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Add lemmas about imfset #112

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29f6477
Add lemmas about imfset
ana-borges May 29, 2024
d7053e8
Update changelog
ana-borges May 29, 2024
41c7fa5
nitpick
affeldt-aist Dec 2, 2024
a5ad32a
+ nix CI Coq 8.20
CohenCyril Dec 20, 2024
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276 changes: 276 additions & 0 deletions .github/workflows/nix-action-8.20.yml
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Original file line number Diff line number Diff line change
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jobs:
coq:
needs: []
runs-on: ubuntu-latest
steps:
- name: Determine which commit to initially checkout
run: "if [ ${{ github.event_name }} = \"push\" ]; then\n echo \"target_commit=${{
github.sha }}\" >> $GITHUB_ENV\nelse\n echo \"target_commit=${{ github.event.pull_request.head.sha
}}\" >> $GITHUB_ENV\nfi\n"
- name: Git checkout
uses: actions/checkout@v4
with:
fetch-depth: 0
ref: ${{ env.target_commit }}
- name: Determine which commit to test
run: "if [ ${{ github.event_name }} = \"push\" ]; then\n echo \"tested_commit=${{
github.sha }}\" >> $GITHUB_ENV\nelse\n merge_commit=$(git ls-remote ${{ github.event.repository.html_url
}} refs/pull/${{ github.event.number }}/merge | cut -f1)\n mergeable=$(git
merge --no-commit --no-ff ${{ github.event.pull_request.base.sha }} > /dev/null
2>&1; echo $?; git merge --abort > /dev/null 2>&1 || true)\n if [ -z \"$merge_commit\"\
\ -o \"x$mergeable\" != \"x0\" ]; then\n echo \"tested_commit=${{ github.event.pull_request.head.sha
}}\" >> $GITHUB_ENV\n else\n echo \"tested_commit=$merge_commit\" >> $GITHUB_ENV\n\
\ fi\nfi\n"
- name: Git checkout
uses: actions/checkout@v4
with:
fetch-depth: 0
ref: ${{ env.tested_commit }}
- name: Cachix install
uses: cachix/install-nix-action@v30
with:
nix_path: nixpkgs=channel:nixpkgs-unstable
- name: Cachix setup math-comp
uses: cachix/cachix-action@v15
with:
authToken: ${{ secrets.CACHIX_AUTH_TOKEN }}
extraPullNames: coq, coq-community
name: math-comp
- id: stepCheck
name: Checking presence of CI target coq
run: "nb_dry_run=$(NIXPKGS_ALLOW_UNFREE=1 nix-build --no-out-link \\\n --argstr
bundle \"8.20\" --argstr job \"coq\" \\\n --dry-run 2>&1 > /dev/null)\n
echo $nb_dry_run\necho status=$(echo $nb_dry_run | grep \"built:\" | sed \"\
s/.*/built/\") >> $GITHUB_OUTPUT\n"
- if: steps.stepCheck.outputs.status == 'built'
name: Building/fetching current CI target
run: NIXPKGS_ALLOW_UNFREE=1 nix-build --no-out-link --argstr bundle "8.20" --argstr
job "coq"
mathcomp:
needs:
- coq
runs-on: ubuntu-latest
steps:
- name: Determine which commit to initially checkout
run: "if [ ${{ github.event_name }} = \"push\" ]; then\n echo \"target_commit=${{
github.sha }}\" >> $GITHUB_ENV\nelse\n echo \"target_commit=${{ github.event.pull_request.head.sha
}}\" >> $GITHUB_ENV\nfi\n"
- name: Git checkout
uses: actions/checkout@v4
with:
fetch-depth: 0
ref: ${{ env.target_commit }}
- name: Determine which commit to test
run: "if [ ${{ github.event_name }} = \"push\" ]; then\n echo \"tested_commit=${{
github.sha }}\" >> $GITHUB_ENV\nelse\n merge_commit=$(git ls-remote ${{ github.event.repository.html_url
}} refs/pull/${{ github.event.number }}/merge | cut -f1)\n mergeable=$(git
merge --no-commit --no-ff ${{ github.event.pull_request.base.sha }} > /dev/null
2>&1; echo $?; git merge --abort > /dev/null 2>&1 || true)\n if [ -z \"$merge_commit\"\
\ -o \"x$mergeable\" != \"x0\" ]; then\n echo \"tested_commit=${{ github.event.pull_request.head.sha
}}\" >> $GITHUB_ENV\n else\n echo \"tested_commit=$merge_commit\" >> $GITHUB_ENV\n\
\ fi\nfi\n"
- name: Git checkout
uses: actions/checkout@v4
with:
fetch-depth: 0
ref: ${{ env.tested_commit }}
- name: Cachix install
uses: cachix/install-nix-action@v30
with:
nix_path: nixpkgs=channel:nixpkgs-unstable
- name: Cachix setup math-comp
uses: cachix/cachix-action@v15
with:
authToken: ${{ secrets.CACHIX_AUTH_TOKEN }}
extraPullNames: coq, coq-community
name: math-comp
- id: stepCheck
name: Checking presence of CI target mathcomp
run: "nb_dry_run=$(NIXPKGS_ALLOW_UNFREE=1 nix-build --no-out-link \\\n --argstr
bundle \"8.20\" --argstr job \"mathcomp\" \\\n --dry-run 2>&1 > /dev/null)\n
echo $nb_dry_run\necho status=$(echo $nb_dry_run | grep \"built:\" | sed \"\
s/.*/built/\") >> $GITHUB_OUTPUT\n"
- if: steps.stepCheck.outputs.status == 'built'
name: 'Building/fetching previous CI target: coq'
run: NIXPKGS_ALLOW_UNFREE=1 nix-build --no-out-link --argstr bundle "8.20" --argstr
job "coq"
- if: steps.stepCheck.outputs.status == 'built'
name: 'Building/fetching previous CI target: stdlib'
run: NIXPKGS_ALLOW_UNFREE=1 nix-build --no-out-link --argstr bundle "8.20" --argstr
job "stdlib"
- if: steps.stepCheck.outputs.status == 'built'
name: 'Building/fetching previous CI target: mathcomp-ssreflect'
run: NIXPKGS_ALLOW_UNFREE=1 nix-build --no-out-link --argstr bundle "8.20" --argstr
job "mathcomp-ssreflect"
- if: steps.stepCheck.outputs.status == 'built'
name: 'Building/fetching previous CI target: mathcomp-fingroup'
run: NIXPKGS_ALLOW_UNFREE=1 nix-build --no-out-link --argstr bundle "8.20" --argstr
job "mathcomp-fingroup"
- if: steps.stepCheck.outputs.status == 'built'
name: 'Building/fetching previous CI target: mathcomp-algebra'
run: NIXPKGS_ALLOW_UNFREE=1 nix-build --no-out-link --argstr bundle "8.20" --argstr
job "mathcomp-algebra"
- if: steps.stepCheck.outputs.status == 'built'
name: 'Building/fetching previous CI target: mathcomp-solvable'
run: NIXPKGS_ALLOW_UNFREE=1 nix-build --no-out-link --argstr bundle "8.20" --argstr
job "mathcomp-solvable"
- if: steps.stepCheck.outputs.status == 'built'
name: 'Building/fetching previous CI target: mathcomp-field'
run: NIXPKGS_ALLOW_UNFREE=1 nix-build --no-out-link --argstr bundle "8.20" --argstr
job "mathcomp-field"
- if: steps.stepCheck.outputs.status == 'built'
name: 'Building/fetching previous CI target: mathcomp-character'
run: NIXPKGS_ALLOW_UNFREE=1 nix-build --no-out-link --argstr bundle "8.20" --argstr
job "mathcomp-character"
- if: steps.stepCheck.outputs.status == 'built'
name: 'Building/fetching previous CI target: hierarchy-builder'
run: NIXPKGS_ALLOW_UNFREE=1 nix-build --no-out-link --argstr bundle "8.20" --argstr
job "hierarchy-builder"
- if: steps.stepCheck.outputs.status == 'built'
name: Building/fetching current CI target
run: NIXPKGS_ALLOW_UNFREE=1 nix-build --no-out-link --argstr bundle "8.20" --argstr
job "mathcomp"
mathcomp-finmap:
needs:
- coq
runs-on: ubuntu-latest
steps:
- name: Determine which commit to initially checkout
run: "if [ ${{ github.event_name }} = \"push\" ]; then\n echo \"target_commit=${{
github.sha }}\" >> $GITHUB_ENV\nelse\n echo \"target_commit=${{ github.event.pull_request.head.sha
}}\" >> $GITHUB_ENV\nfi\n"
- name: Git checkout
uses: actions/checkout@v4
with:
fetch-depth: 0
ref: ${{ env.target_commit }}
- name: Determine which commit to test
run: "if [ ${{ github.event_name }} = \"push\" ]; then\n echo \"tested_commit=${{
github.sha }}\" >> $GITHUB_ENV\nelse\n merge_commit=$(git ls-remote ${{ github.event.repository.html_url
}} refs/pull/${{ github.event.number }}/merge | cut -f1)\n mergeable=$(git
merge --no-commit --no-ff ${{ github.event.pull_request.base.sha }} > /dev/null
2>&1; echo $?; git merge --abort > /dev/null 2>&1 || true)\n if [ -z \"$merge_commit\"\
\ -o \"x$mergeable\" != \"x0\" ]; then\n echo \"tested_commit=${{ github.event.pull_request.head.sha
}}\" >> $GITHUB_ENV\n else\n echo \"tested_commit=$merge_commit\" >> $GITHUB_ENV\n\
\ fi\nfi\n"
- name: Git checkout
uses: actions/checkout@v4
with:
fetch-depth: 0
ref: ${{ env.tested_commit }}
- name: Cachix install
uses: cachix/install-nix-action@v30
with:
nix_path: nixpkgs=channel:nixpkgs-unstable
- name: Cachix setup math-comp
uses: cachix/cachix-action@v15
with:
authToken: ${{ secrets.CACHIX_AUTH_TOKEN }}
extraPullNames: coq, coq-community
name: math-comp
- id: stepCheck
name: Checking presence of CI target mathcomp-finmap
run: "nb_dry_run=$(NIXPKGS_ALLOW_UNFREE=1 nix-build --no-out-link \\\n --argstr
bundle \"8.20\" --argstr job \"mathcomp-finmap\" \\\n --dry-run 2>&1 > /dev/null)\n
echo $nb_dry_run\necho status=$(echo $nb_dry_run | grep \"built:\" | sed \"\
s/.*/built/\") >> $GITHUB_OUTPUT\n"
- if: steps.stepCheck.outputs.status == 'built'
name: 'Building/fetching previous CI target: coq'
run: NIXPKGS_ALLOW_UNFREE=1 nix-build --no-out-link --argstr bundle "8.20" --argstr
job "coq"
- if: steps.stepCheck.outputs.status == 'built'
name: 'Building/fetching previous CI target: mathcomp-ssreflect'
run: NIXPKGS_ALLOW_UNFREE=1 nix-build --no-out-link --argstr bundle "8.20" --argstr
job "mathcomp-ssreflect"
- if: steps.stepCheck.outputs.status == 'built'
name: Building/fetching current CI target
run: NIXPKGS_ALLOW_UNFREE=1 nix-build --no-out-link --argstr bundle "8.20" --argstr
job "mathcomp-finmap"
multinomials:
needs:
- coq
- mathcomp-finmap
runs-on: ubuntu-latest
steps:
- name: Determine which commit to initially checkout
run: "if [ ${{ github.event_name }} = \"push\" ]; then\n echo \"target_commit=${{
github.sha }}\" >> $GITHUB_ENV\nelse\n echo \"target_commit=${{ github.event.pull_request.head.sha
}}\" >> $GITHUB_ENV\nfi\n"
- name: Git checkout
uses: actions/checkout@v4
with:
fetch-depth: 0
ref: ${{ env.target_commit }}
- name: Determine which commit to test
run: "if [ ${{ github.event_name }} = \"push\" ]; then\n echo \"tested_commit=${{
github.sha }}\" >> $GITHUB_ENV\nelse\n merge_commit=$(git ls-remote ${{ github.event.repository.html_url
}} refs/pull/${{ github.event.number }}/merge | cut -f1)\n mergeable=$(git
merge --no-commit --no-ff ${{ github.event.pull_request.base.sha }} > /dev/null
2>&1; echo $?; git merge --abort > /dev/null 2>&1 || true)\n if [ -z \"$merge_commit\"\
\ -o \"x$mergeable\" != \"x0\" ]; then\n echo \"tested_commit=${{ github.event.pull_request.head.sha
}}\" >> $GITHUB_ENV\n else\n echo \"tested_commit=$merge_commit\" >> $GITHUB_ENV\n\
\ fi\nfi\n"
- name: Git checkout
uses: actions/checkout@v4
with:
fetch-depth: 0
ref: ${{ env.tested_commit }}
- name: Cachix install
uses: cachix/install-nix-action@v30
with:
nix_path: nixpkgs=channel:nixpkgs-unstable
- name: Cachix setup math-comp
uses: cachix/cachix-action@v15
with:
authToken: ${{ secrets.CACHIX_AUTH_TOKEN }}
extraPullNames: coq, coq-community
name: math-comp
- id: stepCheck
name: Checking presence of CI target multinomials
run: "nb_dry_run=$(NIXPKGS_ALLOW_UNFREE=1 nix-build --no-out-link \\\n --argstr
bundle \"8.20\" --argstr job \"multinomials\" \\\n --dry-run 2>&1 > /dev/null)\n
echo $nb_dry_run\necho status=$(echo $nb_dry_run | grep \"built:\" | sed \"\
s/.*/built/\") >> $GITHUB_OUTPUT\n"
- if: steps.stepCheck.outputs.status == 'built'
name: 'Building/fetching previous CI target: coq'
run: NIXPKGS_ALLOW_UNFREE=1 nix-build --no-out-link --argstr bundle "8.20" --argstr
job "coq"
- if: steps.stepCheck.outputs.status == 'built'
name: 'Building/fetching previous CI target: mathcomp-ssreflect'
run: NIXPKGS_ALLOW_UNFREE=1 nix-build --no-out-link --argstr bundle "8.20" --argstr
job "mathcomp-ssreflect"
- if: steps.stepCheck.outputs.status == 'built'
name: 'Building/fetching previous CI target: mathcomp-algebra'
run: NIXPKGS_ALLOW_UNFREE=1 nix-build --no-out-link --argstr bundle "8.20" --argstr
job "mathcomp-algebra"
- if: steps.stepCheck.outputs.status == 'built'
name: 'Building/fetching previous CI target: mathcomp-finmap'
run: NIXPKGS_ALLOW_UNFREE=1 nix-build --no-out-link --argstr bundle "8.20" --argstr
job "mathcomp-finmap"
- if: steps.stepCheck.outputs.status == 'built'
name: 'Building/fetching previous CI target: mathcomp-fingroup'
run: NIXPKGS_ALLOW_UNFREE=1 nix-build --no-out-link --argstr bundle "8.20" --argstr
job "mathcomp-fingroup"
- if: steps.stepCheck.outputs.status == 'built'
name: 'Building/fetching previous CI target: mathcomp-bigenough'
run: NIXPKGS_ALLOW_UNFREE=1 nix-build --no-out-link --argstr bundle "8.20" --argstr
job "mathcomp-bigenough"
- if: steps.stepCheck.outputs.status == 'built'
name: Building/fetching current CI target
run: NIXPKGS_ALLOW_UNFREE=1 nix-build --no-out-link --argstr bundle "8.20" --argstr
job "multinomials"
name: Nix CI for bundle 8.20
on:
pull_request:
paths:
- .github/workflows/nix-action-8.20.yml
pull_request_target:
paths-ignore:
- .github/workflows/nix-action-8.20.yml
types:
- opened
- synchronize
- reopened
push:
branches:
- master
3 changes: 3 additions & 0 deletions .nix/config.nix
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Original file line number Diff line number Diff line change
Expand Up @@ -75,6 +75,9 @@
"8.19".coqPackages = common-bundles // {
coq.override.version = "8.19";
};
"8.20".coqPackages = common-bundles // {
coq.override.version = "8.20";
};
"master".coqPackages = {
coq.override.version = "master";
coq-elpi.override.version = "coq-master";
Expand Down
3 changes: 2 additions & 1 deletion CHANGELOG_UNRELEASED.md
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Original file line number Diff line number Diff line change
Expand Up @@ -5,7 +5,8 @@
### Added

- in `finmap.v`:
+ lemmas `bigfcup_imfset`, `fbig_pred1_inj`
+ lemmas `fset_seq1`, `imfset0`, `imfset_fset1`, `imfset_fset2`, `imfsetU`,
`imfsetU1`, `imfsetI`, `bigfcup_imfset`

### Changed

Expand Down
62 changes: 57 additions & 5 deletions finmap.v
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Original file line number Diff line number Diff line change
Expand Up @@ -5,7 +5,7 @@ From HB Require Import structures.
Set Warnings "-notation-incompatible-format".
From mathcomp Require Import ssreflect ssrbool ssrnat eqtype ssrfun seq.
Set Warnings "notation-incompatible-format".
From mathcomp Require Import choice path finset finfun fintype bigop.
From mathcomp Require Import choice finset finfun fintype bigop.

(*****************************************************************************)
(* This file provides representations for finite sets over a choiceType K, *)
Expand Down Expand Up @@ -1606,6 +1606,11 @@ Proof. by apply/fsetP=> x; rewrite in_fset_cons !inE. Qed.
Lemma fset_nil : [fset[key] x in [::] : seq K] = fset0.
Proof. by apply/fsetP=> x; rewrite in_fset_nil. Qed.

Lemma fset_seq1 a : [:: a] = [fset a].
Proof.
by rewrite (@perm_small_eq _ [fset a] [:: a])//; apply: uniq_perm=>// ? /[!inE].
Qed.

Lemma fset_cat s s' :
[fset[key] x in s ++ s'] = [fset[key] x in s] `|` [fset[key] x in s'].
Proof. by apply/fsetP=> x; rewrite !inE !in_fset_cat. Qed.
Expand Down Expand Up @@ -2131,7 +2136,7 @@ End Enum.

Section ImfsetTh.
Variables (key : unit) (K V V' : choiceType).
Implicit Types (f : K -> V) (g : V -> V') (A V : {fset K}).
Implicit Types (f : K -> V) (g : V -> V') (A B : {fset K}).

Lemma imfset_id (A : {fset K}) : id @` A = A.
Proof. by apply/fsetP=> a; rewrite in_fset. Qed.
Expand Down Expand Up @@ -2159,6 +2164,39 @@ move=> eq_f eqP; apply/fsetP => x; apply/imfsetP/imfsetP => /= [] [k Pk ->];
by exists k => //=; rewrite ?eq_f ?eqP in Pk *.
Qed.

Lemma imfsetU f A B : f @` (A `|` B) = f @` A `|` f @` B.
Proof.
apply/fsetP => v; apply/imfsetP/fsetUP.
by move=> [k /fsetUP [? ->|? ->]]; [left|right]; apply/imfsetP; exists k.
by move=> [|] /imfsetP /= [k kin ->]; exists k => //; rewrite inE kin ?orbT.
Qed.

Lemma imfset0 f : f @` fset0 = fset0.
Proof. by apply/fsetP => v; apply/imfsetP; rewrite inE => -[k /[!inE]]. Qed.

Lemma imfset_fset1 f x : f @` [fset x] = [fset f x].
Proof.
apply/fsetP => y.
by apply/imfsetP/fset1P => [[x' /fset1P -> //]|->]; exists x; rewrite ?fset11.
Qed.

Lemma imfset_fset2 f k1 k2 : f @` [fset k1; k2] = [fset f k1; f k2].
Proof. by rewrite imfsetU 2!imfset_fset1. Qed.

Lemma imfsetU1 f a A : f @` (a |` A) = f a |` (f @` A).
Proof. by rewrite imfsetU imfset_fset1. Qed.

Lemma imfsetI f A B :
{in A & B, injective f} -> f @` (A `&` B) = f @` A `&` f @` B.
Proof.
move=> injf; apply/fsetP => v.
apply/imfsetP/fsetIP => /=.
by move=> [k /fsetIP [kinA kinB] ->]; split; apply/imfsetP; exists k.
move=> [/imfsetP /= [ka kainA eqka] /imfsetP /= [kb kbinB eqkb]].
have eqk : ka = kb by apply: injf => //; rewrite -eqka -eqkb.
by exists ka => //; apply/fsetIP; split=> //; rewrite eqk.
Qed.

End ImfsetTh.

Section PowerSetTheory.
Expand Down Expand Up @@ -2477,15 +2515,29 @@ Qed.

End BigFOpsSeq.

Lemma bigfcup_imfset1 (I T : choiceType) (P : {fset I}) (f : I -> T) :
\bigcup_(i <- P) [fset f i] = f @` P.
Section BigFOps.

Variables (I T : choiceType).
Implicit Types (f : I -> T).

Lemma bigfcup_imfset1 (P : {fset I}) f : \bigcup_(i <- P) [fset f i] = f @` P.
Proof.
apply/eqP; rewrite eqEfsubset; apply/andP; split; apply/fsubsetP => x.
- by case/bigfcupP=> i /andP [] iP _; rewrite inE => /eqP ->; apply/imfsetP; exists i.
- by case/bigfcupP=> i /andP [] iP _ /[!inE] /eqP ->; apply/imfsetP; exists i.
- case/imfsetP => i /= iP ->; apply/bigfcupP; exists i; rewrite ?andbT //.
by apply/imfsetP; exists (f i); rewrite ?inE.
Qed.

Lemma bigfcup_imfset (V : choiceType) f (F : V -> {fset I}) (A : {fset V}):
\bigcup_(a <- A) f @` F a = f @` (\bigcup_(a <- A) F a).
Proof.
apply/fsetP => t; apply/bigfcupP/imfsetP.
by move=> [v ? /imfsetP [i ? ->]]; exists i => //; apply/bigfcupP; exists v.
by move=> [i /bigfcupP [v ? ?] ->]; exists v => //; apply/imfsetP; exists i.
Qed.

End BigFOps.

Section fbig_pred1_inj.
Variables (R : Type) (idx : R) (op : Monoid.com_law idx).

Expand Down
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