diff --git a/coq/QLearn/jaakkola_vector.v b/coq/QLearn/jaakkola_vector.v index a0d98acf..25b1ce74 100644 --- a/coq/QLearn/jaakkola_vector.v +++ b/coq/QLearn/jaakkola_vector.v @@ -6978,11 +6978,7 @@ Proof. (adapt_beta : IsAdapted (Rvector_borel_sa (S N)) β F) {rvX0 : RandomVariable (F 0%nat) (Rvector_borel_sa (S N)) (X 0%nat)} {isl2 : forall k i pf, IsLp prts 2 (vecrvnth i pf (XF k))} - {rvXF : forall k, RandomVariable (F (S k)) (Rvector_borel_sa (S N)) (XF k)} -(* should be able to remove following *) - {vec_rvXF_I : forall k, RandomVariable dom (Rvector_borel_sa (S N)) (XF k)} -(* {vec_isfe : forall k, vector_IsFiniteExpectation prts (XF k)} *) : - + {rvXF : forall k, RandomVariable (F (S k)) (Rvector_borel_sa (S N)) (XF k)} : 0 < γ < 1 -> almost prts (fun ω => forall k i pf, 0 <= vector_nth i pf (α k ω)) -> @@ -6994,10 +6990,10 @@ Proof. almost prts (fun ω => forall i pf, is_lim_seq (sum_n (fun k => vector_nth i pf (β k ω))) p_infty) -> (forall i pf, almost prts (fun ω => ex_series (fun n => Rsqr (vector_nth i pf (α n ω))))) -> (forall i pf, almost prts (fun ω => ex_series (fun n => Rsqr (vector_nth i pf (β n ω))))) -> - almost prts + almost prts (fun ω => (forall k, - (pos_scaled_Rvector_max_abs ((vector_FiniteConditionalExpectation _ (filt_sub k) (XF k) (* (rv := vec_rvXF_I filt_sub XF k) *)) ω) W) < + (pos_scaled_Rvector_max_abs ((vector_FiniteConditionalExpectation prts (filt_sub k) (XF k) (rv := vec_rvXF_I filt_sub XF k) (isfe := vec_isfe XF (vec_rvXF_I := vec_rvXF_I filt_sub XF) k)) ω) W) < (γ * (pos_scaled_Rvector_max_abs (X k ω) W)))) -> (forall i pf, is_lim_seq'_uniform_almost (fun n ω => sum_n (fun k => rvsqr (vecrvnth i pf (α k)) ω) n) @@ -7005,7 +7001,7 @@ Proof. (forall i pf, is_lim_seq'_uniform_almost (fun n ω => sum_n (fun k => rvsqr (vecrvnth i pf (β k)) ω) n) (fun ω => Lim_seq (sum_n (fun k => rvsqr (vecrvnth i pf (β k)) ω)))) -> - (exists (C : R), + (exists (C : R), (0 < C) /\ almost prts (fun ω => @@ -7019,7 +7015,8 @@ Proof. is_lim_seq (fun m => vector_nth i pf (X m ω)) 0). Proof. intros. - apply (Jaakkola_alpha_beta_unbounded_uniformly_W W γ X XF α β isfilt filt_sub) with (isl2 := isl2) (vec_rvXF_I := vec_rvXF_I) (vec_isfe := vec_isfe XF). + apply (Jaakkola_alpha_beta_unbounded_uniformly_W W γ X XF α β isfilt filt_sub) + with (isl2 := isl2) (vec_rvXF_I := vec_rvXF_I filt_sub XF) (vec_isfe := vec_isfe XF (vec_rvXF_I := vec_rvXF_I filt_sub XF)). - trivial. - trivial. - trivial.