs":{"75":{"tf":1.4142135623730951}}}}},"d":{"d":{"_":{"df":0,"docs":{},"z":{"df":0,"docs":{},"e":{"df":0,"docs":{},"r":{"df":0,"docs":{},"o":{"df":1,"docs":{"24":{"tf":1.4142135623730951}}}}}}},"df":0,"docs":{}},"df":0,"docs":{}},"df":0,"docs":{},"e":{"df":0,"docs":{},"s":{"df":0,"docs":{},"o":{"df":0,"docs":{},"p":{"df":5,"docs":{"3":{"tf":3.4641016151377544},"35":{"tf":1.0},"63":{"tf":1.4142135623730951},"73":{"tf":1.4142135623730951},"74":{"tf":1.0}}}}}},"p":{"df":0,"docs":{},"p":{"df":0,"docs":{},"l":{"df":0,"docs":{},"i":{"df":14,"docs":{"10":{"tf":3.0},"20":{"tf":1.4142135623730951},"21":{"tf":1.4142135623730951},"3":{"tf":1.0},"4":{"tf":1.0},"48":{"tf":1.0},"5":{"tf":2.23606797749979},"54":{"tf":1.7320508075688772},"6":{"tf":1.4142135623730951},"63":{"tf":2.0},"7":{"tf":1.0},"72":{"tf":1.4142135623730951},"8":{"tf":1.7320508075688772},"9":{"tf":1.4142135623730951}}},"y":{"_":{"a":{"df":0,"docs":{},"s":{"df":0,"docs":{},"s":{"df":0,"docs":{},"u":{"df":0,"docs":{},"m":{"df":0,"docs":{},"p":{"df":0,"docs":{},"t":{"df":2,"docs":{"4":{"tf":2.8284271247461903},"9":{"tf":1.4142135623730951}}}}}}}}},"df":0,"docs":{}},"df":0,"docs":{}}}}},"r":{"df":0,"docs":{},"i":{"df":0,"docs":{},"t":{"df":0,"docs":{},"h":{"df":0,"docs":{},"m":{"df":0,"docs":{},"e":{"df":0,"docs":{},"t":{"df":2,"docs":{"49":{"tf":1.0},"51":{"tf":1.0}}}}}}}}},"s":{"df":0,"docs":{},"s":{"df":0,"docs":{},"o":{"c":{"df":1,"docs":{"66":{"tf":1.4142135623730951}}},"df":0,"docs":{}},"u":{"df":0,"docs":{},"m":{"df":0,"docs":{},"p":{"df":0,"docs":{},"t":{"df":7,"docs":{"11":{"tf":1.7320508075688772},"12":{"tf":1.0},"13":{"tf":1.0},"32":{"tf":1.4142135623730951},"40":{"tf":1.0},"46":{"tf":1.0},"48":{"tf":1.4142135623730951}}}}}}}},"t":{"df":0,"docs":{},"t":{"df":0,"docs":{},"r":{"df":0,"docs":{},"i":{"b":{"df":0,"docs":{},"u":{"df":0,"docs":{},"t":{"df":2,"docs":{"58":{"tf":1.4142135623730951},"66":{"tf":1.0}}}}},"df":0,"docs":{}}}}},"x":{"df":0,"docs":{},"i":{"df":0,"docs":{},"o":{"df":0,"docs":{},"m":{"df":1,"docs":{"10":{"tf":1.4142135623730951}}}}}}},"b":{"`":{"df":0,"docs":{},"と":{"`":{"df":0,"docs":{},"g":{"df":1,"docs":{"66":{"tf":1.0}}}},"df":0,"docs":{}}},"df":10,"docs":{"10":{"tf":2.0},"29":{"tf":2.0},"35":{"tf":2.449489742783178},"51":{"tf":1.7320508075688772},"56":{"tf":2.0},"61":{"tf":2.449489742783178},"62":{"tf":3.3166247903554},"66":{"tf":4.0},"71":{"tf":1.4142135623730951},"75":{"tf":4.123105625617661}},"o":{"df":0,"docs":{},"o":{"df":0,"docs":{},"l":{"df":1,"docs":{"64":{"tf":1.4142135623730951}}}}},"s":{"df":1,"docs":{"24":{"tf":1.7320508075688772}}},"y":{"_":{"c":{"a":{"df":0,"docs":{},"s":{"df":1,"docs":{"13":{"tf":2.0}}}},"df":0,"docs":{},"o":{"df":0,"docs":{},"n":{"df":0,"docs":{},"t":{"df":0,"docs":{},"r":{"a":{"df":1,"docs":{"14":{"tf":2.0}}},"df":0,"docs":{}}}}}},"df":0,"docs":{}},"df":0,"docs":{}}},"c":{"`":{"df":0,"docs":{},"の":{"df":0,"docs":{},"合":{"df":0,"docs":{},"成":{"df":0,"docs":{},"を":{"`":{"df":0,"docs":{},"f":{"df":1,"docs":{"66":{"tf":1.0}}}},"df":0,"docs":{}}}}}},"a":{"df":0,"docs":{},"l":{"c":{"df":2,"docs":{"17":{"tf":1.4142135623730951},"57":{"tf":1.0}}},"df":0,"docs":{}},"s":{"df":0,"docs":{},"e":{"df":7,"docs":{"13":{"tf":1.4142135623730951},"18":{"tf":2.8284271247461903},"19":{"tf":2.449489742783178},"20":{"tf":1.7320508075688772},"21":{"tf":1.4142135623730951},"44":{"tf":1.4142135623730951},"71":{"tf":1.4142135623730951}}}},"t":{"df":0,"docs":{},"e":{"df":0,"docs":{},"g":{"df":0,"docs":{},"o":{"df":0,"docs":{},"r":{"df":0,"docs":{},"i":{"df":1,"docs":{"66":{"tf":1.4142135623730951}}},"y":{".":{"c":{"df":0,"docs":{},"o":{"df":0,"docs":{},"m":{"df":0,"docs":{},"p":{"df":1,"docs":{"66":{"tf":1.0}}}}}},"df":0,"docs":{},"h":{"df":0,"docs":{},"o":{"df":0,"docs":{},"g":{"df":1,"docs":{"66":{"tf":1.0}}}}},"{":{"df":0,"docs":{},"u":{"df":1,"docs":{"66":{"tf":1.0}}}}},"df":0,"docs":{}}}}}}}},"df":5,"docs":{"29":{"tf":2.0},"56":{"tf":1.4142135623730951},"61":{"tf":1.7320508075688772},"62":{"tf":1.4142135623730951},"66":{"tf":4.58257569495584}},"h":{"df":0,"docs":{},"o":{"df":0,"docs":{},"o":{"df":0,"docs":{},"s":{"df":2,"docs":{"22":{"tf":1.7320508075688772},"23":{"tf":1.0}}}}}},"i":{"df":2,"docs":{"3":{"tf":1.0},"64":{"tf":1.0}}},"l":{"a":{"df":0,"docs":{},"s":{"df":0,"docs":{},"s":{"df":1,"docs":{"66":{"tf":1.0}},"i":{"c":{"a":{"df":0,"docs":{},"l":{".":{"c":{"df":0,"docs":{},"h":{"df":0,"docs":{},"o":{"df":0,"docs":{},"i":{"c":{"df":1,"docs":{"23":{"tf":1.4142135623730951}}},"df":0,"docs":{}}}}},"df":0,"docs":{}},"df":0,"docs":{}}},"df":0,"docs":{}},"df":0,"docs":{}}}}},"df":0,"docs":{}},"o":{"df":0,"docs":{},"m":{"df":0,"docs":{},"p":{"_":{"a":{"df":0,"docs":{},"p":{"df":0,"docs":{},"p":{"df":0,"docs":{},"l":{"df":0,"docs":{},"i":{"df":2,"docs":{"3":{"tf":1.0},"63":{"tf":1.0}}}}}}},"df":0,"docs":{},"i":{"d":{"df":1,"docs":{"66":{"tf":1.4142135623730951}}},"df":0,"docs":{}}},"df":1,"docs":{"66":{"tf":2.6457513110645907}}}},"n":{"df":0,"docs":{},"g":{"df":0,"docs":{},"r":{"df":1,"docs":{"24":{"tf":2.6457513110645907}},"u":{"df":0,"docs":{},"e":{"df":0,"docs":{},"n":{"c":{"df":1,"docs":{"24":{"tf":1.0}}},"df":0,"docs":{}}}}}},"s":{"df":0,"docs":{},"t":{"df":0,"docs":{},"r":{"df":0,"docs":{},"u":{"c":{"df":0,"docs":{},"t":{"df":0,"docs":{},"o":{"df":0,"docs":{},"r":{"df":4,"docs":{"25":{"tf":1.7320508075688772},"26":{"tf":1.4142135623730951},"55":{"tf":2.6457513110645907},"65":{"tf":1.0}}}}}},"df":0,"docs":{}}}}},"t":{"df":0,"docs":{},"r":{"a":{"d":{"df":0,"docs":{},"i":{"c":{"df":0,"docs":{},"t":{"df":5,"docs":{"13":{"tf":1.0},"14":{"tf":1.0},"27":{"tf":2.23606797749979},"47":{"tf":1.0},"74":{"tf":1.0}}}},"df":0,"docs":{}}},"df":0,"docs":{}},"df":0,"docs":{}}},"v":{"df":1,"docs":{"28":{"tf":1.4142135623730951}},"e":{"df":0,"docs":{},"r":{"df":0,"docs":{},"t":{"df":1,"docs":{"29":{"tf":1.7320508075688772}}}}}}}}},"d":{"df":3,"docs":{"56":{"tf":1.4142135623730951},"61":{"tf":1.7320508075688772},"66":{"tf":2.23606797749979}},"e":{"df":0,"docs":{},"f":{"df":4,"docs":{"36":{"tf":1.4142135623730951},"42":{"tf":1.0},"70":{"tf":1.0},"71":{"tf":1.0}}},"p":{"df":0,"docs":{},"e":{"df":0,"docs":{},"n":{"d":{"df":1,"docs":{"10":{"tf":1.0}}},"df":0,"docs":{}}}}},"o":{"df":0,"docs":{},"n":{"df":0,"docs":{},"e":{"df":4,"docs":{"10":{"tf":1.4142135623730951},"30":{"tf":1.4142135623730951},"33":{"tf":1.0},"4":{"tf":1.0}}}}},"s":{"df":0,"docs":{},"i":{"df":0,"docs":{},"m":{"df":0,"docs":{},"p":{"df":2,"docs":{"36":{"tf":1.0},"69":{"tf":1.4142135623730951}}}}}}},"df":0,"docs":{},"e":{"df":2,"docs":{"61":{"tf":1.7320508075688772},"66":{"tf":1.4142135623730951}},"v":{"df":0,"docs":{},"e":{"df":0,"docs":{},"n":{"df":1,"docs":{"57":{"tf":1.7320508075688772}}}}},"x":{"a":{"c":{"df":0,"docs":{},"t":{"df":30,"docs":{"10":{"tf":1.0},"12":{"tf":1.4142135623730951},"15":{"tf":1.0},"16":{"tf":1.0},"18":{"tf":1.4142135623730951},"19":{"tf":1.4142135623730951},"21":{"tf":1.0},"22":{"tf":1.0},"23":{"tf":1.0},"24":{"tf":1.0},"25":{"tf":1.7320508075688772},"29":{"tf":1.4142135623730951},"31":{"tf":2.23606797749979},"32":{"tf":1.4142135623730951},"33":{"tf":3.1622776601683795},"37":{"tf":1.0},"38":{"tf":1.4142135623730951},"4":{"tf":1.0},"46":{"tf":1.0},"5":{"tf":1.7320508075688772},"52":{"tf":1.0},"53":{"tf":1.4142135623730951},"55":{"tf":2.449489742783178},"6":{"tf":1.0},"62":{"tf":1.0},"63":{"tf":2.23606797749979},"65":{"tf":1.4142135623730951},"72":{"tf":1.0},"73":{"tf":1.4142135623730951},"8":{"tf":1.4142135623730951}}}},"df":0,"docs":{},"m":{"df":0,"docs":{},"p":{"df":0,"docs":{},"l":{"df":60,"docs":{"10":{"tf":1.0},"11":{"tf":1.0},"13":{"tf":1.0},"14":{"tf":1.0},"15":{"tf":1.4142135623730951},"16":{"tf":1.0},"18":{"tf":1.0},"19":{"tf":1.0},"20":{"tf":1.0},"21":{"tf":1.4142135623730951},"22":{"tf":1.0},"23":{"tf":1.0},"24":{"tf":1.4142135623730951},"25":{"tf":1.4142135623730951},"26":{"tf":1.0},"27":{"tf":2.0},"29":{"tf":1.0},"3":{"tf":1.4142135623730951},"31":{"tf":1.4142135623730951},"33":{"tf":1.4142135623730951},"34":{"tf":1.0},"35":{"tf":1.0},"36":{"tf":1.0},"37":{"tf":1.0},"38":{"tf":1.0},"4":{"tf":1.4142135623730951},"40":{"tf":1.0},"41":{"tf":1.0},"42":{"tf":1.0},"43":{"tf":1.0},"44":{"tf":1.0},"45":{"tf":1.0},"46":{"tf":1.4142135623730951},"47":{"tf":1.0},"48":{"tf":1.4142135623730951},"49":{"tf":1.4142135623730951},"5":{"tf":1.4142135623730951},"50":{"tf":1.0},"51":{"tf":1.0},"52":{"tf":1.4142135623730951},"53":{"tf":1.0},"54":{"tf":1.0},"55":{"tf":1.4142135623730951},"56":{"tf":1.4142135623730951},"57":{"tf":1.0},"58":{"tf":1.4142135623730951},"59":{"tf":1.7320508075688772},"6":{"tf":1.0},"60":{"tf":1.4142135623730951},"61":{"tf":1.0},"62":{"tf":1.0},"63":{"tf":1.4142135623730951},"65":{"tf":1.0},"66":{"tf":1.0},"71":{"tf":1.0},"72":{"tf":1.0},"73":{"tf":2.0},"74":{"tf":1.4142135623730951},"75":{"tf":1.0},"8":{"tf":1.0}}}}}},"df":0,"docs":{},"i":{"df":0,"docs":{},"s":{"df":0,"docs":{},"t":{"df":5,"docs":{"23":{"tf":1.0},"34":{"tf":2.0},"41":{"tf":1.0},"52":{"tf":1.0},"57":{"tf":1.0}}}}},"p":{"df":0,"docs":{},"l":{"df":0,"docs":{},"o":{"df":0,"docs":{},"s":{"df":0,"docs":{},"i":{"df":0,"docs":{},"o":{"df":0,"docs":{},"n":{")":{"df":0,"docs":{},"と":{"df":0,"docs":{},"呼":{"df":0,"docs":{},"び":{"df":0,"docs":{},"ま":{"df":0,"docs":{},"す":{"df":0,"docs":{},"が":{"df":0,"docs":{},"，":{"c":{"df":0,"docs":{},"o":{"df":0,"docs":{},"n":{"df":0,"docs":{},"t":{"df":0,"docs":{},"r":{"a":{"d":{"df":0,"docs":{},"i":{"c":{"df":0,"docs":{},"t":{"df":1,"docs":{"27":{"tf":1.0}}}},"df":0,"docs":{}}},"df":0,"docs":{}},"df":0,"docs":{}}}}}},"df":0,"docs":{}}}}}}}}},"df":0,"docs":{}}}}}}}},"t":{"df":1,"docs":{"35":{"tf":2.0}},"e":{"df":0,"docs":{},"n":{"df":0,"docs":{},"s":{"df":0,"docs":{},"i":{"df":0,"docs":{},"o":{"df":0,"docs":{},"n":{"df":1,"docs":{"35":{"tf":1.0}}}}}}}}}}},"f":{"a":{"c":{"df":2,"docs":{"42":{"tf":2.6457513110645907},"43":{"tf":1.7320508075688772}}},"df":0,"docs":{},"l":{"df":0,"docs":{},"s":{"df":7,"docs":{"14":{"tf":1.4142135623730951},"27":{"tf":1.4142135623730951},"4":{"tf":1.0},"47":{"tf":2.0},"50":{"tf":1.0},"6":{"tf":1.7320508075688772},"74":{"tf":1.0}}}}},"df":11,"docs":{"10":{"tf":2.23606797749979},"22":{"tf":2.8284271247461903},"23":{"tf":3.0},"24":{"tf":3.7416573867739413},"29":{"tf":1.7320508075688772},"3":{"tf":3.1622776601683795},"35":{"tf":1.7320508075688772},"36":{"tf":2.449489742783178},"61":{"tf":1.7320508075688772},"63":{"tf":2.23606797749979},"66":{"tf":3.605551275463989}},"e":{"df":0,"docs":{},"r":{"df":0,"docs":{},"m":{"a":{"df":0,"docs":{},"t":{"df":1,"docs":{"70":{"tf":1.0}},"l":{"a":{"df":0,"docs":{},"s":{"df":0,"docs":{},"t":{"df":0,"docs":{},"t":{"df":0,"docs":{},"h":{"df":0,"docs":{},"e":{"df":0,"docs":{},"o":{"df":0,"docs":{},"r":{"df":0,"docs":{},"e":{"df":0,"docs":{},"m":{"df":1,"docs":{"70":{"tf":1.4142135623730951}}}}}}}}}}}},"df":0,"docs":{}}}},"df":0,"docs":{}}}},"l":{"df":0,"docs":{},"t":{"df":1,"docs":{"70":{"tf":1.0}}}},"u":{"df":0,"docs":{},"n":{"c":{"df":0,"docs":{},"t":{"df":0,"docs":{},"i":{"df":0,"docs":{},"o":{"df":0,"docs":{},"n":{"df":1,"docs":{"3":{"tf":1.0}}}}}}},"df":4,"docs":{"15":{"tf":1.0},"16":{"tf":1.0},"23":{"tf":1.4142135623730951},"36":{"tf":1.4142135623730951}},"e":{"df":0,"docs":{},"x":{"df":0,"docs":{},"t":{"df":1,"docs":{"36":{"tf":1.7320508075688772}}}}}}}},"g":{"df":9,"docs":{"10":{"tf":1.7320508075688772},"22":{"tf":2.8284271247461903},"24":{"tf":2.23606797749979},"3":{"tf":2.23606797749979},"35":{"tf":1.7320508075688772},"36":{"tf":2.449489742783178},"62":{"tf":1.7320508075688772},"63":{"tf":1.7320508075688772},"66":{"tf":2.6457513110645907}},"e":{"_":{"df":0,"docs":{},"i":{"df":0,"docs":{},"f":{"df":0,"docs":{},"f":{"_":{"df":0,"docs":{},"l":{"df":1,"docs":{"71":{"tf":1.4142135623730951}}}},"df":0,"docs":{}}}}},"df":0,"docs":{},"n":{"df":0,"docs":{},"e":{"df":0,"docs":{},"r":{"a":{"df":0,"docs":{},"r":{"df":1,"docs":{"75":{"tf":1.0}}}},"df":1,"docs":{"44":{"tf":1.0}}}}}},"o":{"a":{"df":0,"docs":{},"l":{"df":1,"docs":{"25":{"tf":1.0}}}},"df":0,"docs":{}},"r":{"df":0,"docs":{},"o":{"df":0,"docs":{},"u":{"df":0,"docs":{},"p":{"df":2,"docs":{"10":{"tf":1.4142135623730951},"62":{"tf":1.0}}}}}},"u":{"a":{"df":0,"docs":{},"r":{"d":{"_":{"df":0,"docs":{},"h":{"df":0,"docs":{},"y":{"df":0,"docs":{},"p":{"df":8,"docs":{"13":{"tf":1.4142135623730951},"22":{"tf":1.4142135623730951},"37":{"tf":1.7320508075688772},"44":{"tf":1.7320508075688772},"45":{"tf":1.0},"57":{"tf":1.4142135623730951},"71":{"tf":1.4142135623730951},"75":{"tf":1.7320508075688772}}}}},"m":{"df":0,"docs":{},"s":{"df":0,"docs":{},"g":{"df":1,"docs":{"10":{"tf":1.0}}}}}},"df":0,"docs":{}},"df":0,"docs":{}}},"df":0,"docs":{}}},"h":{".":{"df":0,"docs":{},"l":{"df":0,"docs":{},"e":{"df":0,"docs":{},"f":{"df":0,"docs":{},"t":{"df":1,"docs":{"25":{"tf":1.4142135623730951}}}}}},"r":{"df":0,"docs":{},"i":{"df":0,"docs":{},"g":{"df":0,"docs":{},"h":{"df":0,"docs":{},"t":{"df":1,"docs":{"25":{"tf":1.0}}}}}}}},"1":{"df":4,"docs":{"49":{"tf":1.0},"50":{"tf":1.0},"56":{"tf":2.0},"61":{"tf":1.4142135623730951}}},"2":{"df":4,"docs":{"49":{"tf":1.0},"50":{"tf":1.0},"56":{"tf":1.4142135623730951},"61":{"tf":1.4142135623730951}}},"a":{"b":{"df":1,"docs":{"61":{"tf":1.7320508075688772}}},"df":0,"docs":{}},"c":{"df":1,"docs":{"29":{"tf":1.4142135623730951}}},"df":30,"docs":{"10":{"tf":1.4142135623730951},"13":{"tf":1.0},"14":{"tf":2.0},"15":{"tf":1.0},"18":{"tf":2.23606797749979},"19":{"tf":1.7320508075688772},"20":{"tf":1.4142135623730951},"21":{"tf":2.449489742783178},"22":{"tf":1.4142135623730951},"23":{"tf":1.7320508075688772},"24":{"tf":2.0},"25":{"tf":1.4142135623730951},"27":{"tf":1.7320508075688772},"29":{"tf":3.0},"38":{"tf":1.4142135623730951},"44":{"tf":1.7320508075688772},"46":{"tf":1.4142135623730951},"47":{"tf":1.7320508075688772},"5":{"tf":2.8284271247461903},"51":{"tf":1.0},"52":{"tf":1.4142135623730951},"54":{"tf":1.7320508075688772},"57":{"tf":1.7320508075688772},"61":{"tf":2.449489742783178},"66":{"tf":3.1622776601683795},"71":{"tf":3.1622776601683795},"73":{"tf":1.4142135623730951},"74":{"tf":1.0},"75":{"tf":2.23606797749979},"8":{"tf":1.4142135623730951}},"e":{"a":{"d":{"df":1,"docs":{"4":{"tf":1.4142135623730951}}},"df":0,"docs":{}},"df":0,"docs":{},"l":{"df":0,"docs":{},"p":{"df":1,"docs":{"1":{"tf":1.0}}}}},"f":{"df":2,"docs":{"22":{"tf":2.0},"24":{"tf":1.4142135623730951}}},"g":{"df":1,"docs":{"22":{"tf":1.7320508075688772}},"f":{"df":0,"docs":{},"i":{"df":0,"docs":{},"n":{"df":0,"docs":{},"j":{"df":2,"docs":{"3":{"tf":1.7320508075688772},"63":{"tf":1.4142135623730951}}}}}}},"k":{"df":1,"docs":{"57":{"tf":2.6457513110645907}}},"n":{"df":2,"docs":{"57":{"tf":1.4142135623730951},"6":{"tf":2.0}},"e":{"_":{"df":0,"docs":{},"s":{"df":0,"docs":{},"t":{"df":1,"docs":{"23":{"tf":1.4142135623730951}}}}},"df":0,"docs":{}},"n":{"df":0,"docs":{},"p":{"df":1,"docs":{"13":{"tf":1.0}}}},"p":{"df":1,"docs":{"27":{"tf":1.0}}},"q":{"df":2,"docs":{"14":{"tf":1.4142135623730951},"47":{"tf":1.4142135623730951}}}},"o":{"df":0,"docs":{},"g":{"df":0,"docs":{},"e":{"df":1,"docs":{"66":{"tf":1.0}}}},"m":{"df":1,"docs":{"66":{"tf":4.0}}}},"p":{"df":27,"docs":{"11":{"tf":1.0},"13":{"tf":1.7320508075688772},"14":{"tf":1.0},"15":{"tf":2.0},"16":{"tf":2.0},"18":{"tf":1.4142135623730951},"19":{"tf":1.4142135623730951},"20":{"tf":1.4142135623730951},"21":{"tf":2.23606797749979},"25":{"tf":1.4142135623730951},"27":{"tf":1.0},"31":{"tf":2.8284271247461903},"37":{"tf":1.7320508075688772},"38":{"tf":1.7320508075688772},"4":{"tf":1.4142135623730951},"40":{"tf":1.0},"46":{"tf":1.7320508075688772},"47":{"tf":2.0},"48":{"tf":1.4142135623730951},"5":{"tf":2.23606797749979},"53":{"tf":1.4142135623730951},"54":{"tf":1.4142135623730951},"55":{"tf":2.0},"6":{"tf":1.4142135623730951},"63":{"tf":1.4142135623730951},"65":{"tf":1.4142135623730951},"8":{"tf":1.4142135623730951}},"q":{"df":10,"docs":{"15":{"tf":2.0},"16":{"tf":1.7320508075688772},"33":{"tf":1.4142135623730951},"38":{"tf":1.7320508075688772},"4":{"tf":1.7320508075688772},"40":{"tf":1.4142135623730951},"46":{"tf":1.7320508075688772},"54":{"tf":1.4142135623730951},"61":{"tf":2.0},"63":{"tf":1.4142135623730951}}},"r":{"df":4,"docs":{"18":{"tf":1.4142135623730951},"19":{"tf":1.4142135623730951},"20":{"tf":1.4142135623730951},"21":{"tf":1.4142135623730951}}}},"q":{"df":15,"docs":{"18":{"tf":1.4142135623730951},"19":{"tf":1.4142135623730951},"20":{"tf":1.4142135623730951},"21":{"tf":2.23606797749979},"25":{"tf":1.4142135623730951},"31":{"tf":1.7320508075688772},"33":{"tf":1.4142135623730951},"38":{"tf":1.7320508075688772},"4":{"tf":1.0},"40":{"tf":1.0},"46":{"tf":1.7320508075688772},"47":{"tf":1.4142135623730951},"53":{"tf":1.4142135623730951},"55":{"tf":2.0},"65":{"tf":1.4142135623730951}},"n":{"df":1,"docs":{"4":{"tf":1.4142135623730951}}},"r":{"df":11,"docs":{"15":{"tf":2.0},"16":{"tf":1.7320508075688772},"18":{"tf":1.4142135623730951},"19":{"tf":1.4142135623730951},"20":{"tf":1.4142135623730951},"21":{"tf":1.4142135623730951},"33":{"tf":1.4142135623730951},"38":{"tf":1.7320508075688772},"4":{"tf":1.0},"46":{"tf":1.7320508075688772},"63":{"tf":1.4142135623730951}}}},"r":{"df":2,"docs":{"55":{"tf":2.0},"63":{"tf":1.4142135623730951}}},"x":{"df":3,"docs":{"26":{"tf":1.4142135623730951},"41":{"tf":2.0},"71":{"tf":1.7320508075688772}}},"y":{"df":1,"docs":{"41":{"tf":1.4142135623730951}},"p":{"df":1,"docs":{"46":{"tf":1.0}}}}},"i":{"d":{"_":{"c":{"df":0,"docs":{},"o":{"df":0,"docs":{},"m":{"df":0,"docs":{},"p":{"df":1,"docs":{"66":{"tf":1.4142135623730951}}}}}},"df":0,"docs":{}},"df":2,"docs":{"49":{"tf":1.7320508075688772},"66":{"tf":2.449489742783178}}},"df":0,"docs":{},"f":{"df":0,"docs":{},"f":{".":{"df":0,"docs":{},"m":{"df":0,"docs":{},"p":{"df":0,"docs":{},"r":{"df":1,"docs":{"72":{"tf":1.0}}}}}},"df":0,"docs":{}}},"h":{"df":4,"docs":{"42":{"tf":1.0},"43":{"tf":1.7320508075688772},"44":{"tf":1.4142135623730951},"45":{"tf":1.4142135623730951}}},"m":{"df":0,"docs":{},"p":{"df":0,"docs":{},"o":{"df":0,"docs":{},"r":{"df":0,"docs":{},"t":{"df":26,"docs":{"10":{"tf":1.7320508075688772},"14":{"tf":1.0},"16":{"tf":1.0},"20":{"tf":1.0},"21":{"tf":1.0},"22":{"tf":1.0},"29":{"tf":1.0},"3":{"tf":1.7320508075688772},"33":{"tf":1.0},"35":{"tf":1.0},"37":{"tf":1.0},"4":{"tf":1.4142135623730951},"43":{"tf":1.0},"48":{"tf":1.0},"49":{"tf":1.0},"51":{"tf":1.0},"52":{"tf":1.0},"56":{"tf":1.0},"57":{"tf":1.0},"58":{"tf":1.7320508075688772},"59":{"tf":1.0},"60":{"tf":1.0},"62":{"tf":1.0},"63":{"tf":1.0},"73":{"tf":1.0},"75":{"tf":1.0}}}}}}},"n":{"d":{"df":0,"docs":{},"u":{"c":{"df":0,"docs":{},"t":{"df":5,"docs":{"42":{"tf":2.23606797749979},"43":{"tf":1.7320508075688772},"44":{"tf":1.4142135623730951},"45":{"tf":1.0},"58":{"tf":1.0}}}},"df":0,"docs":{}}},"df":0,"docs":{},"f":{"df":0,"docs":{},"i":{"df":0,"docs":{},"x":{"df":0,"docs":{},"r":{":":{"8":{"0":{"df":1,"docs":{"66":{"tf":1.0}}},"df":0,"docs":{}},"df":0,"docs":{}},"df":0,"docs":{}}}},"o":{"df":1,"docs":{"10":{"tf":1.0}},"v":{"df":0,"docs":{},"i":{"df":0,"docs":{},"e":{"df":0,"docs":{},"w":{"df":1,"docs":{"63":{"tf":1.0}}}}}}}},"j":{"df":0,"docs":{},"e":{"c":{"df":0,"docs":{},"t":{"df":2,"docs":{"3":{"tf":2.6457513110645907},"63":{"tf":1.7320508075688772}}}},"df":0,"docs":{}}},"l":{"df":4,"docs":{"13":{"tf":1.0},"18":{"tf":1.7320508075688772},"19":{"tf":1.4142135623730951},"71":{"tf":1.0}}},"r":{"df":4,"docs":{"13":{"tf":1.0},"18":{"tf":1.7320508075688772},"19":{"tf":1.4142135623730951},"71":{"tf":1.0}}},"s":{"df":0,"docs":{},"e":{"df":0,"docs":{},"r":{"df":0,"docs":{},"t":{"df":1,"docs":{"18":{"tf":1.4142135623730951}}}}}},"t":{"df":5,"docs":{"24":{"tf":2.0},"52":{"tf":1.4142135623730951},"56":{"tf":1.4142135623730951},"57":{"tf":1.0},"71":{"tf":1.7320508075688772}},"r":{"df":0,"docs":{},"o":{"d":{"df":0,"docs":{},"u":{"c":{"df":1,"docs":{"46":{"tf":1.0}}},"df":0,"docs":{}}},"df":19,"docs":{"13":{"tf":1.0},"14":{"tf":1.0},"15":{"tf":1.0},"16":{"tf":1.0},"18":{"tf":1.0},"19":{"tf":1.0},"20":{"tf":1.0},"21":{"tf":1.4142135623730951},"23":{"tf":1.0},"26":{"tf":1.0},"3":{"tf":1.4142135623730951},"35":{"tf":1.0},"38":{"tf":1.0},"4":{"tf":1.0},"46":{"tf":2.449489742783178},"47":{"tf":1.7320508075688772},"52":{"tf":1.0},"57":{"tf":1.0},"63":{"tf":1.0}}}}}},"t":{"df":0,"docs":{},"e":{"_":{"df":0,"docs":{},"f":{"a":{"df":0,"docs":{},"l":{"df":0,"docs":{},"s":{"df":1,"docs":{"71":{"tf":1.0}}}}},"df":0,"docs":{}},"t":{"df":0,"docs":{},"r":{"df":0,"docs":{},"u":{"df":1,"docs":{"71":{"tf":1.0}}}}}},"df":0,"docs":{}}}},"k":{"df":3,"docs":{"43":{"tf":1.4142135623730951},"45":{"tf":1.7320508075688772},"57":{"tf":3.3166247903554}}},"l":{".":{"df":0,"docs":{},"l":{"df":0,"docs":{},"e":{"df":0,"docs":{},"n":{"df":0,"docs":{},"g":{"df":0,"docs":{},"t":{"df":0,"docs":{},"h":{"df":1,"docs":{"44":{"tf":1.0}}}}}}}}},"df":1,"docs":{"44":{"tf":3.1622776601683795}},"e":{"a":{"df":0,"docs":{},"n":{".":{"df":0,"docs":{},"m":{"df":0,"docs":{},"v":{"a":{"df":0,"docs":{},"r":{"df":0,"docs":{},"i":{"d":{".":{"df":0,"docs":{},"r":{"df":0,"docs":{},"e":{"df":0,"docs":{},"f":{"df":0,"docs":{},"l":{"df":1,"docs":{"59":{"tf":1.0}}}}},"f":{"df":0,"docs":{},"l":{"df":1,"docs":{"59":{"tf":1.0}}}}}},"df":0,"docs":{}},"df":0,"docs":{}}}},"df":0,"docs":{}}}},"4":{"df":3,"docs":{"0":{"tf":1.0},"17":{"tf":1.0},"28":{"tf":1.0}}},"df":8,"docs":{"0":{"tf":1.0},"15":{"tf":1.0},"2":{"tf":2.0},"42":{"tf":1.0},"47":{"tf":1.0},"6":{"tf":1.0},"71":{"tf":1.0},"75":{"tf":1.0}}}},"df":0,"docs":{},"f":{"df":0,"docs":{},"t":{"df":3,"docs":{"18":{"tf":1.0},"25":{"tf":1.0},"48":{"tf":2.0}}}}},"i":{"df":0,"docs":{},"n":{"a":{"df":0,"docs":{},"r":{"df":0,"docs":{},"i":{"df":0,"docs":{},"t":{"df":0,"docs":{},"h":{"df":5,"docs":{"49":{"tf":3.0},"50":{"tf":1.4142135623730951},"51":{"tf":1.7320508075688772},"52":{"tf":1.0},"71":{"tf":1.4142135623730951}}}}}}},"df":0,"docs":{},"e":{"a":{"df":0,"docs":{},"r":{"df":2,"docs":{"49":{"tf":1.0},"51":{"tf":1.0}}}},"df":0,"docs":{}}},"s":{"df":0,"docs":{},"t":{".":{"df":0,"docs":{},"l":{"df":0,"docs":{},"e":{"df":0,"docs":{},"n":{"df":0,"docs":{},"g":{"df":0,"docs":{},"t":{"df":0,"docs":{},"h":{"df":1,"docs":{"44":{"tf":1.7320508075688772}}}}}}}}},"df":1,"docs":{"44":{"tf":1.7320508075688772}}}}},"o":{"df":0,"docs":{},"s":{"df":0,"docs":{},"s":{"df":1,"docs":{"75":{"tf":1.0}}}}}},"m":{"a":{"df":0,"docs":{},"t":{"c":{"df":0,"docs":{},"h":{"df":1,"docs":{"45":{"tf":1.0}}}},"df":0,"docs":{},"h":{"df":0,"docs":{},"e":{"df":0,"docs":{},"m":{"a":{"df":0,"docs":{},"t":{"df":1,"docs":{"2":{"tf":1.0}}}},"df":0,"docs":{}}},"l":{"df":0,"docs":{},"i":{"b":{".":{"a":{"df":0,"docs":{},"l":{"df":0,"docs":{},"g":{"df":0,"docs":{},"e":{"b":{"df":0,"docs":{},"r":{"a":{".":{"df":0,"docs":{},"g":{"df":0,"docs":{},"r":{"df":0,"docs":{},"o":{"df":0,"docs":{},"u":{"df":0,"docs":{},"p":{".":{"d":{"df":0,"docs":{},"e":{"df":0,"docs":{},"f":{"df":1,"docs":{"10":{"tf":1.0}}}}},"df":0,"docs":{}},"df":0,"docs":{}}}}}},"h":{"df":0,"docs":{},"o":{"df":0,"docs":{},"m":{".":{"df":0,"docs":{},"g":{"df":0,"docs":{},"r":{"df":0,"docs":{},"o":{"df":0,"docs":{},"u":{"df":0,"docs":{},"p":{".":{"d":{"df":0,"docs":{},"e":{"df":0,"docs":{},"f":{"df":1,"docs":{"10":{"tf":1.0}}}}},"df":0,"docs":{}},"df":0,"docs":{}}}}}}},"df":0,"docs":{}}}}},"df":0,"docs":{}},"df":0,"docs":{}}},"df":0,"docs":{}}}}},"d":{"a":{"df":0,"docs":{},"t":{"a":{".":{"df":0,"docs":{},"n":{"a":{"df":0,"docs":{},"t":{".":{"b":{"a":{"df":0,"docs":{},"s":{"df":1,"docs":{"58":{"tf":1.0}}}},"df":0,"docs":{}},"df":0,"docs":{}},"df":0,"docs":{}}},"df":0,"docs":{}},"s":{"df":0,"docs":{},"e":{"df":0,"docs":{},"t":{"df":0,"docs":{},"l":{"df":0,"docs":{},"i":{"df":0,"docs":{},"k":{"df":0,"docs":{},"e":{".":{"b":{"a":{"df":0,"docs":{},"s":{"df":1,"docs":{"35":{"tf":1.0}}}},"df":0,"docs":{}},"df":0,"docs":{}},"df":0,"docs":{}}}}}}}}},"df":0,"docs":{}},"df":0,"docs":{}}},"df":0,"docs":{}},"df":0,"docs":{},"i":{"df":0,"docs":{},"n":{"df":0,"docs":{},"i":{"df":0,"docs":{},"t":{".":{"df":0,"docs":{},"f":{"df":0,"docs":{},"u":{"df":0,"docs":{},"n":{"c":{"df":0,"docs":{},"t":{"df":1,"docs":{"3":{"tf":1.0}}}},"df":0,"docs":{}}}}},"df":0,"docs":{}}}}},"t":{"a":{"c":{"df":0,"docs":{},"t":{"df":0,"docs":{},"i":{"c":{".":{"b":{"df":0,"docs":{},"y":{"c":{"df":0,"docs":{},"o":{"df":0,"docs":{},"n":{"df":0,"docs":{},"t":{"df":0,"docs":{},"r":{"a":{"df":1,"docs":{"14":{"tf":1.0}}},"df":0,"docs":{}}}}}},"df":0,"docs":{}}},"c":{"a":{"df":0,"docs":{},"s":{"df":2,"docs":{"20":{"tf":1.0},"43":{"tf":1.0}}}},"df":0,"docs":{},"h":{"df":0,"docs":{},"o":{"df":0,"docs":{},"o":{"df":0,"docs":{},"s":{"df":1,"docs":{"22":{"tf":1.0}}}}}},"o":{"df":0,"docs":{},"n":{"df":0,"docs":{},"v":{"df":0,"docs":{},"e":{"df":0,"docs":{},"r":{"df":0,"docs":{},"t":{"df":1,"docs":{"29":{"tf":1.0}}}}}}}}},"df":0,"docs":{},"g":{"c":{"df":0,"docs":{},"o":{"df":0,"docs":{},"n":{"df":0,"docs":{},"g":{"df":0,"docs":{},"r":{"df":1,"docs":{"56":{"tf":1.0}}}}}}},"df":0,"docs":{}},"l":{"df":0,"docs":{},"e":{"df":0,"docs":{},"f":{"df":0,"docs":{},"t":{"df":0,"docs":{},"r":{"df":0,"docs":{},"i":{"df":0,"docs":{},"g":{"df":0,"docs":{},"h":{"df":0,"docs":{},"t":{"df":1,"docs":{"48":{"tf":1.0}}}}}}}}}},"i":{"b":{"df":0,"docs":{},"r":{"a":{"df":0,"docs":{},"r":{"df":0,"docs":{},"y":{"df":0,"docs":{},"s":{"df":0,"docs":{},"e":{"a":{"df":0,"docs":{},"r":{"c":{"df":0,"docs":{},"h":{"df":2,"docs":{"10":{"tf":1.0},"33":{"tf":1.0}}}},"df":0,"docs":{}}},"df":0,"docs":{}}}}}},"df":0,"docs":{}}},"df":0,"docs":{},"n":{"a":{"df":0,"docs":{},"r":{"df":0,"docs":{},"i":{"df":0,"docs":{},"t":{"df":0,"docs":{},"h":{"df":2,"docs":{"49":{"tf":1.0},"51":{"tf":1.0}}}}}}},"df":0,"docs":{}}}},"n":{"df":0,"docs":{},"t":{"df":0,"docs":{},"h":{"df":0,"docs":{},"r":{"df":0,"docs":{},"e":{"df":0,"docs":{},"w":{"df":0,"docs":{},"r":{"df":0,"docs":{},"i":{"df":0,"docs":{},"t":{"df":1,"docs":{"62":{"tf":1.0}}}}}}}}}}},"p":{"df":0,"docs":{},"u":{"df":0,"docs":{},"s":{"df":0,"docs":{},"h":{"df":0,"docs":{},"n":{"df":0,"docs":{},"e":{"df":0,"docs":{},"g":{"df":1,"docs":{"52":{"tf":1.0}}}}}}}}},"r":{"df":1,"docs":{"60":{"tf":1.0}},"e":{"df":0,"docs":{},"l":{"a":{"df":0,"docs":{},"t":{"df":0,"docs":{},"i":{"df":0,"docs":{},"o":{"df":0,"docs":{},"n":{".":{"df":0,"docs":{},"r":{"df":0,"docs":{},"f":{"df":0,"docs":{},"l":{"df":2,"docs":{"58":{"tf":1.0},"59":{"tf":1.4142135623730951}}}}}},"df":0,"docs":{}}}}}},"df":0,"docs":{}}}},"s":{"a":{"df":0,"docs":{},"y":{"df":2,"docs":{"3":{"tf":1.0},"63":{"tf":1.0}}}},"df":0,"docs":{},"o":{"df":0,"docs":{},"l":{"df":0,"docs":{},"v":{"df":0,"docs":{},"e":{"b":{"df":0,"docs":{},"y":{"df":0,"docs":{},"e":{"df":0,"docs":{},"l":{"df":0,"docs":{},"i":{"df":0,"docs":{},"m":{"df":1,"docs":{"4":{"tf":1.4142135623730951}}}}}}}},"df":0,"docs":{}}}}}},"t":{"a":{"df":0,"docs":{},"u":{"df":0,"docs":{},"t":{"df":0,"docs":{},"o":{"df":1,"docs":{"73":{"tf":1.0}}}}}},"df":0,"docs":{}},"w":{"df":0,"docs":{},"l":{"df":0,"docs":{},"o":{"df":0,"docs":{},"g":{"df":1,"docs":{"75":{"tf":1.0}}}}}}},"df":0,"docs":{}},"df":0,"docs":{}}}},"df":0,"docs":{}},"df":0,"docs":{}}},"4":{"df":2,"docs":{"2":{"tf":1.0},"48":{"tf":1.0}}},"df":0,"docs":{}},"df":0,"docs":{}}}}}},"df":1,"docs":{"45":{"tf":1.7320508075688772}},"o":{"df":0,"docs":{},"n":{"df":0,"docs":{},"o":{"df":0,"docs":{},"i":{"d":{"df":0,"docs":{},"h":{"df":0,"docs":{},"o":{"df":0,"docs":{},"m":{".":{"df":0,"docs":{},"m":{"a":{"df":0,"docs":{},"p":{"_":{"df":0,"docs":{},"m":{"df":0,"docs":{},"u":{"df":0,"docs":{},"l":{"df":1,"docs":{"10":{"tf":1.0}}}}}},"df":0,"docs":{}}},"df":0,"docs":{}}},"df":0,"docs":{}}}}},"df":0,"docs":{}}}}},"u":{"df":0,"docs":{},"l":{"_":{"df":0,"docs":{},"i":{"df":0,"docs":{},"n":{"df":0,"docs":{},"v":{"_":{"df":0,"docs":{},"e":{"df":0,"docs":{},"q":{"_":{"df":0,"docs":{},"i":{"df":0,"docs":{},"f":{"df":0,"docs":{},"f":{"_":{"df":0,"docs":{},"e":{"df":0,"docs":{},"q":{"_":{"df":0,"docs":{},"m":{"df":0,"docs":{},"u":{"df":0,"docs":{},"l":{"df":1,"docs":{"62":{"tf":1.4142135623730951}}}}}},"df":0,"docs":{}}}},"df":0,"docs":{}}}}},"df":0,"docs":{}}}},"df":0,"docs":{}}}},"n":{"df":0,"docs":{},"e":{"df":0,"docs":{},"g":{"df":1,"docs":{"71":{"tf":1.0}}}}}},"df":0,"docs":{}}},"y":{"a":{"b":{"df":1,"docs":{"71":{"tf":2.23606797749979}}},"df":0,"docs":{}},"df":0,"docs":{},"e":{"df":0,"docs":{},"q":{".":{"df":0,"docs":{},"r":{"df":0,"docs":{},"e":{"df":0,"docs":{},"f":{"df":0,"docs":{},"l":{"df":1,"docs":{"58":{"tf":1.0}}}}}}},"df":1,"docs":{"58":{"tf":1.7320508075688772}}}}}},"n":{"a":{"df":0,"docs":{},"m":{"df":0,"docs":{},"e":{"df":11,"docs":{"21":{"tf":1.0},"24":{"tf":1.0},"35":{"tf":1.0},"46":{"tf":1.0},"49":{"tf":1.0},"51":{"tf":1.0},"52":{"tf":1.0},"56":{"tf":1.0},"58":{"tf":1.0},"73":{"tf":1.0},"75":{"tf":1.0}}}},"t":{".":{"d":{"df":0,"docs":{},"v":{"d":{"_":{"df":0,"docs":{},"i":{"df":0,"docs":{},"f":{"df":0,"docs":{},"f":{"_":{"d":{"df":0,"docs":{},"i":{"df":0,"docs":{},"v":{"_":{"df":0,"docs":{},"m":{"df":0,"docs":{},"u":{"df":0,"docs":{},"l":{"_":{"df":0,"docs":{},"e":{"df":0,"docs":{},"q":{"df":1,"docs":{"72":{"tf":1.0}}}}},"df":0,"docs":{}}}}},"df":0,"docs":{}}}},"df":0,"docs":{}},"df":0,"docs":{}}}}},"df":0,"docs":{}},"df":0,"docs":{}}},"df":0,"docs":{},"l":{"df":0,"docs":{},"t":{".":{"b":{"a":{"df":0,"docs":{},"s":{"df":1,"docs":{"33":{"tf":1.0}}}},"df":0,"docs":{}},"df":0,"docs":{}},"df":0,"docs":{}}},"m":{"df":0,"docs":{},"u":{"df":0,"docs":{},"l":{"_":{"a":{"df":0,"docs":{},"s":{"df":0,"docs":{},"s":{"df":0,"docs":{},"o":{"c":{"df":1,"docs":{"61":{"tf":1.4142135623730951}}},"df":0,"docs":{}}}}},"df":0,"docs":{}},"df":0,"docs":{}}}},"s":{"df":0,"docs":{},"t":{"df":0,"docs":{},"r":{"df":0,"docs":{},"o":{"df":0,"docs":{},"n":{"df":0,"docs":{},"g":{"_":{"df":0,"docs":{},"i":{"df":0,"docs":{},"n":{"d":{"df":0,"docs":{},"u":{"c":{"df":0,"docs":{},"t":{"df":0,"docs":{},"i":{"df":0,"docs":{},"o":{"df":0,"docs":{},"n":{"_":{"df":0,"docs":{},"o":{"df":0,"docs":{},"n":{"df":1,"docs":{"45":{"tf":1.0}}}}},"df":0,"docs":{}}}}}},"df":0,"docs":{}}},"df":0,"docs":{}}}},"df":0,"docs":{}}}}}}}},"df":15,"docs":{"10":{"tf":1.0},"26":{"tf":1.0},"27":{"tf":1.0},"29":{"tf":1.4142135623730951},"34":{"tf":1.0},"36":{"tf":1.4142135623730951},"42":{"tf":2.8284271247461903},"43":{"tf":1.0},"45":{"tf":1.4142135623730951},"46":{"tf":1.0},"51":{"tf":1.0},"58":{"tf":1.0},"61":{"tf":1.0},"70":{"tf":1.0},"75":{"tf":1.4142135623730951}}}},"df":8,"docs":{"42":{"tf":3.872983346207417},"43":{"tf":1.7320508075688772},"44":{"tf":2.0},"45":{"tf":3.3166247903554},"46":{"tf":1.7320508075688772},"57":{"tf":3.7416573867739413},"58":{"tf":2.449489742783178},"70":{"tf":2.23606797749979}},"e":{"df":0,"docs":{},"e":{"d":{"df":22,"docs":{"14":{"tf":1.0},"16":{"tf":1.0},"20":{"tf":1.0},"21":{"tf":1.0},"22":{"tf":1.0},"29":{"tf":1.0},"35":{"tf":1.0},"37":{"tf":1.0},"4":{"tf":1.0},"43":{"tf":1.0},"48":{"tf":1.0},"49":{"tf":1.0},"51":{"tf":1.0},"52":{"tf":1.0},"56":{"tf":1.0},"57":{"tf":1.0},"58":{"tf":1.0},"60":{"tf":1.0},"62":{"tf":1.0},"63":{"tf":1.0},"73":{"tf":1.0},"75":{"tf":1.0}}},"df":0,"docs":{}},"g":{"a":{"df":0,"docs":{},"t":{"df":1,"docs":{"52":{"tf":1.0}}}},"df":0,"docs":{}}},"l":{"df":0,"docs":{},"i":{"df":0,"docs":{},"n":{"a":{"df":0,"docs":{},"r":{"df":0,"docs":{},"i":{"df":0,"docs":{},"t":{"df":0,"docs":{},"h":{"df":1,"docs":{"51":{"tf":1.7320508075688772}}}}}}},"df":0,"docs":{}}}},"o":{"df":0,"docs":{},"n":{"c":{"df":0,"docs":{},"o":{"df":0,"docs":{},"m":{"df":0,"docs":{},"p":{"df":0,"docs":{},"u":{"df":0,"docs":{},"t":{"df":1,"docs":{"23":{"tf":1.0}}}}}}}},"df":1,"docs":{"51":{"tf":1.0}},"e":{"df":0,"docs":{},"m":{"df":0,"docs":{},"p":{"df":0,"docs":{},"t":{"df":0,"docs":{},"i":{"df":1,"docs":{"23":{"tf":1.0}}}}}}}}},"t":{"df":0,"docs":{},"h":{"_":{"df":0,"docs":{},"r":{"df":0,"docs":{},"w":{"df":2,"docs":{"57":{"tf":1.0},"62":{"tf":1.4142135623730951}}}}},"df":0,"docs":{}}}},"o":{"b":{"df":0,"docs":{},"t":{"a":{"df":0,"docs":{},"i":{"df":0,"docs":{},"n":{"df":1,"docs":{"57":{"tf":1.0}}}}},"df":0,"docs":{}}},"df":0,"docs":{},"n":{"df":0,"docs":{},"e":{"_":{"df":0,"docs":{},"m":{"df":0,"docs":{},"u":{"df":0,"docs":{},"l":{"df":1,"docs":{"62":{"tf":1.4142135623730951}}}}}},"df":0,"docs":{}}},"p":{"df":0,"docs":{},"e":{"df":0,"docs":{},"n":{"df":2,"docs":{"3":{"tf":1.0},"66":{"tf":1.0}}}},"t":{"df":0,"docs":{},"i":{"df":0,"docs":{},"o":{"df":0,"docs":{},"n":{"df":1,"docs":{"1":{"tf":1.0}}}}}}},"r":{".":{"df":0,"docs":{},"i":{"df":0,"docs":{},"n":{"df":0,"docs":{},"l":{"df":1,"docs":{"48":{"tf":1.4142135623730951}}},"r":{"df":1,"docs":{"48":{"tf":1.0}}}}}},"df":0,"docs":{}}},"p":{"(":{"0":{"df":1,"docs":{"45":{"tf":1.0}}},"df":0,"docs":{},"x":{"df":2,"docs":{"22":{"tf":1.4142135623730951},"46":{"tf":1.0}}}},"df":43,"docs":{"11":{"tf":1.7320508075688772},"13":{"tf":3.3166247903554},"14":{"tf":2.6457513110645907},"15":{"tf":2.8284271247461903},"16":{"tf":1.4142135623730951},"18":{"tf":2.449489742783178},"19":{"tf":1.7320508075688772},"20":{"tf":1.4142135623730951},"21":{"tf":3.0},"23":{"tf":2.449489742783178},"25":{"tf":3.0},"26":{"tf":1.0},"27":{"tf":2.6457513110645907},"31":{"tf":2.449489742783178},"33":{"tf":1.7320508075688772},"34":{"tf":1.7320508075688772},"37":{"tf":1.7320508075688772},"38":{"tf":3.0},"4":{"tf":2.449489742783178},"40":{"tf":2.23606797749979},"41":{"tf":1.4142135623730951},"42":{"tf":2.0},"44":{"tf":2.23606797749979},"45":{"tf":2.449489742783178},"46":{"tf":4.242640687119285},"47":{"tf":3.3166247903554},"48":{"tf":2.449489742783178},"5":{"tf":3.7416573867739413},"52":{"tf":3.4641016151377544},"53":{"tf":2.0},"54":{"tf":2.23606797749979},"55":{"tf":2.6457513110645907},"57":{"tf":1.0},"6":{"tf":2.6457513110645907},"61":{"tf":1.7320508075688772},"63":{"tf":1.4142135623730951},"65":{"tf":2.23606797749979},"66":{"tf":1.4142135623730951},"71":{"tf":1.7320508075688772},"72":{"tf":1.0},"73":{"tf":3.0},"74":{"tf":1.0},"8":{"tf":2.0}},"h":{"df":0,"docs":{},"r":{"a":{"df":0,"docs":{},"s":{"df":0,"docs":{},"e":{"b":{"df":0,"docs":{},"o":{"df":0,"docs":{},"o":{"df":0,"docs":{},"k":{"df":1,"docs":{"2":{"tf":1.0}}}}}},"df":0,"docs":{}}}},"df":0,"docs":{}}},"o":{"df":0,"docs":{},"s":{"df":0,"docs":{},"i":{"df":0,"docs":{},"t":{"df":2,"docs":{"42":{"tf":1.0},"43":{"tf":1.0}}}}}},"r":{"df":0,"docs":{},"i":{"df":0,"docs":{},"n":{"df":0,"docs":{},"t":{"df":1,"docs":{"10":{"tf":1.0}}}}},"o":{"df":0,"docs":{},"p":{"df":9,"docs":{"13":{"tf":1.0},"21":{"tf":1.0},"23":{"tf":1.0},"33":{"tf":1.0},"4":{"tf":1.0},"44":{"tf":1.0},"45":{"tf":1.0},"46":{"tf":1.0},"58":{"tf":1.0}}},"v":{"df":0,"docs":{},"e":{"df":2,"docs":{"17":{"tf":1.0},"28":{"tf":1.0}}}}}},"u":{"df":0,"docs":{},"s":{"df":0,"docs":{},"h":{"_":{"df":0,"docs":{},"n":{"df":0,"docs":{},"e":{"df":0,"docs":{},"g":{"df":1,"docs":{"52":{"tf":2.0}}}}}},"df":1,"docs":{"52":{"tf":1.0}}}}},"y":{"df":1,"docs":{"23":{"tf":1.4142135623730951}}}},"q":{"(":{"df":0,"docs":{},"i":{"df":1,"docs":{"46":{"tf":1.0}}}},"df":32,"docs":{"11":{"tf":1.0},"14":{"tf":2.23606797749979},"15":{"tf":2.0},"16":{"tf":1.4142135623730951},"18":{"tf":2.449489742783178},"19":{"tf":1.7320508075688772},"20":{"tf":1.4142135623730951},"21":{"tf":3.0},"25":{"tf":2.8284271247461903},"26":{"tf":1.0},"27":{"tf":1.0},"31":{"tf":1.4142135623730951},"33":{"tf":1.7320508075688772},"38":{"tf":2.6457513110645907},"4":{"tf":2.449489742783178},"40":{"tf":2.23606797749979},"42":{"tf":2.0},"46":{"tf":3.872983346207417},"47":{"tf":3.0},"48":{"tf":2.0},"5":{"tf":3.4641016151377544},"52":{"tf":3.1622776601683795},"53":{"tf":1.4142135623730951},"54":{"tf":2.0},"55":{"tf":2.8284271247461903},"61":{"tf":1.4142135623730951},"63":{"tf":1.4142135623730951},"65":{"tf":1.7320508075688772},"71":{"tf":1.7320508075688772},"72":{"tf":2.6457513110645907},"73":{"tf":2.23606797749979},"8":{"tf":2.0}}},"r":{"c":{"a":{"df":0,"docs":{},"s":{"df":0,"docs":{},"e":{"df":1,"docs":{"21":{"tf":2.0}}}}},"df":0,"docs":{}},"df":13,"docs":{"15":{"tf":2.449489742783178},"16":{"tf":1.4142135623730951},"18":{"tf":1.7320508075688772},"19":{"tf":1.7320508075688772},"20":{"tf":1.7320508075688772},"21":{"tf":2.0},"33":{"tf":1.4142135623730951},"38":{"tf":2.23606797749979},"4":{"tf":1.7320508075688772},"46":{"tf":2.6457513110645907},"55":{"tf":2.8284271247461903},"63":{"tf":1.4142135623730951},"73":{"tf":1.4142135623730951}},"e":{"c":{"df":0,"docs":{},"u":{"df":0,"docs":{},"r":{"df":0,"docs":{},"s":{"df":1,"docs":{"21":{"tf":1.0}}}}}},"df":0,"docs":{},"f":{"df":0,"docs":{},"i":{"df":0,"docs":{},"n":{"df":4,"docs":{"10":{"tf":1.0},"53":{"tf":1.7320508075688772},"54":{"tf":2.0},"55":{"tf":1.7320508075688772}}}},"l":{"df":2,"docs":{"58":{"tf":2.0},"59":{"tf":1.0}},"e":{"df":0,"docs":{},"x":{"df":1,"docs":{"58":{"tf":1.0}}}}}},"l":{"a":{"df":0,"docs":{},"t":{"df":1,"docs":{"56":{"tf":1.0}}}},"df":1,"docs":{"56":{"tf":2.23606797749979}}},"p":{"df":0,"docs":{},"e":{"a":{"df":0,"docs":{},"t":{"df":1,"docs":{"4":{"tf":1.7320508075688772}}}},"df":0,"docs":{}},"l":{"a":{"c":{"df":2,"docs":{"57":{"tf":2.0},"71":{"tf":1.0}}},"df":0,"docs":{}},"df":0,"docs":{}}}},"f":{"df":0,"docs":{},"l":{"df":5,"docs":{"49":{"tf":1.0},"58":{"tf":2.0},"59":{"tf":2.0},"72":{"tf":1.4142135623730951},"74":{"tf":1.0}}}},"i":{"df":0,"docs":{},"g":{"df":0,"docs":{},"h":{"df":0,"docs":{},"t":{"df":3,"docs":{"18":{"tf":1.0},"25":{"tf":1.0},"48":{"tf":1.7320508075688772}}}}},"n":{"df":0,"docs":{},"g":{"df":4,"docs":{"36":{"tf":1.0},"41":{"tf":1.0},"57":{"tf":2.0},"60":{"tf":2.23606797749979}}}}},"w":{"df":10,"docs":{"26":{"tf":1.0},"29":{"tf":1.0},"3":{"tf":1.4142135623730951},"41":{"tf":1.0},"46":{"tf":1.0},"57":{"tf":1.4142135623730951},"61":{"tf":3.4641016151377544},"62":{"tf":1.0},"63":{"tf":1.0},"67":{"tf":1.0}}}},"s":{"a":{"df":0,"docs":{},"y":{"df":0,"docs":{},"s":{".":{"df":0,"docs":{},"n":{"df":0,"docs":{},"o":{"_":{"df":0,"docs":{},"v":{"df":0,"docs":{},"e":{"df":0,"docs":{},"r":{"df":0,"docs":{},"i":{"df":0,"docs":{},"f":{"df":0,"docs":{},"y":{"_":{"df":0,"docs":{},"i":{"df":0,"docs":{},"n":{"_":{"c":{"df":0,"docs":{},"i":{"df":2,"docs":{"3":{"tf":1.0},"64":{"tf":1.0}}}},"df":0,"docs":{}},"df":0,"docs":{}}}},"df":0,"docs":{}}}}}}}},"df":0,"docs":{}}},"v":{"df":0,"docs":{},"e":{"df":0,"docs":{},"r":{"df":0,"docs":{},"i":{"df":0,"docs":{},"f":{"df":0,"docs":{},"i":{"df":1,"docs":{"64":{"tf":1.0}}}}}}}}},"df":0,"docs":{}}}},"df":2,"docs":{"35":{"tf":2.449489742783178},"63":{"tf":1.4142135623730951}},"e":{"df":0,"docs":{},"t":{"_":{"df":0,"docs":{},"o":{"df":0,"docs":{},"p":{"df":0,"docs":{},"t":{"df":2,"docs":{"1":{"tf":1.0},"3":{"tf":1.0}}}}}},"df":1,"docs":{"35":{"tf":1.0}}}},"h":{"df":0,"docs":{},"o":{"df":0,"docs":{},"w":{"_":{"df":0,"docs":{},"t":{"df":0,"docs":{},"e":{"df":0,"docs":{},"r":{"df":0,"docs":{},"m":{"df":1,"docs":{"60":{"tf":1.4142135623730951}}}}}}},"df":16,"docs":{"14":{"tf":1.0},"24":{"tf":1.4142135623730951},"29":{"tf":1.0},"3":{"tf":1.0},"4":{"tf":1.7320508075688772},"44":{"tf":1.4142135623730951},"46":{"tf":1.4142135623730951},"47":{"tf":1.0},"5":{"tf":1.0},"52":{"tf":1.4142135623730951},"53":{"tf":1.0},"54":{"tf":1.0},"55":{"tf":2.6457513110645907},"65":{"tf":2.0},"71":{"tf":1.7320508075688772},"75":{"tf":1.4142135623730951}}}}},"i":{"df":0,"docs":{},"m":{"df":0,"docs":{},"p":{"_":{"a":{"df":0,"docs":{},"l":{"df":4,"docs":{"26":{"tf":1.0},"3":{"tf":1.0},"63":{"tf":1.0},"68":{"tf":1.4142135623730951}}}},"df":0,"docs":{}},"df":11,"docs":{"24":{"tf":1.4142135623730951},"3":{"tf":1.0},"42":{"tf":1.4142135623730951},"43":{"tf":1.4142135623730951},"60":{"tf":1.0},"63":{"tf":1.0},"66":{"tf":2.8284271247461903},"67":{"tf":1.4142135623730951},"68":{"tf":1.0},"69":{"tf":1.0},"71":{"tf":2.449489742783178}}}}},"o":{"df":0,"docs":{},"r":{"df":0,"docs":{},"r":{"df":0,"docs":{},"i":{"df":4,"docs":{"10":{"tf":1.4142135623730951},"44":{"tf":1.4142135623730951},"45":{"tf":1.4142135623730951},"70":{"tf":2.0}}},"y":{"a":{"df":0,"docs":{},"x":{"df":1,"docs":{"10":{"tf":1.7320508075688772}}}},"df":0,"docs":{}}}}},"p":{"df":0,"docs":{},"l":{"df":0,"docs":{},"i":{"df":0,"docs":{},"t":{"df":1,"docs":{"71":{"tf":2.23606797749979}}}}}},"t":{"d":{".":{"df":0,"docs":{},"t":{"a":{"c":{"df":0,"docs":{},"t":{"df":0,"docs":{},"i":{"c":{".":{"df":0,"docs":{},"e":{"df":0,"docs":{},"x":{"df":0,"docs":{},"t":{"df":1,"docs":{"35":{"tf":1.0}}}}},"g":{"df":0,"docs":{},"u":{"a":{"df":0,"docs":{},"r":{"d":{"df":0,"docs":{},"e":{"df":0,"docs":{},"x":{"df":0,"docs":{},"p":{"df":0,"docs":{},"r":{"df":1,"docs":{"37":{"tf":1.0}}}}}}},"df":0,"docs":{}}},"df":0,"docs":{}}},"r":{"c":{"a":{"df":0,"docs":{},"s":{"df":1,"docs":{"21":{"tf":1.0}}}},"df":0,"docs":{}},"df":0,"docs":{},"e":{"df":0,"docs":{},"p":{"df":0,"docs":{},"l":{"a":{"c":{"df":1,"docs":{"57":{"tf":1.0}}},"df":0,"docs":{}},"df":0,"docs":{}}}}},"s":{"df":0,"docs":{},"h":{"df":0,"docs":{},"o":{"df":0,"docs":{},"w":{"df":0,"docs":{},"t":{"df":0,"docs":{},"e":{"df":0,"docs":{},"r":{"df":0,"docs":{},"m":{"df":1,"docs":{"16":{"tf":1.0}}}}}}}}}}},"df":0,"docs":{}},"df":0,"docs":{}}}},"df":0,"docs":{}},"df":0,"docs":{}}},"df":0,"docs":{}},"df":0,"docs":{}},"u":{"c":{"c":{"df":2,"docs":{"42":{"tf":2.6457513110645907},"44":{"tf":1.0}}},"df":0,"docs":{}},"df":0,"docs":{},"f":{"df":0,"docs":{},"f":{"df":0,"docs":{},"i":{"c":{"df":1,"docs":{"72":{"tf":2.6457513110645907}}},"df":0,"docs":{}}}}}},"t":{"a":{"c":{"df":0,"docs":{},"t":{"df":0,"docs":{},"i":{"c":{"df":1,"docs":{"2":{"tf":1.0}}},"df":0,"docs":{}}}},"df":0,"docs":{},"u":{"df":0,"docs":{},"t":{"df":0,"docs":{},"o":{"df":1,"docs":{"73":{"tf":2.449489742783178}},"l":{"df":0,"docs":{},"o":{"df":0,"docs":{},"g":{"df":1,"docs":{"73":{"tf":1.0}}}}}}}}},"df":2,"docs":{"10":{"tf":1.7320508075688772},"35":{"tf":2.449489742783178}},"h":{"df":0,"docs":{},"e":{"df":0,"docs":{},"o":{"df":0,"docs":{},"r":{"df":0,"docs":{},"e":{"df":0,"docs":{},"m":{"df":4,"docs":{"10":{"tf":1.0},"17":{"tf":1.0},"28":{"tf":1.0},"70":{"tf":1.0}}}},"i":{"df":1,"docs":{"2":{"tf":1.0}}}}}}},"r":{"df":0,"docs":{},"i":{"df":7,"docs":{"16":{"tf":1.0},"29":{"tf":1.0},"33":{"tf":1.4142135623730951},"49":{"tf":1.0},"51":{"tf":1.0},"63":{"tf":1.7320508075688772},"73":{"tf":1.4142135623730951}},"v":{"df":0,"docs":{},"i":{"a":{"df":0,"docs":{},"l":{"df":1,"docs":{"74":{"tf":2.449489742783178}}}},"df":0,"docs":{}}}},"u":{"df":0,"docs":{},"e":{"df":3,"docs":{"1":{"tf":1.0},"3":{"tf":1.0},"64":{"tf":1.4142135623730951}}}}},"y":{"df":0,"docs":{},"p":{"df":0,"docs":{},"e":{"df":6,"docs":{"2":{"tf":1.0},"3":{"tf":1.0},"35":{"tf":1.0},"58":{"tf":1.0},"59":{"tf":1.0},"66":{"tf":1.7320508075688772}}}}}},"u":{"df":2,"docs":{"58":{"tf":1.0},"66":{"tf":1.7320508075688772}},"n":{"df":0,"docs":{},"f":{"df":0,"docs":{},"o":{"df":0,"docs":{},"l":{"d":{"df":1,"docs":{"71":{"tf":1.0}}},"df":0,"docs":{}}}},"i":{"df":0,"docs":{},"v":{"df":0,"docs":{},"e":{"df":0,"docs":{},"r":{"df":0,"docs":{},"s":{"df":1,"docs":{"66":{"tf":1.0}}}}}}}},"s":{"df":2,"docs":{"22":{"tf":1.4142135623730951},"45":{"tf":1.0}}}},"v":{"a":{"df":0,"docs":{},"r":{"df":0,"docs":{},"i":{"a":{"b":{"df":0,"docs":{},"l":{"df":10,"docs":{"21":{"tf":1.0},"23":{"tf":1.0},"3":{"tf":1.0},"33":{"tf":1.0},"35":{"tf":1.4142135623730951},"4":{"tf":1.0},"45":{"tf":1.0},"59":{"tf":1.0},"62":{"tf":1.0},"66":{"tf":1.0}}}},"df":0,"docs":{}},"df":0,"docs":{}}}},"df":1,"docs":{"66":{"tf":1.7320508075688772}}},"w":{"a":{"df":0,"docs":{},"r":{"df":0,"docs":{},"n":{"df":1,"docs":{"1":{"tf":1.0}},"i":{"df":0,"docs":{},"n":{"df":0,"docs":{},"g":{"a":{"df":0,"docs":{},"s":{"df":0,"docs":{},"e":{"df":0,"docs":{},"r":{"df":0,"docs":{},"r":{"df":0,"docs":{},"o":{"df":0,"docs":{},"r":{"df":1,"docs":{"1":{"tf":1.0}}}}}}}}},"df":0,"docs":{}}}}}}},"df":0,"docs":{},"i":{"df":0,"docs":{},"t":{"df":0,"docs":{},"h":{"df":0,"docs":{},"o":{"df":0,"docs":{},"u":{"df":0,"docs":{},"t":{"df":1,"docs":{"75":{"tf":1.0}}}}}}}},"l":{"df":0,"docs":{},"o":{"df":0,"docs":{},"g":{"df":1,"docs":{"75":{"tf":1.7320508075688772}}}}}},"x":{")":{".":{"df":0,"docs":{},"p":{"df":0,"docs":{},"r":{"df":0,"docs":{},"o":{"df":0,"docs":{},"p":{"df":0,"docs":{},"e":{"df":0,"docs":{},"r":{"df":0,"docs":{},"t":{"df":0,"docs":{},"i":{"df":1,"docs":{"23":{"tf":1.0}}}}}}}}}},"v":{"a":{"df":0,"docs":{},"l":{"df":1,"docs":{"23":{"tf":1.0}}}},"df":0,"docs":{}}},"df":0,"docs":{}},"`":{"df":0,"docs":{},"が":{"df":0,"docs":{},"偶":{"df":0,"docs":{},"数":{"df":0,"docs":{},"の":{"df":0,"docs":{},"と":{"df":0,"docs":{},"き":{"`":{"3":{"df":1,"docs":{"41":{"tf":1.0}}},"df":0,"docs":{}},"df":0,"docs":{}}}}}}}},"df":23,"docs":{"10":{"tf":1.7320508075688772},"22":{"tf":3.1622776601683795},"23":{"tf":4.358898943540674},"24":{"tf":3.4641016151377544},"26":{"tf":2.6457513110645907},"27":{"tf":1.7320508075688772},"3":{"tf":2.23606797749979},"33":{"tf":1.7320508075688772},"34":{"tf":3.3166247903554},"35":{"tf":2.6457513110645907},"36":{"tf":3.872983346207417},"41":{"tf":3.4641016151377544},"46":{"tf":2.449489742783178},"49":{"tf":2.8284271247461903},"50":{"tf":1.4142135623730951},"52":{"tf":3.1622776601683795},"56":{"tf":2.23606797749979},"59":{"tf":1.7320508075688772},"60":{"tf":2.449489742783178},"63":{"tf":2.8284271247461903},"64":{"tf":1.4142135623730951},"70":{"tf":1.7320508075688772},"71":{"tf":5.196152422706632}}},"y":{"df":13,"docs":{"10":{"tf":1.7320508075688772},"22":{"tf":4.0},"23":{"tf":3.3166247903554},"3":{"tf":2.449489742783178},"41":{"tf":2.449489742783178},"46":{"tf":3.3166247903554},"49":{"tf":1.4142135623730951},"50":{"tf":1.4142135623730951},"52":{"tf":2.0},"60":{"tf":2.449489742783178},"63":{"tf":2.6457513110645907},"64":{"tf":2.0},"70":{"tf":1.7320508075688772}}},"z":{"df":5,"docs":{"3":{"tf":2.0},"41":{"tf":1.4142135623730951},"49":{"tf":1.4142135623730951},"63":{"tf":1.0},"70":{"tf":1.7320508075688772}},"e":{"df":0,"docs":{},"r":{"df":0,"docs":{},"o":{"df":2,"docs":{"42":{"tf":1.7320508075688772},"44":{"tf":1.0}}}}}}}},"breadcrumbs":{"root":{"0":{"df":14,"docs":{"24":{"tf":1.4142135623730951},"26":{"tf":1.7320508075688772},"29":{"tf":1.4142135623730951},"42":{"tf":2.0},"43":{"tf":1.0},"44":{"tf":1.4142135623730951},"45":{"tf":1.0},"49":{"tf":1.4142135623730951},"52":{"tf":1.4142135623730951},"56":{"tf":1.0},"59":{"tf":1.0},"70":{"tf":1.0},"71":{"tf":3.3166247903554},"72":{"tf":1.0}}},"1":{"0":{"0":{"df":1,"docs":{"60":{"tf":1.0}}},"df":0,"docs":{}},"2":{"df":1,"docs":{"49":{"tf":1.0}}},"3":{"df":2,"docs":{"59":{"tf":1.0},"72":{"tf":1.7320508075688772}}},"df":15,"docs":{"24":{"tf":1.0},"26":{"tf":2.449489742783178},"33":{"tf":1.0},"34":{"tf":1.0},"42":{"tf":2.0},"44":{"tf":1.4142135623730951},"45":{"tf":1.0},"46":{"tf":2.8284271247461903},"50":{"tf":1.0},"52":{"tf":1.7320508075688772},"57":{"tf":1.0},"59":{"tf":1.4142135623730951},"62":{"tf":1.7320508075688772},"71":{"tf":1.4142135623730951},"74":{"tf":1.4142135623730951}}},"2":{"df":19,"docs":{"10":{"tf":1.4142135623730951},"24":{"tf":3.1622776601683795},"27":{"tf":1.4142135623730951},"34":{"tf":1.0},"35":{"tf":1.0},"36":{"tf":1.4142135623730951},"41":{"tf":1.7320508075688772},"49":{"tf":1.4142135623730951},"50":{"tf":1.4142135623730951},"51":{"tf":1.4142135623730951},"56":{"tf":1.7320508075688772},"57":{"tf":2.6457513110645907},"59":{"tf":1.4142135623730951},"60":{"tf":2.8284271247461903},"62":{"tf":1.0},"70":{"tf":1.0},"71":{"tf":3.872983346207417},"72":{"tf":1.7320508075688772},"74":{"tf":1.0}},"回":{"df":0,"docs":{},"出":{"df":0,"docs":{},"現":{"df":0,"docs":{},"す":{"df":0,"docs":{},"る":{"df":0,"docs":{},"が":{"df":0,"docs":{},"，":{"2":{"df":1,"docs":{"62":{"tf":1.0}}},"df":0,"docs":{}}}}}}}}},"3":{"df":7,"docs":{"27":{"tf":1.0},"34":{"tf":1.0},"41":{"tf":1.4142135623730951},"49":{"tf":1.0},"59":{"tf":1.0},"72":{"tf":1.7320508075688772},"73":{"tf":1.0}}},"4":{"df":2,"docs":{"49":{"tf":1.4142135623730951},"57":{"tf":1.4142135623730951}}},"5":{"df":1,"docs":{"57":{"tf":2.449489742783178}}},"7":{"0":{"df":2,"docs":{"59":{"tf":1.4142135623730951},"72":{"tf":2.449489742783178}}},"df":1,"docs":{"34":{"tf":1.0}}},"_":{"df":9,"docs":{"10":{"tf":1.0},"11":{"tf":1.0},"24":{"tf":1.0},"4":{"tf":1.0},"40":{"tf":1.0},"53":{"tf":1.0},"54":{"tf":1.4142135623730951},"55":{"tf":1.7320508075688772},"57":{"tf":1.7320508075688772}}},"a":{"b":{"df":0,"docs":{},"e":{"df":0,"docs":{},"l":{"df":1,"docs":{"75":{"tf":1.4142135623730951}}}}},"d":{"d":{"_":{"df":0,"docs":{},"z":{"df":0,"docs":{},"e":{"df":0,"docs":{},"r":{"df":0,"docs":{},"o":{"df":1,"docs":{"24":{"tf":1.4142135623730951}}}}}}},"df":0,"docs":{}},"df":0,"docs":{}},"df":0,"docs":{},"e":{"df":0,"docs":{},"s":{"df":0,"docs":{},"o":{"df":0,"docs":{},"p":{"df":5,"docs":{"3":{"tf":3.7416573867739413},"35":{"tf":1.0},"63":{"tf":1.4142135623730951},"73":{"tf":1.4142135623730951},"74":{"tf":1.0}}}}}},"p":{"df":0,"docs":{},"p":{"df":0,"docs":{},"l":{"df":0,"docs":{},"i":{"df":14,"docs":{"10":{"tf":3.4641016151377544},"20":{"tf":1.4142135623730951},"21":{"tf":1.4142135623730951},"3":{"tf":1.0},"4":{"tf":1.0},"48":{"tf":1.0},"5":{"tf":2.6457513110645907},"54":{"tf":2.0},"6":{"tf":1.7320508075688772},"63":{"tf":2.0},"7":{"tf":1.4142135623730951},"72":{"tf":1.4142135623730951},"8":{"tf":2.0},"9":{"tf":1.7320508075688772}}},"y":{"_":{"a":{"df":0,"docs":{},"s":{"df":0,"docs":{},"s":{"df":0,"docs":{},"u":{"df":0,"docs":{},"m":{"df":0,"docs":{},"p":{"df":0,"docs":{},"t":{"df":2,"docs":{"4":{"tf":3.1622776601683795},"9":{"tf":1.7320508075688772}}}}}}}}},"df":0,"docs":{}},"df":0,"docs":{}}}}},"r":{"df":0,"docs":{},"i":{"df":0,"docs":{},"t":{"df":0,"docs":{},"h":{"df":0,"docs":{},"m":{"df":0,"docs":{},"e":{"df":0,"docs":{},"t":{"df":2,"docs":{"49":{"tf":1.0},"51":{"tf":1.0}}}}}}}}},"s":{"df":0,"docs":{},"s":{"df":0,"docs":{},"o":{"c":{"df":1,"docs":{"66":{"tf":1.4142135623730951}}},"df":0,"docs":{}},"u":{"df":0,"docs":{},"m":{"df":0,"docs":{},"p":{"df":0,"docs":{},"t":{"df":7,"docs":{"11":{"tf":2.23606797749979},"12":{"tf":1.4142135623730951},"13":{"tf":1.0},"32":{"tf":1.7320508075688772},"40":{"tf":1.0},"46":{"tf":1.0},"48":{"tf":1.4142135623730951}}}}}}}},"t":{"df":0,"docs":{},"t":{"df":0,"docs":{},"r":{"df":0,"docs":{},"i":{"b":{"df":0,"docs":{},"u":{"df":0,"docs":{},"t":{"df":2,"docs":{"58":{"tf":1.4142135623730951},"66":{"tf":1.0}}}}},"df":0,"docs":{}}}}},"x":{"df":0,"docs":{},"i":{"df":0,"docs":{},"o":{"df":0,"docs":{},"m":{"df":1,"docs":{"10":{"tf":1.4142135623730951}}}}}}},"b":{"`":{"df":0,"docs":{},"と":{"`":{"df":0,"docs":{},"g":{"df":1,"docs":{"66":{"tf":1.0}}}},"df":0,"docs":{}}},"df":10,"docs":{"10":{"tf":2.0},"29":{"tf":2.0},"35":{"tf":2.449489742783178},"51":{"tf":1.7320508075688772},"56":{"tf":2.0},"61":{"tf":2.449489742783178},"62":{"tf":3.3166247903554},"66":{"tf":4.0},"71":{"tf":1.4142135623730951},"75":{"tf":4.123105625617661}},"o":{"df":0,"docs":{},"o":{"df":0,"docs":{},"l":{"df":1,"docs":{"64":{"tf":1.4142135623730951}}}}},"s":{"df":1,"docs":{"24":{"tf":1.7320508075688772}}},"y":{"_":{"c":{"a":{"df":0,"docs":{},"s":{"df":1,"docs":{"13":{"tf":2.449489742783178}}}},"df":0,"docs":{},"o":{"df":0,"docs":{},"n":{"df":0,"docs":{},"t":{"df":0,"docs":{},"r":{"a":{"df":1,"docs":{"14":{"tf":2.449489742783178}}},"df":0,"docs":{}}}}}},"df":0,"docs":{}},"df":0,"docs":{}}},"c":{"`":{"df":0,"docs":{},"の":{"df":0,"docs":{},"合":{"df":0,"docs":{},"成":{"df":0,"docs":{},"を":{"`":{"df":0,"docs":{},"f":{"df":1,"docs":{"66":{"tf":1.0}}}},"df":0,"docs":{}}}}}},"a":{"df":0,"docs":{},"l":{"c":{"df":2,"docs":{"17":{"tf":2.0},"57":{"tf":1.0}}},"df":0,"docs":{}},"s":{"df":0,"docs":{},"e":{"df":7,"docs":{"13":{"tf":1.4142135623730951},"18":{"tf":3.1622776601683795},"19":{"tf":2.8284271247461903},"20":{"tf":2.23606797749979},"21":{"tf":1.7320508075688772},"44":{"tf":1.4142135623730951},"71":{"tf":1.4142135623730951}}}},"t":{"df":0,"docs":{},"e":{"df":0,"docs":{},"g":{"df":0,"docs":{},"o":{"df":0,"docs":{},"r":{"df":0,"docs":{},"i":{"df":1,"docs":{"66":{"tf":1.4142135623730951}}},"y":{".":{"c":{"df":0,"docs":{},"o":{"df":0,"docs":{},"m":{"df":0,"docs":{},"p":{"df":1,"docs":{"66":{"tf":1.0}}}}}},"df":0,"docs":{},"h":{"df":0,"docs":{},"o":{"df":0,"docs":{},"g":{"df":1,"docs":{"66":{"tf":1.0}}}}},"{":{"df":0,"docs":{},"u":{"df":1,"docs":{"66":{"tf":1.0}}}}},"df":0,"docs":{}}}}}}}},"df":5,"docs":{"29":{"tf":2.0},"56":{"tf":1.4142135623730951},"61":{"tf":1.7320508075688772},"62":{"tf":1.4142135623730951},"66":{"tf":4.58257569495584}},"h":{"df":0,"docs":{},"o":{"df":0,"docs":{},"o":{"df":0,"docs":{},"s":{"df":2,"docs":{"22":{"tf":2.23606797749979},"23":{"tf":1.4142135623730951}}}}}},"i":{"df":2,"docs":{"3":{"tf":1.0},"64":{"tf":1.0}}},"l":{"a":{"df":0,"docs":{},"s":{"df":0,"docs":{},"s":{"df":1,"docs":{"66":{"tf":1.0}},"i":{"c":{"a":{"df":0,"docs":{},"l":{".":{"c":{"df":0,"docs":{},"h":{"df":0,"docs":{},"o":{"df":0,"docs":{},"i":{"c":{"df":1,"docs":{"23":{"tf":1.4142135623730951}}},"df":0,"docs":{}}}}},"df":0,"docs":{}},"df":0,"docs":{}}},"df":0,"docs":{}},"df":0,"docs":{}}}}},"df":0,"docs":{}},"o":{"df":0,"docs":{},"m":{"df":0,"docs":{},"p":{"_":{"a":{"df":0,"docs":{},"p":{"df":0,"docs":{},"p":{"df":0,"docs":{},"l":{"df":0,"docs":{},"i":{"df":2,"docs":{"3":{"tf":1.0},"63":{"tf":1.0}}}}}}},"df":0,"docs":{},"i":{"d":{"df":1,"docs":{"66":{"tf":1.4142135623730951}}},"df":0,"docs":{}}},"df":1,"docs":{"66":{"tf":2.6457513110645907}}}},"n":{"df":0,"docs":{},"g":{"df":0,"docs":{},"r":{"df":1,"docs":{"24":{"tf":3.0}},"u":{"df":0,"docs":{},"e":{"df":0,"docs":{},"n":{"c":{"df":1,"docs":{"24":{"tf":1.0}}},"df":0,"docs":{}}}}}},"s":{"df":0,"docs":{},"t":{"df":0,"docs":{},"r":{"df":0,"docs":{},"u":{"c":{"df":0,"docs":{},"t":{"df":0,"docs":{},"o":{"df":0,"docs":{},"r":{"df":4,"docs":{"25":{"tf":2.23606797749979},"26":{"tf":1.7320508075688772},"55":{"tf":2.8284271247461903},"65":{"tf":1.0}}}}}},"df":0,"docs":{}}}}},"t":{"df":0,"docs":{},"r":{"a":{"d":{"df":0,"docs":{},"i":{"c":{"df":0,"docs":{},"t":{"df":5,"docs":{"13":{"tf":1.0},"14":{"tf":1.0},"27":{"tf":2.6457513110645907},"47":{"tf":1.0},"74":{"tf":1.0}}}},"df":0,"docs":{}}},"df":0,"docs":{}},"df":0,"docs":{}}},"v":{"df":1,"docs":{"28":{"tf":2.0}},"e":{"df":0,"docs":{},"r":{"df":0,"docs":{},"t":{"df":1,"docs":{"29":{"tf":2.23606797749979}}}}}}}}},"d":{"df":3,"docs":{"56":{"tf":1.4142135623730951},"61":{"tf":1.7320508075688772},"66":{"tf":2.23606797749979}},"e":{"df":0,"docs":{},"f":{"df":4,"docs":{"36":{"tf":1.4142135623730951},"42":{"tf":1.0},"70":{"tf":1.0},"71":{"tf":1.0}}},"p":{"df":0,"docs":{},"e":{"df":0,"docs":{},"n":{"d":{"df":1,"docs":{"10":{"tf":1.0}}},"df":0,"docs":{}}}}},"o":{"df":0,"docs":{},"n":{"df":0,"docs":{},"e":{"df":4,"docs":{"10":{"tf":1.4142135623730951},"30":{"tf":2.0},"33":{"tf":1.0},"4":{"tf":1.0}}}}},"s":{"df":0,"docs":{},"i":{"df":0,"docs":{},"m":{"df":0,"docs":{},"p":{"df":2,"docs":{"36":{"tf":1.0},"69":{"tf":1.7320508075688772}}}}}}},"df":0,"docs":{},"e":{"df":2,"docs":{"61":{"tf":1.7320508075688772},"66":{"tf":1.4142135623730951}},"v":{"df":0,"docs":{},"e":{"df":0,"docs":{},"n":{"df":1,"docs":{"57":{"tf":1.7320508075688772}}}}},"x":{"a":{"c":{"df":0,"docs":{},"t":{"df":30,"docs":{"10":{"tf":1.0},"12":{"tf":1.7320508075688772},"15":{"tf":1.0},"16":{"tf":1.0},"18":{"tf":1.4142135623730951},"19":{"tf":1.4142135623730951},"21":{"tf":1.0},"22":{"tf":1.0},"23":{"tf":1.0},"24":{"tf":1.0},"25":{"tf":1.7320508075688772},"29":{"tf":1.4142135623730951},"31":{"tf":2.6457513110645907},"32":{"tf":1.7320508075688772},"33":{"tf":3.605551275463989},"37":{"tf":1.0},"38":{"tf":1.4142135623730951},"4":{"tf":1.0},"46":{"tf":1.0},"5":{"tf":1.7320508075688772},"52":{"tf":1.0},"53":{"tf":1.4142135623730951},"55":{"tf":2.449489742783178},"6":{"tf":1.0},"62":{"tf":1.0},"63":{"tf":2.23606797749979},"65":{"tf":1.4142135623730951},"72":{"tf":1.0},"73":{"tf":1.4142135623730951},"8":{"tf":1.7320508075688772}}}},"df":0,"docs":{},"m":{"df":0,"docs":{},"p":{"df":0,"docs":{},"l":{"df":60,"docs":{"10":{"tf":1.0},"11":{"tf":1.0},"13":{"tf":1.0},"14":{"tf":1.0},"15":{"tf":1.4142135623730951},"16":{"tf":1.0},"18":{"tf":1.0},"19":{"tf":1.0},"20":{"tf":1.0},"21":{"tf":1.4142135623730951},"22":{"tf":1.0},"23":{"tf":1.0},"24":{"tf":1.4142135623730951},"25":{"tf":1.4142135623730951},"26":{"tf":1.0},"27":{"tf":2.0},"29":{"tf":1.0},"3":{"tf":1.4142135623730951},"31":{"tf":1.4142135623730951},"33":{"tf":1.4142135623730951},"34":{"tf":1.0},"35":{"tf":1.0},"36":{"tf":1.0},"37":{"tf":1.0},"38":{"tf":1.0},"4":{"tf":1.4142135623730951},"40":{"tf":1.0},"41":{"tf":1.0},"42":{"tf":1.0},"43":{"tf":1.0},"44":{"tf":1.0},"45":{"tf":1.0},"46":{"tf":1.4142135623730951},"47":{"tf":1.0},"48":{"tf":1.4142135623730951},"49":{"tf":1.4142135623730951},"5":{"tf":1.4142135623730951},"50":{"tf":1.0},"51":{"tf":1.0},"52":{"tf":1.4142135623730951},"53":{"tf":1.0},"54":{"tf":1.0},"55":{"tf":1.4142135623730951},"56":{"tf":1.4142135623730951},"57":{"tf":1.0},"58":{"tf":1.4142135623730951},"59":{"tf":1.7320508075688772},"6":{"tf":1.0},"60":{"tf":1.4142135623730951},"61":{"tf":1.0},"62":{"tf":1.0},"63":{"tf":1.4142135623730951},"65":{"tf":1.0},"66":{"tf":1.0},"71":{"tf":1.0},"72":{"tf":1.0},"73":{"tf":2.0},"74":{"tf":1.4142135623730951},"75":{"tf":1.0},"8":{"tf":1.0}}}}}},"df":0,"docs":{},"i":{"df":0,"docs":{},"s":{"df":0,"docs":{},"t":{"df":5,"docs":{"23":{"tf":1.0},"34":{"tf":2.449489742783178},"41":{"tf":1.0},"52":{"tf":1.0},"57":{"tf":1.0}}}}},"p":{"df":0,"docs":{},"l":{"df":0,"docs":{},"o":{"df":0,"docs":{},"s":{"df":0,"docs":{},"i":{"df":0,"docs":{},"o":{"df":0,"docs":{},"n":{")":{"df":0,"docs":{},"と":{"df":0,"docs":{},"呼":{"df":0,"docs":{},"び":{"df":0,"docs":{},"ま":{"df":0,"docs":{},"す":{"df":0,"docs":{},"が":{"df":0,"docs":{},"，":{"c":{"df":0,"docs":{},"o":{"df":0,"docs":{},"n":{"df":0,"docs":{},"t":{"df":0,"docs":{},"r":{"a":{"d":{"df":0,"docs":{},"i":{"c":{"df":0,"docs":{},"t":{"df":1,"docs":{"27":{"tf":1.0}}}},"df":0,"docs":{}}},"df":0,"docs":{}},"df":0,"docs":{}}}}}},"df":0,"docs":{}}}}}}}}},"df":0,"docs":{}}}}}}}},"t":{"df":1,"docs":{"35":{"tf":2.449489742783178}},"e":{"df":0,"docs":{},"n":{"df":0,"docs":{},"s":{"df":0,"docs":{},"i":{"df":0,"docs":{},"o":{"df":0,"docs":{},"n":{"df":1,"docs":{"35":{"tf":1.0}}}}}}}}}}},"f":{"a":{"c":{"df":2,"docs":{"42":{"tf":2.6457513110645907},"43":{"tf":1.7320508075688772}}},"df":0,"docs":{},"l":{"df":0,"docs":{},"s":{"df":7,"docs":{"14":{"tf":1.4142135623730951},"27":{"tf":1.4142135623730951},"4":{"tf":1.0},"47":{"tf":2.0},"50":{"tf":1.0},"6":{"tf":1.7320508075688772},"74":{"tf":1.0}}}}},"df":11,"docs":{"10":{"tf":2.23606797749979},"22":{"tf":2.8284271247461903},"23":{"tf":3.0},"24":{"tf":3.7416573867739413},"29":{"tf":1.7320508075688772},"3":{"tf":3.1622776601683795},"35":{"tf":1.7320508075688772},"36":{"tf":2.449489742783178},"61":{"tf":1.7320508075688772},"63":{"tf":2.23606797749979},"66":{"tf":3.605551275463989}},"e":{"df":0,"docs":{},"r":{"df":0,"docs":{},"m":{"a":{"df":0,"docs":{},"t":{"df":1,"docs":{"70":{"tf":1.0}},"l":{"a":{"df":0,"docs":{},"s":{"df":0,"docs":{},"t":{"df":0,"docs":{},"t":{"df":0,"docs":{},"h":{"df":0,"docs":{},"e":{"df":0,"docs":{},"o":{"df":0,"docs":{},"r":{"df":0,"docs":{},"e":{"df":0,"docs":{},"m":{"df":1,"docs":{"70":{"tf":1.4142135623730951}}}}}}}}}}}},"df":0,"docs":{}}}},"df":0,"docs":{}}}},"l":{"df":0,"docs":{},"t":{"df":1,"docs":{"70":{"tf":1.0}}}},"u":{"df":0,"docs":{},"n":{"c":{"df":0,"docs":{},"t":{"df":0,"docs":{},"i":{"df":0,"docs":{},"o":{"df":0,"docs":{},"n":{"df":1,"docs":{"3":{"tf":1.0}}}}}}},"df":4,"docs":{"15":{"tf":1.0},"16":{"tf":1.0},"23":{"tf":1.4142135623730951},"36":{"tf":1.4142135623730951}},"e":{"df":0,"docs":{},"x":{"df":0,"docs":{},"t":{"df":1,"docs":{"36":{"tf":2.23606797749979}}}}}}}},"g":{"df":9,"docs":{"10":{"tf":1.7320508075688772},"22":{"tf":2.8284271247461903},"24":{"tf":2.23606797749979},"3":{"tf":2.23606797749979},"35":{"tf":1.7320508075688772},"36":{"tf":2.449489742783178},"62":{"tf":1.7320508075688772},"63":{"tf":1.7320508075688772},"66":{"tf":2.6457513110645907}},"e":{"_":{"df":0,"docs":{},"i":{"df":0,"docs":{},"f":{"df":0,"docs":{},"f":{"_":{"df":0,"docs":{},"l":{"df":1,"docs":{"71":{"tf":1.4142135623730951}}}},"df":0,"docs":{}}}}},"df":0,"docs":{},"n":{"df":0,"docs":{},"e":{"df":0,"docs":{},"r":{"a":{"df":0,"docs":{},"r":{"df":1,"docs":{"75":{"tf":1.0}}}},"df":1,"docs":{"44":{"tf":1.0}}}}}},"o":{"a":{"df":0,"docs":{},"l":{"df":1,"docs":{"25":{"tf":1.0}}}},"df":0,"docs":{}},"r":{"df":0,"docs":{},"o":{"df":0,"docs":{},"u":{"df":0,"docs":{},"p":{"df":2,"docs":{"10":{"tf":1.4142135623730951},"62":{"tf":1.0}}}}}},"u":{"a":{"df":0,"docs":{},"r":{"d":{"_":{"df":0,"docs":{},"h":{"df":0,"docs":{},"y":{"df":0,"docs":{},"p":{"df":8,"docs":{"13":{"tf":1.4142135623730951},"22":{"tf":1.4142135623730951},"37":{"tf":2.23606797749979},"44":{"tf":1.7320508075688772},"45":{"tf":1.0},"57":{"tf":1.4142135623730951},"71":{"tf":1.4142135623730951},"75":{"tf":1.7320508075688772}}}}},"m":{"df":0,"docs":{},"s":{"df":0,"docs":{},"g":{"df":1,"docs":{"10":{"tf":1.0}}}}}},"df":0,"docs":{}},"df":0,"docs":{}}},"df":0,"docs":{}}},"h":{".":{"df":0,"docs":{},"l":{"df":0,"docs":{},"e":{"df":0,"docs":{},"f":{"df":0,"docs":{},"t":{"df":1,"docs":{"25":{"tf":1.4142135623730951}}}}}},"r":{"df":0,"docs":{},"i":{"df":0,"docs":{},"g":{"df":0,"docs":{},"h":{"df":0,"docs":{},"t":{"df":1,"docs":{"25":{"tf":1.0}}}}}}}},"1":{"df":4,"docs":{"49":{"tf":1.0},"50":{"tf":1.0},"56":{"tf":2.0},"61":{"tf":1.4142135623730951}}},"2":{"df":4,"docs":{"49":{"tf":1.0},"50":{"tf":1.0},"56":{"tf":1.4142135623730951},"61":{"tf":1.4142135623730951}}},"a":{"b":{"df":1,"docs":{"61":{"tf":1.7320508075688772}}},"df":0,"docs":{}},"c":{"df":1,"docs":{"29":{"tf":1.4142135623730951}}},"df":30,"docs":{"10":{"tf":1.4142135623730951},"13":{"tf":1.0},"14":{"tf":2.0},"15":{"tf":1.0},"18":{"tf":2.23606797749979},"19":{"tf":1.7320508075688772},"20":{"tf":1.4142135623730951},"21":{"tf":2.449489742783178},"22":{"tf":1.4142135623730951},"23":{"tf":1.7320508075688772},"24":{"tf":2.0},"25":{"tf":1.4142135623730951},"27":{"tf":1.7320508075688772},"29":{"tf":3.0},"38":{"tf":1.4142135623730951},"44":{"tf":1.7320508075688772},"46":{"tf":1.4142135623730951},"47":{"tf":1.7320508075688772},"5":{"tf":2.8284271247461903},"51":{"tf":1.0},"52":{"tf":1.4142135623730951},"54":{"tf":1.7320508075688772},"57":{"tf":1.7320508075688772},"61":{"tf":2.449489742783178},"66":{"tf":3.1622776601683795},"71":{"tf":3.1622776601683795},"73":{"tf":1.4142135623730951},"74":{"tf":1.0},"75":{"tf":2.23606797749979},"8":{"tf":1.4142135623730951}},"e":{"a":{"d":{"df":1,"docs":{"4":{"tf":1.4142135623730951}}},"df":0,"docs":{}},"df":0,"docs":{},"l":{"df":0,"docs":{},"p":{"df":1,"docs":{"1":{"tf":1.0}}}}},"f":{"df":2,"docs":{"22":{"tf":2.0},"24":{"tf":1.4142135623730951}}},"g":{"df":1,"docs":{"22":{"tf":1.7320508075688772}},"f":{"df":0,"docs":{},"i":{"df":0,"docs":{},"n":{"df":0,"docs":{},"j":{"df":2,"docs":{"3":{"tf":1.7320508075688772},"63":{"tf":1.4142135623730951}}}}}}},"k":{"df":1,"docs":{"57":{"tf":2.6457513110645907}}},"n":{"df":2,"docs":{"57":{"tf":1.4142135623730951},"6":{"tf":2.0}},"e":{"_":{"df":0,"docs":{},"s":{"df":0,"docs":{},"t":{"df":1,"docs":{"23":{"tf":1.4142135623730951}}}}},"df":0,"docs":{}},"n":{"df":0,"docs":{},"p":{"df":1,"docs":{"13":{"tf":1.0}}}},"p":{"df":1,"docs":{"27":{"tf":1.0}}},"q":{"df":2,"docs":{"14":{"tf":1.4142135623730951},"47":{"tf":1.4142135623730951}}}},"o":{"df":0,"docs":{},"g":{"df":0,"docs":{},"e":{"df":1,"docs":{"66":{"tf":1.0}}}},"m":{"df":1,"docs":{"66":{"tf":4.0}}}},"p":{"df":27,"docs":{"11":{"tf":1.0},"13":{"tf":1.7320508075688772},"14":{"tf":1.0},"15":{"tf":2.0},"16":{"tf":2.0},"18":{"tf":1.4142135623730951},"19":{"tf":1.4142135623730951},"20":{"tf":1.4142135623730951},"21":{"tf":2.23606797749979},"25":{"tf":1.4142135623730951},"27":{"tf":1.0},"31":{"tf":2.8284271247461903},"37":{"tf":1.7320508075688772},"38":{"tf":1.7320508075688772},"4":{"tf":1.4142135623730951},"40":{"tf":1.0},"46":{"tf":1.7320508075688772},"47":{"tf":2.0},"48":{"tf":1.4142135623730951},"5":{"tf":2.23606797749979},"53":{"tf":1.4142135623730951},"54":{"tf":1.4142135623730951},"55":{"tf":2.0},"6":{"tf":1.4142135623730951},"63":{"tf":1.4142135623730951},"65":{"tf":1.4142135623730951},"8":{"tf":1.4142135623730951}},"q":{"df":10,"docs":{"15":{"tf":2.0},"16":{"tf":1.7320508075688772},"33":{"tf":1.4142135623730951},"38":{"tf":1.7320508075688772},"4":{"tf":1.7320508075688772},"40":{"tf":1.4142135623730951},"46":{"tf":1.7320508075688772},"54":{"tf":1.4142135623730951},"61":{"tf":2.0},"63":{"tf":1.4142135623730951}}},"r":{"df":4,"docs":{"18":{"tf":1.4142135623730951},"19":{"tf":1.4142135623730951},"20":{"tf":1.4142135623730951},"21":{"tf":1.4142135623730951}}}},"q":{"df":15,"docs":{"18":{"tf":1.4142135623730951},"19":{"tf":1.4142135623730951},"20":{"tf":1.4142135623730951},"21":{"tf":2.23606797749979},"25":{"tf":1.4142135623730951},"31":{"tf":1.7320508075688772},"33":{"tf":1.4142135623730951},"38":{"tf":1.7320508075688772},"4":{"tf":1.0},"40":{"tf":1.0},"46":{"tf":1.7320508075688772},"47":{"tf":1.4142135623730951},"53":{"tf":1.4142135623730951},"55":{"tf":2.0},"65":{"tf":1.4142135623730951}},"n":{"df":1,"docs":{"4":{"tf":1.4142135623730951}}},"r":{"df":11,"docs":{"15":{"tf":2.0},"16":{"tf":1.7320508075688772},"18":{"tf":1.4142135623730951},"19":{"tf":1.4142135623730951},"20":{"tf":1.4142135623730951},"21":{"tf":1.4142135623730951},"33":{"tf":1.4142135623730951},"38":{"tf":1.7320508075688772},"4":{"tf":1.0},"46":{"tf":1.7320508075688772},"63":{"tf":1.4142135623730951}}}},"r":{"df":2,"docs":{"55":{"tf":2.0},"63":{"tf":1.4142135623730951}}},"x":{"df":3,"docs":{"26":{"tf":1.4142135623730951},"41":{"tf":2.0},"71":{"tf":1.7320508075688772}}},"y":{"df":1,"docs":{"41":{"tf":1.4142135623730951}},"p":{"df":1,"docs":{"46":{"tf":1.0}}}}},"i":{"d":{"_":{"c":{"df":0,"docs":{},"o":{"df":0,"docs":{},"m":{"df":0,"docs":{},"p":{"df":1,"docs":{"66":{"tf":1.4142135623730951}}}}}},"df":0,"docs":{}},"df":2,"docs":{"49":{"tf":1.7320508075688772},"66":{"tf":2.449489742783178}}},"df":0,"docs":{},"f":{"df":0,"docs":{},"f":{".":{"df":0,"docs":{},"m":{"df":0,"docs":{},"p":{"df":0,"docs":{},"r":{"df":1,"docs":{"72":{"tf":1.0}}}}}},"df":0,"docs":{}}},"h":{"df":4,"docs":{"42":{"tf":1.0},"43":{"tf":1.7320508075688772},"44":{"tf":1.4142135623730951},"45":{"tf":1.4142135623730951}}},"m":{"df":0,"docs":{},"p":{"df":0,"docs":{},"o":{"df":0,"docs":{},"r":{"df":0,"docs":{},"t":{"df":26,"docs":{"10":{"tf":1.7320508075688772},"14":{"tf":1.0},"16":{"tf":1.0},"20":{"tf":1.0},"21":{"tf":1.0},"22":{"tf":1.0},"29":{"tf":1.0},"3":{"tf":1.7320508075688772},"33":{"tf":1.0},"35":{"tf":1.0},"37":{"tf":1.0},"4":{"tf":1.4142135623730951},"43":{"tf":1.0},"48":{"tf":1.0},"49":{"tf":1.0},"51":{"tf":1.0},"52":{"tf":1.0},"56":{"tf":1.0},"57":{"tf":1.0},"58":{"tf":1.7320508075688772},"59":{"tf":1.0},"60":{"tf":1.0},"62":{"tf":1.0},"63":{"tf":1.0},"73":{"tf":1.0},"75":{"tf":1.0}}}}}}},"n":{"d":{"df":0,"docs":{},"u":{"c":{"df":0,"docs":{},"t":{"df":5,"docs":{"42":{"tf":2.6457513110645907},"43":{"tf":2.23606797749979},"44":{"tf":1.7320508075688772},"45":{"tf":1.4142135623730951},"58":{"tf":1.0}}}},"df":0,"docs":{}}},"df":0,"docs":{},"f":{"df":0,"docs":{},"i":{"df":0,"docs":{},"x":{"df":0,"docs":{},"r":{":":{"8":{"0":{"df":1,"docs":{"66":{"tf":1.0}}},"df":0,"docs":{}},"df":0,"docs":{}},"df":0,"docs":{}}}},"o":{"df":1,"docs":{"10":{"tf":1.0}},"v":{"df":0,"docs":{},"i":{"df":0,"docs":{},"e":{"df":0,"docs":{},"w":{"df":1,"docs":{"63":{"tf":1.0}}}}}}}},"j":{"df":0,"docs":{},"e":{"c":{"df":0,"docs":{},"t":{"df":2,"docs":{"3":{"tf":2.6457513110645907},"63":{"tf":1.7320508075688772}}}},"df":0,"docs":{}}},"l":{"df":4,"docs":{"13":{"tf":1.0},"18":{"tf":1.7320508075688772},"19":{"tf":1.4142135623730951},"71":{"tf":1.0}}},"r":{"df":4,"docs":{"13":{"tf":1.0},"18":{"tf":1.7320508075688772},"19":{"tf":1.4142135623730951},"71":{"tf":1.0}}},"s":{"df":0,"docs":{},"e":{"df":0,"docs":{},"r":{"df":0,"docs":{},"t":{"df":1,"docs":{"18":{"tf":1.4142135623730951}}}}}},"t":{"df":5,"docs":{"24":{"tf":2.0},"52":{"tf":1.4142135623730951},"56":{"tf":1.4142135623730951},"57":{"tf":1.0},"71":{"tf":1.7320508075688772}},"r":{"df":0,"docs":{},"o":{"d":{"df":0,"docs":{},"u":{"c":{"df":1,"docs":{"46":{"tf":1.0}}},"df":0,"docs":{}}},"df":19,"docs":{"13":{"tf":1.0},"14":{"tf":1.0},"15":{"tf":1.0},"16":{"tf":1.0},"18":{"tf":1.0},"19":{"tf":1.0},"20":{"tf":1.0},"21":{"tf":1.4142135623730951},"23":{"tf":1.0},"26":{"tf":1.0},"3":{"tf":1.4142135623730951},"35":{"tf":1.0},"38":{"tf":1.0},"4":{"tf":1.0},"46":{"tf":2.8284271247461903},"47":{"tf":2.0},"52":{"tf":1.0},"57":{"tf":1.0},"63":{"tf":1.0}}}}}},"t":{"df":0,"docs":{},"e":{"_":{"df":0,"docs":{},"f":{"a":{"df":0,"docs":{},"l":{"df":0,"docs":{},"s":{"df":1,"docs":{"71":{"tf":1.0}}}}},"df":0,"docs":{}},"t":{"df":0,"docs":{},"r":{"df":0,"docs":{},"u":{"df":1,"docs":{"71":{"tf":1.0}}}}}},"df":0,"docs":{}}}},"k":{"df":3,"docs":{"43":{"tf":1.4142135623730951},"45":{"tf":1.7320508075688772},"57":{"tf":3.3166247903554}}},"l":{".":{"df":0,"docs":{},"l":{"df":0,"docs":{},"e":{"df":0,"docs":{},"n":{"df":0,"docs":{},"g":{"df":0,"docs":{},"t":{"df":0,"docs":{},"h":{"df":1,"docs":{"44":{"tf":1.0}}}}}}}}},"df":1,"docs":{"44":{"tf":3.1622776601683795}},"e":{"a":{"df":0,"docs":{},"n":{".":{"df":0,"docs":{},"m":{"df":0,"docs":{},"v":{"a":{"df":0,"docs":{},"r":{"df":0,"docs":{},"i":{"d":{".":{"df":0,"docs":{},"r":{"df":0,"docs":{},"e":{"df":0,"docs":{},"f":{"df":0,"docs":{},"l":{"df":1,"docs":{"59":{"tf":1.0}}}}},"f":{"df":0,"docs":{},"l":{"df":1,"docs":{"59":{"tf":1.0}}}}}},"df":0,"docs":{}},"df":0,"docs":{}}}},"df":0,"docs":{}}}},"4":{"df":5,"docs":{"0":{"tf":1.7320508075688772},"1":{"tf":1.0},"17":{"tf":1.0},"2":{"tf":1.0},"28":{"tf":1.0}}},"df":8,"docs":{"0":{"tf":1.0},"15":{"tf":1.0},"2":{"tf":2.0},"42":{"tf":1.0},"47":{"tf":1.0},"6":{"tf":1.0},"71":{"tf":1.0},"75":{"tf":1.0}}}},"df":0,"docs":{},"f":{"df":0,"docs":{},"t":{"df":3,"docs":{"18":{"tf":1.0},"25":{"tf":1.0},"48":{"tf":2.449489742783178}}}}},"i":{"df":0,"docs":{},"n":{"a":{"df":0,"docs":{},"r":{"df":0,"docs":{},"i":{"df":0,"docs":{},"t":{"df":0,"docs":{},"h":{"df":5,"docs":{"49":{"tf":3.3166247903554},"50":{"tf":1.7320508075688772},"51":{"tf":1.7320508075688772},"52":{"tf":1.0},"71":{"tf":1.4142135623730951}}}}}}},"df":0,"docs":{},"e":{"a":{"df":0,"docs":{},"r":{"df":2,"docs":{"49":{"tf":1.0},"51":{"tf":1.0}}}},"df":0,"docs":{}}},"s":{"df":0,"docs":{},"t":{".":{"df":0,"docs":{},"l":{"df":0,"docs":{},"e":{"df":0,"docs":{},"n":{"df":0,"docs":{},"g":{"df":0,"docs":{},"t":{"df":0,"docs":{},"h":{"df":1,"docs":{"44":{"tf":1.7320508075688772}}}}}}}}},"df":1,"docs":{"44":{"tf":1.7320508075688772}}}}},"o":{"df":0,"docs":{},"s":{"df":0,"docs":{},"s":{"df":1,"docs":{"75":{"tf":1.0}}}}}},"m":{"a":{"df":0,"docs":{},"t":{"c":{"df":0,"docs":{},"h":{"df":1,"docs":{"45":{"tf":1.0}}}},"df":0,"docs":{},"h":{"df":0,"docs":{},"e":{"df":0,"docs":{},"m":{"a":{"df":0,"docs":{},"t":{"df":1,"docs":{"2":{"tf":1.0}}}},"df":0,"docs":{}}},"l":{"df":0,"docs":{},"i":{"b":{".":{"a":{"df":0,"docs":{},"l":{"df":0,"docs":{},"g":{"df":0,"docs":{},"e":{"b":{"df":0,"docs":{},"r":{"a":{".":{"df":0,"docs":{},"g":{"df":0,"docs":{},"r":{"df":0,"docs":{},"o":{"df":0,"docs":{},"u":{"df":0,"docs":{},"p":{".":{"d":{"df":0,"docs":{},"e":{"df":0,"docs":{},"f":{"df":1,"docs":{"10":{"tf":1.0}}}}},"df":0,"docs":{}},"df":0,"docs":{}}}}}},"h":{"df":0,"docs":{},"o":{"df":0,"docs":{},"m":{".":{"df":0,"docs":{},"g":{"df":0,"docs":{},"r":{"df":0,"docs":{},"o":{"df":0,"docs":{},"u":{"df":0,"docs":{},"p":{".":{"d":{"df":0,"docs":{},"e":{"df":0,"docs":{},"f":{"df":1,"docs":{"10":{"tf":1.0}}}}},"df":0,"docs":{}},"df":0,"docs":{}}}}}}},"df":0,"docs":{}}}}},"df":0,"docs":{}},"df":0,"docs":{}}},"df":0,"docs":{}}}}},"d":{"a":{"df":0,"docs":{},"t":{"a":{".":{"df":0,"docs":{},"n":{"a":{"df":0,"docs":{},"t":{".":{"b":{"a":{"df":0,"docs":{},"s":{"df":1,"docs":{"58":{"tf":1.0}}}},"df":0,"docs":{}},"df":0,"docs":{}},"df":0,"docs":{}}},"df":0,"docs":{}},"s":{"df":0,"docs":{},"e":{"df":0,"docs":{},"t":{"df":0,"docs":{},"l":{"df":0,"docs":{},"i":{"df":0,"docs":{},"k":{"df":0,"docs":{},"e":{".":{"b":{"a":{"df":0,"docs":{},"s":{"df":1,"docs":{"35":{"tf":1.0}}}},"df":0,"docs":{}},"df":0,"docs":{}},"df":0,"docs":{}}}}}}}}},"df":0,"docs":{}},"df":0,"docs":{}}},"df":0,"docs":{}},"df":0,"docs":{},"i":{"df":0,"docs":{},"n":{"df":0,"docs":{},"i":{"df":0,"docs":{},"t":{".":{"df":0,"docs":{},"f":{"df":0,"docs":{},"u":{"df":0,"docs":{},"n":{"c":{"df":0,"docs":{},"t":{"df":1,"docs":{"3":{"tf":1.0}}}},"df":0,"docs":{}}}}},"df":0,"docs":{}}}}},"t":{"a":{"c":{"df":0,"docs":{},"t":{"df":0,"docs":{},"i":{"c":{".":{"b":{"df":0,"docs":{},"y":{"c":{"df":0,"docs":{},"o":{"df":0,"docs":{},"n":{"df":0,"docs":{},"t":{"df":0,"docs":{},"r":{"a":{"df":1,"docs":{"14":{"tf":1.0}}},"df":0,"docs":{}}}}}},"df":0,"docs":{}}},"c":{"a":{"df":0,"docs":{},"s":{"df":2,"docs":{"20":{"tf":1.0},"43":{"tf":1.0}}}},"df":0,"docs":{},"h":{"df":0,"docs":{},"o":{"df":0,"docs":{},"o":{"df":0,"docs":{},"s":{"df":1,"docs":{"22":{"tf":1.0}}}}}},"o":{"df":0,"docs":{},"n":{"df":0,"docs":{},"v":{"df":0,"docs":{},"e":{"df":0,"docs":{},"r":{"df":0,"docs":{},"t":{"df":1,"docs":{"29":{"tf":1.0}}}}}}}}},"df":0,"docs":{},"g":{"c":{"df":0,"docs":{},"o":{"df":0,"docs":{},"n":{"df":0,"docs":{},"g":{"df":0,"docs":{},"r":{"df":1,"docs":{"56":{"tf":1.0}}}}}}},"df":0,"docs":{}},"l":{"df":0,"docs":{},"e":{"df":0,"docs":{},"f":{"df":0,"docs":{},"t":{"df":0,"docs":{},"r":{"df":0,"docs":{},"i":{"df":0,"docs":{},"g":{"df":0,"docs":{},"h":{"df":0,"docs":{},"t":{"df":1,"docs":{"48":{"tf":1.0}}}}}}}}}},"i":{"b":{"df":0,"docs":{},"r":{"a":{"df":0,"docs":{},"r":{"df":0,"docs":{},"y":{"df":0,"docs":{},"s":{"df":0,"docs":{},"e":{"a":{"df":0,"docs":{},"r":{"c":{"df":0,"docs":{},"h":{"df":2,"docs":{"10":{"tf":1.0},"33":{"tf":1.0}}}},"df":0,"docs":{}}},"df":0,"docs":{}}}}}},"df":0,"docs":{}}},"df":0,"docs":{},"n":{"a":{"df":0,"docs":{},"r":{"df":0,"docs":{},"i":{"df":0,"docs":{},"t":{"df":0,"docs":{},"h":{"df":2,"docs":{"49":{"tf":1.0},"51":{"tf":1.0}}}}}}},"df":0,"docs":{}}}},"n":{"df":0,"docs":{},"t":{"df":0,"docs":{},"h":{"df":0,"docs":{},"r":{"df":0,"docs":{},"e":{"df":0,"docs":{},"w":{"df":0,"docs":{},"r":{"df":0,"docs":{},"i":{"df":0,"docs":{},"t":{"df":1,"docs":{"62":{"tf":1.0}}}}}}}}}}},"p":{"df":0,"docs":{},"u":{"df":0,"docs":{},"s":{"df":0,"docs":{},"h":{"df":0,"docs":{},"n":{"df":0,"docs":{},"e":{"df":0,"docs":{},"g":{"df":1,"docs":{"52":{"tf":1.0}}}}}}}}},"r":{"df":1,"docs":{"60":{"tf":1.0}},"e":{"df":0,"docs":{},"l":{"a":{"df":0,"docs":{},"t":{"df":0,"docs":{},"i":{"df":0,"docs":{},"o":{"df":0,"docs":{},"n":{".":{"df":0,"docs":{},"r":{"df":0,"docs":{},"f":{"df":0,"docs":{},"l":{"df":2,"docs":{"58":{"tf":1.0},"59":{"tf":1.4142135623730951}}}}}},"df":0,"docs":{}}}}}},"df":0,"docs":{}}}},"s":{"a":{"df":0,"docs":{},"y":{"df":2,"docs":{"3":{"tf":1.0},"63":{"tf":1.0}}}},"df":0,"docs":{},"o":{"df":0,"docs":{},"l":{"df":0,"docs":{},"v":{"df":0,"docs":{},"e":{"b":{"df":0,"docs":{},"y":{"df":0,"docs":{},"e":{"df":0,"docs":{},"l":{"df":0,"docs":{},"i":{"df":0,"docs":{},"m":{"df":1,"docs":{"4":{"tf":1.4142135623730951}}}}}}}},"df":0,"docs":{}}}}}},"t":{"a":{"df":0,"docs":{},"u":{"df":0,"docs":{},"t":{"df":0,"docs":{},"o":{"df":1,"docs":{"73":{"tf":1.0}}}}}},"df":0,"docs":{}},"w":{"df":0,"docs":{},"l":{"df":0,"docs":{},"o":{"df":0,"docs":{},"g":{"df":1,"docs":{"75":{"tf":1.0}}}}}}},"df":0,"docs":{}},"df":0,"docs":{}}}},"df":0,"docs":{}},"df":0,"docs":{}}},"4":{"df":2,"docs":{"2":{"tf":1.0},"48":{"tf":1.0}}},"df":0,"docs":{}},"df":0,"docs":{}}}}}},"df":1,"docs":{"45":{"tf":1.7320508075688772}},"o":{"df":0,"docs":{},"n":{"df":0,"docs":{},"o":{"df":0,"docs":{},"i":{"d":{"df":0,"docs":{},"h":{"df":0,"docs":{},"o":{"df":0,"docs":{},"m":{".":{"df":0,"docs":{},"m":{"a":{"df":0,"docs":{},"p":{"_":{"df":0,"docs":{},"m":{"df":0,"docs":{},"u":{"df":0,"docs":{},"l":{"df":1,"docs":{"10":{"tf":1.0}}}}}},"df":0,"docs":{}}},"df":0,"docs":{}}},"df":0,"docs":{}}}}},"df":0,"docs":{}}}}},"u":{"df":0,"docs":{},"l":{"_":{"df":0,"docs":{},"i":{"df":0,"docs":{},"n":{"df":0,"docs":{},"v":{"_":{"df":0,"docs":{},"e":{"df":0,"docs":{},"q":{"_":{"df":0,"docs":{},"i":{"df":0,"docs":{},"f":{"df":0,"docs":{},"f":{"_":{"df":0,"docs":{},"e":{"df":0,"docs":{},"q":{"_":{"df":0,"docs":{},"m":{"df":0,"docs":{},"u":{"df":0,"docs":{},"l":{"df":1,"docs":{"62":{"tf":1.4142135623730951}}}}}},"df":0,"docs":{}}}},"df":0,"docs":{}}}}},"df":0,"docs":{}}}},"df":0,"docs":{}}}},"n":{"df":0,"docs":{},"e":{"df":0,"docs":{},"g":{"df":1,"docs":{"71":{"tf":1.0}}}}}},"df":0,"docs":{}}},"y":{"a":{"b":{"df":1,"docs":{"71":{"tf":2.23606797749979}}},"df":0,"docs":{}},"df":0,"docs":{},"e":{"df":0,"docs":{},"q":{".":{"df":0,"docs":{},"r":{"df":0,"docs":{},"e":{"df":0,"docs":{},"f":{"df":0,"docs":{},"l":{"df":1,"docs":{"58":{"tf":1.0}}}}}}},"df":1,"docs":{"58":{"tf":1.7320508075688772}}}}}},"n":{"a":{"df":0,"docs":{},"m":{"df":0,"docs":{},"e":{"df":11,"docs":{"21":{"tf":1.0},"24":{"tf":1.0},"35":{"tf":1.0},"46":{"tf":1.0},"49":{"tf":1.0},"51":{"tf":1.0},"52":{"tf":1.0},"56":{"tf":1.0},"58":{"tf":1.0},"73":{"tf":1.0},"75":{"tf":1.0}}}},"t":{".":{"d":{"df":0,"docs":{},"v":{"d":{"_":{"df":0,"docs":{},"i":{"df":0,"docs":{},"f":{"df":0,"docs":{},"f":{"_":{"d":{"df":0,"docs":{},"i":{"df":0,"docs":{},"v":{"_":{"df":0,"docs":{},"m":{"df":0,"docs":{},"u":{"df":0,"docs":{},"l":{"_":{"df":0,"docs":{},"e":{"df":0,"docs":{},"q":{"df":1,"docs":{"72":{"tf":1.0}}}}},"df":0,"docs":{}}}}},"df":0,"docs":{}}}},"df":0,"docs":{}},"df":0,"docs":{}}}}},"df":0,"docs":{}},"df":0,"docs":{}}},"df":0,"docs":{},"l":{"df":0,"docs":{},"t":{".":{"b":{"a":{"df":0,"docs":{},"s":{"df":1,"docs":{"33":{"tf":1.0}}}},"df":0,"docs":{}},"df":0,"docs":{}},"df":0,"docs":{}}},"m":{"df":0,"docs":{},"u":{"df":0,"docs":{},"l":{"_":{"a":{"df":0,"docs":{},"s":{"df":0,"docs":{},"s":{"df":0,"docs":{},"o":{"c":{"df":1,"docs":{"61":{"tf":1.4142135623730951}}},"df":0,"docs":{}}}}},"df":0,"docs":{}},"df":0,"docs":{}}}},"s":{"df":0,"docs":{},"t":{"df":0,"docs":{},"r":{"df":0,"docs":{},"o":{"df":0,"docs":{},"n":{"df":0,"docs":{},"g":{"_":{"df":0,"docs":{},"i":{"df":0,"docs":{},"n":{"d":{"df":0,"docs":{},"u":{"c":{"df":0,"docs":{},"t":{"df":0,"docs":{},"i":{"df":0,"docs":{},"o":{"df":0,"docs":{},"n":{"_":{"df":0,"docs":{},"o":{"df":0,"docs":{},"n":{"df":1,"docs":{"45":{"tf":1.0}}}}},"df":0,"docs":{}}}}}},"df":0,"docs":{}}},"df":0,"docs":{}}}},"df":0,"docs":{}}}}}}}},"df":15,"docs":{"10":{"tf":1.0},"26":{"tf":1.0},"27":{"tf":1.0},"29":{"tf":1.4142135623730951},"34":{"tf":1.0},"36":{"tf":1.4142135623730951},"42":{"tf":2.8284271247461903},"43":{"tf":1.0},"45":{"tf":1.4142135623730951},"46":{"tf":1.0},"51":{"tf":1.0},"58":{"tf":1.0},"61":{"tf":1.0},"70":{"tf":1.0},"75":{"tf":1.4142135623730951}}}},"df":8,"docs":{"42":{"tf":3.872983346207417},"43":{"tf":1.7320508075688772},"44":{"tf":2.0},"45":{"tf":3.3166247903554},"46":{"tf":1.7320508075688772},"57":{"tf":3.7416573867739413},"58":{"tf":2.449489742783178},"70":{"tf":2.23606797749979}},"e":{"df":0,"docs":{},"e":{"d":{"df":22,"docs":{"14":{"tf":1.0},"16":{"tf":1.0},"20":{"tf":1.0},"21":{"tf":1.0},"22":{"tf":1.0},"29":{"tf":1.0},"35":{"tf":1.0},"37":{"tf":1.0},"4":{"tf":1.0},"43":{"tf":1.0},"48":{"tf":1.0},"49":{"tf":1.0},"51":{"tf":1.0},"52":{"tf":1.0},"56":{"tf":1.0},"57":{"tf":1.0},"58":{"tf":1.0},"60":{"tf":1.0},"62":{"tf":1.0},"63":{"tf":1.0},"73":{"tf":1.0},"75":{"tf":1.0}}},"df":0,"docs":{}},"g":{"a":{"df":0,"docs":{},"t":{"df":1,"docs":{"52":{"tf":1.0}}}},"df":0,"docs":{}}},"l":{"df":0,"docs":{},"i":{"df":0,"docs":{},"n":{"a":{"df":0,"docs":{},"r":{"df":0,"docs":{},"i":{"df":0,"docs":{},"t":{"df":0,"docs":{},"h":{"df":1,"docs":{"51":{"tf":2.23606797749979}}}}}}},"df":0,"docs":{}}}},"o":{"df":0,"docs":{},"n":{"c":{"df":0,"docs":{},"o":{"df":0,"docs":{},"m":{"df":0,"docs":{},"p":{"df":0,"docs":{},"u":{"df":0,"docs":{},"t":{"df":1,"docs":{"23":{"tf":1.0}}}}}}}},"df":1,"docs":{"51":{"tf":1.0}},"e":{"df":0,"docs":{},"m":{"df":0,"docs":{},"p":{"df":0,"docs":{},"t":{"df":0,"docs":{},"i":{"df":1,"docs":{"23":{"tf":1.0}}}}}}}}},"t":{"df":0,"docs":{},"h":{"_":{"df":0,"docs":{},"r":{"df":0,"docs":{},"w":{"df":2,"docs":{"57":{"tf":1.0},"62":{"tf":1.7320508075688772}}}}},"df":0,"docs":{}}}},"o":{"b":{"df":0,"docs":{},"t":{"a":{"df":0,"docs":{},"i":{"df":0,"docs":{},"n":{"df":1,"docs":{"57":{"tf":1.0}}}}},"df":0,"docs":{}}},"df":0,"docs":{},"n":{"df":0,"docs":{},"e":{"_":{"df":0,"docs":{},"m":{"df":0,"docs":{},"u":{"df":0,"docs":{},"l":{"df":1,"docs":{"62":{"tf":1.4142135623730951}}}}}},"df":0,"docs":{}}},"p":{"df":0,"docs":{},"e":{"df":0,"docs":{},"n":{"df":2,"docs":{"3":{"tf":1.0},"66":{"tf":1.0}}}},"t":{"df":0,"docs":{},"i":{"df":0,"docs":{},"o":{"df":0,"docs":{},"n":{"df":1,"docs":{"1":{"tf":1.0}}}}}}},"r":{".":{"df":0,"docs":{},"i":{"df":0,"docs":{},"n":{"df":0,"docs":{},"l":{"df":1,"docs":{"48":{"tf":1.4142135623730951}}},"r":{"df":1,"docs":{"48":{"tf":1.0}}}}}},"df":0,"docs":{}}},"p":{"(":{"0":{"df":1,"docs":{"45":{"tf":1.0}}},"df":0,"docs":{},"x":{"df":2,"docs":{"22":{"tf":1.4142135623730951},"46":{"tf":1.0}}}},"df":43,"docs":{"11":{"tf":1.7320508075688772},"13":{"tf":3.3166247903554},"14":{"tf":2.6457513110645907},"15":{"tf":2.8284271247461903},"16":{"tf":1.4142135623730951},"18":{"tf":2.449489742783178},"19":{"tf":1.7320508075688772},"20":{"tf":1.4142135623730951},"21":{"tf":3.0},"23":{"tf":2.449489742783178},"25":{"tf":3.0},"26":{"tf":1.0},"27":{"tf":2.6457513110645907},"31":{"tf":2.449489742783178},"33":{"tf":1.7320508075688772},"34":{"tf":1.7320508075688772},"37":{"tf":1.7320508075688772},"38":{"tf":3.0},"4":{"tf":2.449489742783178},"40":{"tf":2.23606797749979},"41":{"tf":1.4142135623730951},"42":{"tf":2.0},"44":{"tf":2.23606797749979},"45":{"tf":2.449489742783178},"46":{"tf":4.242640687119285},"47":{"tf":3.3166247903554},"48":{"tf":2.449489742783178},"5":{"tf":3.7416573867739413},"52":{"tf":3.4641016151377544},"53":{"tf":2.0},"54":{"tf":2.23606797749979},"55":{"tf":2.6457513110645907},"57":{"tf":1.0},"6":{"tf":2.6457513110645907},"61":{"tf":1.7320508075688772},"63":{"tf":1.4142135623730951},"65":{"tf":2.23606797749979},"66":{"tf":1.4142135623730951},"71":{"tf":1.7320508075688772},"72":{"tf":1.0},"73":{"tf":3.0},"74":{"tf":1.0},"8":{"tf":2.0}},"h":{"df":0,"docs":{},"r":{"a":{"df":0,"docs":{},"s":{"df":0,"docs":{},"e":{"b":{"df":0,"docs":{},"o":{"df":0,"docs":{},"o":{"df":0,"docs":{},"k":{"df":1,"docs":{"2":{"tf":1.0}}}}}},"df":0,"docs":{}}}},"df":0,"docs":{}}},"o":{"df":0,"docs":{},"s":{"df":0,"docs":{},"i":{"df":0,"docs":{},"t":{"df":2,"docs":{"42":{"tf":1.0},"43":{"tf":1.0}}}}}},"r":{"df":0,"docs":{},"i":{"df":0,"docs":{},"n":{"df":0,"docs":{},"t":{"df":1,"docs":{"10":{"tf":1.0}}}}},"o":{"df":0,"docs":{},"p":{"df":9,"docs":{"13":{"tf":1.0},"21":{"tf":1.0},"23":{"tf":1.0},"33":{"tf":1.0},"4":{"tf":1.0},"44":{"tf":1.0},"45":{"tf":1.0},"46":{"tf":1.0},"58":{"tf":1.0}}},"v":{"df":0,"docs":{},"e":{"df":2,"docs":{"17":{"tf":1.0},"28":{"tf":1.0}}}}}},"u":{"df":0,"docs":{},"s":{"df":0,"docs":{},"h":{"_":{"df":0,"docs":{},"n":{"df":0,"docs":{},"e":{"df":0,"docs":{},"g":{"df":1,"docs":{"52":{"tf":2.449489742783178}}}}}},"df":1,"docs":{"52":{"tf":1.0}}}}},"y":{"df":1,"docs":{"23":{"tf":1.4142135623730951}}}},"q":{"(":{"df":0,"docs":{},"i":{"df":1,"docs":{"46":{"tf":1.0}}}},"df":32,"docs":{"11":{"tf":1.0},"14":{"tf":2.23606797749979},"15":{"tf":2.0},"16":{"tf":1.4142135623730951},"18":{"tf":2.449489742783178},"19":{"tf":1.7320508075688772},"20":{"tf":1.4142135623730951},"21":{"tf":3.0},"25":{"tf":2.8284271247461903},"26":{"tf":1.0},"27":{"tf":1.0},"31":{"tf":1.4142135623730951},"33":{"tf":1.7320508075688772},"38":{"tf":2.6457513110645907},"4":{"tf":2.449489742783178},"40":{"tf":2.23606797749979},"42":{"tf":2.0},"46":{"tf":3.872983346207417},"47":{"tf":3.0},"48":{"tf":2.0},"5":{"tf":3.4641016151377544},"52":{"tf":3.1622776601683795},"53":{"tf":1.4142135623730951},"54":{"tf":2.0},"55":{"tf":2.8284271247461903},"61":{"tf":1.4142135623730951},"63":{"tf":1.4142135623730951},"65":{"tf":1.7320508075688772},"71":{"tf":1.7320508075688772},"72":{"tf":2.6457513110645907},"73":{"tf":2.23606797749979},"8":{"tf":2.0}}},"r":{"c":{"a":{"df":0,"docs":{},"s":{"df":0,"docs":{},"e":{"df":1,"docs":{"21":{"tf":2.23606797749979}}}}},"df":0,"docs":{}},"df":13,"docs":{"15":{"tf":2.449489742783178},"16":{"tf":1.4142135623730951},"18":{"tf":1.7320508075688772},"19":{"tf":1.7320508075688772},"20":{"tf":1.7320508075688772},"21":{"tf":2.0},"33":{"tf":1.4142135623730951},"38":{"tf":2.23606797749979},"4":{"tf":1.7320508075688772},"46":{"tf":2.6457513110645907},"55":{"tf":2.8284271247461903},"63":{"tf":1.4142135623730951},"73":{"tf":1.4142135623730951}},"e":{"c":{"df":0,"docs":{},"u":{"df":0,"docs":{},"r":{"df":0,"docs":{},"s":{"df":1,"docs":{"21":{"tf":1.0}}}}}},"df":0,"docs":{},"f":{"df":0,"docs":{},"i":{"df":0,"docs":{},"n":{"df":4,"docs":{"10":{"tf":1.0},"53":{"tf":2.23606797749979},"54":{"tf":2.23606797749979},"55":{"tf":2.0}}}},"l":{"df":2,"docs":{"58":{"tf":2.0},"59":{"tf":1.0}},"e":{"df":0,"docs":{},"x":{"df":1,"docs":{"58":{"tf":1.0}}}}}},"l":{"a":{"df":0,"docs":{},"t":{"df":1,"docs":{"56":{"tf":1.0}}}},"df":1,"docs":{"56":{"tf":2.6457513110645907}}},"p":{"df":0,"docs":{},"e":{"a":{"df":0,"docs":{},"t":{"df":1,"docs":{"4":{"tf":1.7320508075688772}}}},"df":0,"docs":{}},"l":{"a":{"c":{"df":2,"docs":{"57":{"tf":2.449489742783178},"71":{"tf":1.0}}},"df":0,"docs":{}},"df":0,"docs":{}}}},"f":{"df":0,"docs":{},"l":{"df":5,"docs":{"49":{"tf":1.0},"58":{"tf":2.449489742783178},"59":{"tf":2.23606797749979},"72":{"tf":1.4142135623730951},"74":{"tf":1.0}}}},"i":{"df":0,"docs":{},"g":{"df":0,"docs":{},"h":{"df":0,"docs":{},"t":{"df":3,"docs":{"18":{"tf":1.0},"25":{"tf":1.0},"48":{"tf":2.23606797749979}}}}},"n":{"df":0,"docs":{},"g":{"df":4,"docs":{"36":{"tf":1.0},"41":{"tf":1.0},"57":{"tf":2.0},"60":{"tf":2.6457513110645907}}}}},"w":{"df":10,"docs":{"26":{"tf":1.0},"29":{"tf":1.0},"3":{"tf":1.4142135623730951},"41":{"tf":1.0},"46":{"tf":1.0},"57":{"tf":1.4142135623730951},"61":{"tf":3.7416573867739413},"62":{"tf":1.4142135623730951},"63":{"tf":1.0},"67":{"tf":1.0}}}},"s":{"a":{"df":0,"docs":{},"y":{"df":0,"docs":{},"s":{".":{"df":0,"docs":{},"n":{"df":0,"docs":{},"o":{"_":{"df":0,"docs":{},"v":{"df":0,"docs":{},"e":{"df":0,"docs":{},"r":{"df":0,"docs":{},"i":{"df":0,"docs":{},"f":{"df":0,"docs":{},"y":{"_":{"df":0,"docs":{},"i":{"df":0,"docs":{},"n":{"_":{"c":{"df":0,"docs":{},"i":{"df":2,"docs":{"3":{"tf":1.0},"64":{"tf":1.0}}}},"df":0,"docs":{}},"df":0,"docs":{}}}},"df":0,"docs":{}}}}}}}},"df":0,"docs":{}}},"v":{"df":0,"docs":{},"e":{"df":0,"docs":{},"r":{"df":0,"docs":{},"i":{"df":0,"docs":{},"f":{"df":0,"docs":{},"i":{"df":1,"docs":{"64":{"tf":1.0}}}}}}}}},"df":0,"docs":{}}}},"df":2,"docs":{"35":{"tf":2.449489742783178},"63":{"tf":1.4142135623730951}},"e":{"df":0,"docs":{},"t":{"_":{"df":0,"docs":{},"o":{"df":0,"docs":{},"p":{"df":0,"docs":{},"t":{"df":2,"docs":{"1":{"tf":1.0},"3":{"tf":1.0}}}}}},"df":1,"docs":{"35":{"tf":1.0}}}},"h":{"df":0,"docs":{},"o":{"df":0,"docs":{},"w":{"_":{"df":0,"docs":{},"t":{"df":0,"docs":{},"e":{"df":0,"docs":{},"r":{"df":0,"docs":{},"m":{"df":1,"docs":{"60":{"tf":1.4142135623730951}}}}}}},"df":16,"docs":{"14":{"tf":1.0},"24":{"tf":1.4142135623730951},"29":{"tf":1.0},"3":{"tf":1.0},"4":{"tf":1.7320508075688772},"44":{"tf":1.4142135623730951},"46":{"tf":1.4142135623730951},"47":{"tf":1.0},"5":{"tf":1.0},"52":{"tf":1.4142135623730951},"53":{"tf":1.0},"54":{"tf":1.0},"55":{"tf":2.6457513110645907},"65":{"tf":2.449489742783178},"71":{"tf":1.7320508075688772},"75":{"tf":1.4142135623730951}}}}},"i":{"df":0,"docs":{},"m":{"df":0,"docs":{},"p":{"_":{"a":{"df":0,"docs":{},"l":{"df":4,"docs":{"26":{"tf":1.0},"3":{"tf":1.0},"63":{"tf":1.0},"68":{"tf":1.7320508075688772}}}},"df":0,"docs":{}},"df":11,"docs":{"24":{"tf":1.4142135623730951},"3":{"tf":1.0},"42":{"tf":1.4142135623730951},"43":{"tf":1.4142135623730951},"60":{"tf":1.0},"63":{"tf":1.0},"66":{"tf":3.1622776601683795},"67":{"tf":2.0},"68":{"tf":1.4142135623730951},"69":{"tf":1.4142135623730951},"71":{"tf":2.449489742783178}}}}},"o":{"df":0,"docs":{},"r":{"df":0,"docs":{},"r":{"df":0,"docs":{},"i":{"df":4,"docs":{"10":{"tf":1.4142135623730951},"44":{"tf":1.4142135623730951},"45":{"tf":1.4142135623730951},"70":{"tf":2.449489742783178}}},"y":{"a":{"df":0,"docs":{},"x":{"df":1,"docs":{"10":{"tf":1.7320508075688772}}}},"df":0,"docs":{}}}}},"p":{"df":0,"docs":{},"l":{"df":0,"docs":{},"i":{"df":0,"docs":{},"t":{"df":1,"docs":{"71":{"tf":2.6457513110645907}}}}}},"t":{"d":{".":{"df":0,"docs":{},"t":{"a":{"c":{"df":0,"docs":{},"t":{"df":0,"docs":{},"i":{"c":{".":{"df":0,"docs":{},"e":{"df":0,"docs":{},"x":{"df":0,"docs":{},"t":{"df":1,"docs":{"35":{"tf":1.0}}}}},"g":{"df":0,"docs":{},"u":{"a":{"df":0,"docs":{},"r":{"d":{"df":0,"docs":{},"e":{"df":0,"docs":{},"x":{"df":0,"docs":{},"p":{"df":0,"docs":{},"r":{"df":1,"docs":{"37":{"tf":1.0}}}}}}},"df":0,"docs":{}}},"df":0,"docs":{}}},"r":{"c":{"a":{"df":0,"docs":{},"s":{"df":1,"docs":{"21":{"tf":1.0}}}},"df":0,"docs":{}},"df":0,"docs":{},"e":{"df":0,"docs":{},"p":{"df":0,"docs":{},"l":{"a":{"c":{"df":1,"docs":{"57":{"tf":1.0}}},"df":0,"docs":{}},"df":0,"docs":{}}}}},"s":{"df":0,"docs":{},"h":{"df":0,"docs":{},"o":{"df":0,"docs":{},"w":{"df":0,"docs":{},"t":{"df":0,"docs":{},"e":{"df":0,"docs":{},"r":{"df":0,"docs":{},"m":{"df":1,"docs":{"16":{"tf":1.0}}}}}}}}}}},"df":0,"docs":{}},"df":0,"docs":{}}}},"df":0,"docs":{}},"df":0,"docs":{}}},"df":0,"docs":{}},"df":0,"docs":{}},"u":{"c":{"c":{"df":2,"docs":{"42":{"tf":2.6457513110645907},"44":{"tf":1.0}}},"df":0,"docs":{}},"df":0,"docs":{},"f":{"df":0,"docs":{},"f":{"df":0,"docs":{},"i":{"c":{"df":1,"docs":{"72":{"tf":3.0}}},"df":0,"docs":{}}}}}},"t":{"a":{"c":{"df":0,"docs":{},"t":{"df":0,"docs":{},"i":{"c":{"df":1,"docs":{"2":{"tf":1.0}}},"df":0,"docs":{}}}},"df":0,"docs":{},"u":{"df":0,"docs":{},"t":{"df":0,"docs":{},"o":{"df":1,"docs":{"73":{"tf":2.8284271247461903}},"l":{"df":0,"docs":{},"o":{"df":0,"docs":{},"g":{"df":1,"docs":{"73":{"tf":1.0}}}}}}}}},"df":2,"docs":{"10":{"tf":1.7320508075688772},"35":{"tf":2.449489742783178}},"h":{"df":0,"docs":{},"e":{"df":0,"docs":{},"o":{"df":0,"docs":{},"r":{"df":0,"docs":{},"e":{"df":0,"docs":{},"m":{"df":4,"docs":{"10":{"tf":1.0},"17":{"tf":1.0},"28":{"tf":1.0},"70":{"tf":1.0}}}},"i":{"df":1,"docs":{"2":{"tf":1.0}}}}}}},"r":{"df":0,"docs":{},"i":{"df":7,"docs":{"16":{"tf":1.0},"29":{"tf":1.0},"33":{"tf":1.4142135623730951},"49":{"tf":1.0},"51":{"tf":1.0},"63":{"tf":1.7320508075688772},"73":{"tf":1.4142135623730951}},"v":{"df":0,"docs":{},"i":{"a":{"df":0,"docs":{},"l":{"df":1,"docs":{"74":{"tf":2.8284271247461903}}}},"df":0,"docs":{}}}},"u":{"df":0,"docs":{},"e":{"df":3,"docs":{"1":{"tf":1.0},"3":{"tf":1.0},"64":{"tf":1.4142135623730951}}}}},"y":{"df":0,"docs":{},"p":{"df":0,"docs":{},"e":{"df":6,"docs":{"2":{"tf":1.0},"3":{"tf":1.0},"35":{"tf":1.0},"58":{"tf":1.0},"59":{"tf":1.0},"66":{"tf":1.7320508075688772}}}}}},"u":{"df":2,"docs":{"58":{"tf":1.0},"66":{"tf":1.7320508075688772}},"n":{"df":0,"docs":{},"f":{"df":0,"docs":{},"o":{"df":0,"docs":{},"l":{"d":{"df":1,"docs":{"71":{"tf":1.0}}},"df":0,"docs":{}}}},"i":{"df":0,"docs":{},"v":{"df":0,"docs":{},"e":{"df":0,"docs":{},"r":{"df":0,"docs":{},"s":{"df":1,"docs":{"66":{"tf":1.0}}}}}}}},"s":{"df":2,"docs":{"22":{"tf":1.4142135623730951},"45":{"tf":1.0}}}},"v":{"a":{"df":0,"docs":{},"r":{"df":0,"docs":{},"i":{"a":{"b":{"df":0,"docs":{},"l":{"df":10,"docs":{"21":{"tf":1.0},"23":{"tf":1.0},"3":{"tf":1.0},"33":{"tf":1.0},"35":{"tf":1.4142135623730951},"4":{"tf":1.0},"45":{"tf":1.0},"59":{"tf":1.0},"62":{"tf":1.0},"66":{"tf":1.0}}}},"df":0,"docs":{}},"df":0,"docs":{}}}},"df":1,"docs":{"66":{"tf":1.7320508075688772}}},"w":{"a":{"df":0,"docs":{},"r":{"df":0,"docs":{},"n":{"df":1,"docs":{"1":{"tf":1.0}},"i":{"df":0,"docs":{},"n":{"df":0,"docs":{},"g":{"a":{"df":0,"docs":{},"s":{"df":0,"docs":{},"e":{"df":0,"docs":{},"r":{"df":0,"docs":{},"r":{"df":0,"docs":{},"o":{"df":0,"docs":{},"r":{"df":1,"docs":{"1":{"tf":1.0}}}}}}}}},"df":0,"docs":{}}}}}}},"df":0,"docs":{},"i":{"df":0,"docs":{},"t":{"df":0,"docs":{},"h":{"df":0,"docs":{},"o":{"df":0,"docs":{},"u":{"df":0,"docs":{},"t":{"df":1,"docs":{"75":{"tf":1.0}}}}}}}},"l":{"df":0,"docs":{},"o":{"df":0,"docs":{},"g":{"df":1,"docs":{"75":{"tf":2.23606797749979}}}}}},"x":{")":{".":{"df":0,"docs":{},"p":{"df":0,"docs":{},"r":{"df":0,"docs":{},"o":{"df":0,"docs":{},"p":{"df":0,"docs":{},"e":{"df":0,"docs":{},"r":{"df":0,"docs":{},"t":{"df":0,"docs":{},"i":{"df":1,"docs":{"23":{"tf":1.0}}}}}}}}}},"v":{"a":{"df":0,"docs":{},"l":{"df":1,"docs":{"23":{"tf":1.0}}}},"df":0,"docs":{}}},"df":0,"docs":{}},"`":{"df":0,"docs":{},"が":{"df":0,"docs":{},"偶":{"df":0,"docs":{},"数":{"df":0,"docs":{},"の":{"df":0,"docs":{},"と":{"df":0,"docs":{},"き":{"`":{"3":{"df":1,"docs":{"41":{"tf":1.0}}},"df":0,"docs":{}},"df":0,"docs":{}}}}}}}},"df":23,"docs":{"10":{"tf":1.7320508075688772},"22":{"tf":3.1622776601683795},"23":{"tf":4.358898943540674},"24":{"tf":3.4641016151377544},"26":{"tf":2.6457513110645907},"27":{"tf":1.7320508075688772},"3":{"tf":2.23606797749979},"33":{"tf":1.7320508075688772},"34":{"tf":3.3166247903554},"35":{"tf":2.6457513110645907},"36":{"tf":3.872983346207417},"41":{"tf":3.4641016151377544},"46":{"tf":2.449489742783178},"49":{"tf":2.8284271247461903},"50":{"tf":1.4142135623730951},"52":{"tf":3.1622776601683795},"56":{"tf":2.23606797749979},"59":{"tf":1.7320508075688772},"60":{"tf":2.449489742783178},"63":{"tf":2.8284271247461903},"64":{"tf":1.4142135623730951},"70":{"tf":1.7320508075688772},"71":{"tf":5.196152422706632}}},"y":{"df":13,"docs":{"10":{"tf":1.7320508075688772},"22":{"tf":4.0},"23":{"tf":3.3166247903554},"3":{"tf":2.449489742783178},"41":{"tf":2.449489742783178},"46":{"tf":3.3166247903554},"49":{"tf":1.4142135623730951},"50":{"tf":1.4142135623730951},"52":{"tf":2.0},"60":{"tf":2.449489742783178},"63":{"tf":2.6457513110645907},"64":{"tf":2.0},"70":{"tf":1.7320508075688772}}},"z":{"df":5,"docs":{"3":{"tf":2.0},"41":{"tf":1.4142135623730951},"49":{"tf":1.4142135623730951},"63":{"tf":1.0},"70":{"tf":1.7320508075688772}},"e":{"df":0,"docs":{},"r":{"df":0,"docs":{},"o":{"df":2,"docs":{"42":{"tf":1.7320508075688772},"44":{"tf":1.0}}}}}}}},"title":{"root":{"a":{"df":0,"docs":{},"e":{"df":0,"docs":{},"s":{"df":0,"docs":{},"o":{"df":0,"docs":{},"p":{"df":1,"docs":{"3":{"tf":1.0}}}}}},"p":{"df":0,"docs":{},"p":{"df":0,"docs":{},"l":{"df":0,"docs":{},"i":{"df":3,"docs":{"10":{"tf":1.0},"5":{"tf":1.0},"54":{"tf":1.0}}},"y":{"_":{"a":{"df":0,"docs":{},"s":{"df":0,"docs":{},"s":{"df":0,"docs":{},"u":{"df":0,"docs":{},"m":{"df":0,"docs":{},"p":{"df":0,"docs":{},"t":{"df":2,"docs":{"4":{"tf":1.0},"9":{"tf":1.0}}}}}}}}},"df":0,"docs":{}},"df":0,"docs":{}}}}},"s":{"df":0,"docs":{},"s":{"df":0,"docs":{},"u":{"df":0,"docs":{},"m":{"df":0,"docs":{},"p":{"df":0,"docs":{},"t":{"df":2,"docs":{"11":{"tf":1.0},"32":{"tf":1.0}}}}}}}}},"b":{"df":0,"docs":{},"y":{"_":{"c":{"a":{"df":0,"docs":{},"s":{"df":1,"docs":{"13":{"tf":1.0}}}},"df":0,"docs":{},"o":{"df":0,"docs":{},"n":{"df":0,"docs":{},"t":{"df":0,"docs":{},"r":{"a":{"df":1,"docs":{"14":{"tf":1.0}}},"df":0,"docs":{}}}}}},"df":0,"docs":{}},"df":0,"docs":{}}},"c":{"a":{"df":0,"docs":{},"l":{"c":{"df":1,"docs":{"17":{"tf":1.0}}},"df":0,"docs":{}},"s":{"df":0,"docs":{},"e":{"df":3,"docs":{"18":{"tf":1.0},"19":{"tf":1.0},"20":{"tf":1.0}}}}},"df":0,"docs":{},"h":{"df":0,"docs":{},"o":{"df":0,"docs":{},"o":{"df":0,"docs":{},"s":{"df":1,"docs":{"22":{"tf":1.0}}}}}},"o":{"df":0,"docs":{},"n":{"df":0,"docs":{},"g":{"df":0,"docs":{},"r":{"df":1,"docs":{"24":{"tf":1.0}}}},"s":{"df":0,"docs":{},"t":{"df":0,"docs":{},"r":{"df":0,"docs":{},"u":{"c":{"df":0,"docs":{},"t":{"df":0,"docs":{},"o":{"df":0,"docs":{},"r":{"df":2,"docs":{"25":{"tf":1.0},"55":{"tf":1.0}}}}}},"df":0,"docs":{}}}}},"t":{"df":0,"docs":{},"r":{"a":{"d":{"df":0,"docs":{},"i":{"c":{"df":0,"docs":{},"t":{"df":1,"docs":{"27":{"tf":1.0}}}},"df":0,"docs":{}}},"df":0,"docs":{}},"df":0,"docs":{}}},"v":{"df":1,"docs":{"28":{"tf":1.0}},"e":{"df":0,"docs":{},"r":{"df":0,"docs":{},"t":{"df":1,"docs":{"29":{"tf":1.0}}}}}}}}},"d":{"df":0,"docs":{},"o":{"df":0,"docs":{},"n":{"df":0,"docs":{},"e":{"df":1,"docs":{"30":{"tf":1.0}}}}},"s":{"df":0,"docs":{},"i":{"df":0,"docs":{},"m":{"df":0,"docs":{},"p":{"df":1,"docs":{"69":{"tf":1.0}}}}}}},"df":0,"docs":{},"e":{"df":0,"docs":{},"x":{"a":{"c":{"df":0,"docs":{},"t":{"df":4,"docs":{"12":{"tf":1.0},"31":{"tf":1.0},"33":{"tf":1.0},"8":{"tf":1.0}}}},"df":0,"docs":{}},"df":0,"docs":{},"i":{"df":0,"docs":{},"s":{"df":0,"docs":{},"t":{"df":1,"docs":{"34":{"tf":1.0}}}}},"t":{"df":1,"docs":{"35":{"tf":1.0}}}}},"f":{"df":0,"docs":{},"u":{"df":0,"docs":{},"n":{"df":0,"docs":{},"e":{"df":0,"docs":{},"x":{"df":0,"docs":{},"t":{"df":1,"docs":{"36":{"tf":1.0}}}}}}}},"g":{"df":0,"docs":{},"u":{"a":{"df":0,"docs":{},"r":{"d":{"_":{"df":0,"docs":{},"h":{"df":0,"docs":{},"y":{"df":0,"docs":{},"p":{"df":1,"docs":{"37":{"tf":1.0}}}}}},"df":0,"docs":{}},"df":0,"docs":{}}},"df":0,"docs":{}}},"i":{"df":0,"docs":{},"n":{"d":{"df":0,"docs":{},"u":{"c":{"df":0,"docs":{},"t":{"df":2,"docs":{"42":{"tf":1.0},"43":{"tf":1.0}}}},"df":0,"docs":{}}},"df":0,"docs":{},"t":{"df":0,"docs":{},"r":{"df":0,"docs":{},"o":{"df":1,"docs":{"46":{"tf":1.0}}}}}}},"l":{"df":0,"docs":{},"e":{"a":{"df":0,"docs":{},"n":{"4":{"df":1,"docs":{"0":{"tf":1.0}}},"df":0,"docs":{}}},"df":0,"docs":{},"f":{"df":0,"docs":{},"t":{"df":1,"docs":{"48":{"tf":1.0}}}}},"i":{"df":0,"docs":{},"n":{"a":{"df":0,"docs":{},"r":{"df":0,"docs":{},"i":{"df":0,"docs":{},"t":{"df":0,"docs":{},"h":{"df":1,"docs":{"49":{"tf":1.0}}}}}}},"df":0,"docs":{}}}},"n":{"df":0,"docs":{},"l":{"df":0,"docs":{},"i":{"df":0,"docs":{},"n":{"a":{"df":0,"docs":{},"r":{"df":0,"docs":{},"i":{"df":0,"docs":{},"t":{"df":0,"docs":{},"h":{"df":1,"docs":{"51":{"tf":1.0}}}}}}},"df":0,"docs":{}}}},"t":{"df":0,"docs":{},"h":{"_":{"df":0,"docs":{},"r":{"df":0,"docs":{},"w":{"df":1,"docs":{"62":{"tf":1.0}}}}},"df":0,"docs":{}}}},"p":{"df":0,"docs":{},"u":{"df":0,"docs":{},"s":{"df":0,"docs":{},"h":{"_":{"df":0,"docs":{},"n":{"df":0,"docs":{},"e":{"df":0,"docs":{},"g":{"df":1,"docs":{"52":{"tf":1.0}}}}}},"df":0,"docs":{}}}}},"r":{"c":{"a":{"df":0,"docs":{},"s":{"df":0,"docs":{},"e":{"df":1,"docs":{"21":{"tf":1.0}}}}},"df":0,"docs":{}},"df":0,"docs":{},"e":{"df":0,"docs":{},"f":{"df":0,"docs":{},"i":{"df":0,"docs":{},"n":{"df":1,"docs":{"53":{"tf":1.0}}}}},"l":{"df":1,"docs":{"56":{"tf":1.0}}},"p":{"df":0,"docs":{},"l":{"a":{"c":{"df":1,"docs":{"57":{"tf":1.0}}},"df":0,"docs":{}},"df":0,"docs":{}}}},"f":{"df":0,"docs":{},"l":{"df":1,"docs":{"58":{"tf":1.0}}}},"i":{"df":0,"docs":{},"g":{"df":0,"docs":{},"h":{"df":0,"docs":{},"t":{"df":1,"docs":{"48":{"tf":1.0}}}}},"n":{"df":0,"docs":{},"g":{"df":1,"docs":{"60":{"tf":1.0}}}}},"w":{"df":1,"docs":{"61":{"tf":1.0}}}},"s":{"df":0,"docs":{},"h":{"df":0,"docs":{},"o":{"df":0,"docs":{},"w":{"df":1,"docs":{"65":{"tf":1.0}}}}},"i":{"df":0,"docs":{},"m":{"df":0,"docs":{},"p":{"_":{"a":{"df":0,"docs":{},"l":{"df":1,"docs":{"68":{"tf":1.0}}}},"df":0,"docs":{}},"df":2,"docs":{"66":{"tf":1.0},"67":{"tf":1.0}}}}},"o":{"df":0,"docs":{},"r":{"df":0,"docs":{},"r":{"df":0,"docs":{},"i":{"df":1,"docs":{"70":{"tf":1.0}}}}}},"p":{"df":0,"docs":{},"l":{"df":0,"docs":{},"i":{"df":0,"docs":{},"t":{"df":1,"docs":{"71":{"tf":1.0}}}}}},"u":{"df":0,"docs":{},"f":{"df":0,"docs":{},"f":{"df":0,"docs":{},"i":{"c":{"df":1,"docs":{"72":{"tf":1.0}}},"df":0,"docs":{}}}}}},"t":{"a":{"df":0,"docs":{},"u":{"df":0,"docs":{},"t":{"df":0,"docs":{},"o":{"df":1,"docs":{"73":{"tf":1.0}}}}}},"df":0,"docs":{},"r":{"df":0,"docs":{},"i":{"df":0,"docs":{},"v":{"df":0,"docs":{},"i":{"a":{"df":0,"docs":{},"l":{"df":1,"docs":{"74":{"tf":1.0}}}},"df":0,"docs":{}}}}}},"w":{"df":0,"docs":{},"l":{"df":0,"docs":{},"o":{"df":0,"docs":{},"g":{"df":1,"docs":{"75":{"tf":1.0}}}}}}}}},"lang":"English","pipeline":["trimmer","stopWordFilter","stemmer"],"ref":"id","version":"0.9.5"},"results_options":{"limit_results":30,"teaser_word_count":30},"search_options":{"bool":"OR","expand":true,"fields":{"body":{"boost":1},"breadcrumbs":{"boost":1},"title":{"boost":2}}}}
\ No newline at end of file
diff --git a/show.html b/show.html
index 125c28c1..2157e1bd 100644
--- a/show.html
+++ b/show.html
@@ -88,7 +88,7 @@
 
         
diff --git a/simp.html b/simp.html
index ea9780af..e4797aee 100644
--- a/simp.html
+++ b/simp.html
@@ -88,7 +88,7 @@
 
         
diff --git a/sorry.html b/sorry.html
index e4fb9450..8ade27df 100644
--- a/sorry.html
+++ b/sorry.html
@@ -88,7 +88,7 @@
 
         
diff --git a/split.html b/split.html
index 21965a99..b8827645 100644
--- a/split.html
+++ b/split.html
@@ -88,7 +88,7 @@
 
         
diff --git a/suffices.html b/suffices.html
index 07875257..9a34ecbb 100644
--- a/suffices.html
+++ b/suffices.html
@@ -88,7 +88,7 @@
 
         
diff --git a/tauto.html b/tauto.html
index 40cce45e..36df1eae 100644
--- a/tauto.html
+++ b/tauto.html
@@ -88,7 +88,7 @@
 
         
diff --git a/trivial.html b/trivial.html
index 46c956f7..95cad570 100644
--- a/trivial.html
+++ b/trivial.html
@@ -88,7 +88,7 @@
 
         
diff --git a/wlog.html b/wlog.html
index 92383765..e2c68e51 100644
--- a/wlog.html
+++ b/wlog.html
@@ -88,7 +88,7 @@