From b6e187ff7580c3dbec8bf467915d0ccd0dfd65a8 Mon Sep 17 00:00:00 2001 From: Enrico Tassi Date: Wed, 21 Jan 2009 13:57:40 +0000 Subject: [PATCH] a bit of work done while travelling to padova --- .../overlap/basic_pairs_to_o-basic_pairs.ma | 41 ++++++++++++------- .../formal_topology/overlap/o-basic_pairs.ma | 4 +- 2 files changed, 29 insertions(+), 16 deletions(-) diff --git a/helm/software/matita/contribs/formal_topology/overlap/basic_pairs_to_o-basic_pairs.ma b/helm/software/matita/contribs/formal_topology/overlap/basic_pairs_to_o-basic_pairs.ma index 7dbd3a80a..2aec4f7e8 100644 --- a/helm/software/matita/contribs/formal_topology/overlap/basic_pairs_to_o-basic_pairs.ma +++ b/helm/software/matita/contribs/formal_topology/overlap/basic_pairs_to_o-basic_pairs.ma @@ -79,23 +79,34 @@ definition BP_to_OBP: carr3 (arrows3 CAT2 (category2_of_category1 BP) OBP). apply (respects_comp2 ?? SUBSETS' (concr o1) (concr o2) (concr o3) f1\sub\c f2\sub\c);] qed. - -(* theorem BP_to_OBP_faithful: ∀S,T.∀f,g:arrows2 (category2_of_category1 BP) S T. map_arrows2 ?? BP_to_OBP ?? f = map_arrows2 ?? BP_to_OBP ?? g → f=g. - intros; unfold BP_to_OBP in e; simplify in e; cases e; - unfold orelation_of_relation in e3; simplify in e3; clear e e1 e2 e4; - intros 2; change in match or_f_ in e3 with (λq,w,x.fun12 ?? (or_f q w) x); - simplify in e3; STOP lapply (e3 (singleton ? x)); cases Hletin; - split; intro; [ lapply (s y); | lapply (s1 y); ] - [2,4: exists; [1,3:apply x] split; [1,3: assumption |*: change with (x=x); apply rule #] - |*: cases Hletin1; cases x1; change in f3 with (eq1 ? x w); apply (. f3‡#); assumption;] + intros; change with ( (⊩) ∘ f \sub \c = (⊩) ∘ g \sub \c); + apply (SUBSETS_faithful); + apply (.= respects_comp2 ?? SUBSETS' (concr S) (concr T) (form T) f \sub \c (⊩ \sub T)); + apply sym2; + apply (.= respects_comp2 ?? SUBSETS' (concr S) (concr T) (form T) g \sub \c (⊩ \sub T)); + apply sym2; + apply e; qed. -*) -(* -theorem SUBSETS_full: ∀S,T.∀f. exT22 ? (λg. map_arrows2 ?? BP_to_OBP S T g = f). - intros; exists; - -*) \ No newline at end of file +theorem BP_to_OBP_full: ∀S,T.∀f. exT22 ? (λg. map_arrows2 ?? BP_to_OBP S T g = f). + intros; + cases (SUBSETS_full (concr S) (concr T) (Oconcr_rel ?? f)) (gc Hgc); + cases (SUBSETS_full (form S) (form T) (Oform_rel ?? f)) (gf Hgf); + exists[ + constructor 1; [apply gc|apply gf] + apply (SUBSETS_faithful); + apply (let xxxx ≝SUBSETS' in .= respects_comp2 ?? SUBSETS' (concr S) (concr T) (form T) gc (rel T)); + apply rule (.= Hgc‡#); + apply (.= Ocommute ?? f); + apply (.= #‡Hgf^-1); + apply (let xxxx ≝SUBSETS' in (respects_comp2 ?? SUBSETS' (concr S) (form S) (form T) (rel S) gf)^-1)] + split; + [ change in match or_f_minus_star_ with (λq,w,x.fun12 ?? (or_f_minus_star q w) x); + | change in match or_f_minus_ with (λq,w,x.fun12 ?? (or_f_minus q w) x); + | change in match or_f_ with (λq,w,x.fun12 ?? (or_f q w) x); + | change in match or_f_star_ with (λq,w,x.fun12 ?? (or_f_star q w) x);] + simplify; apply (†(Hgc‡#)); +qed. diff --git a/helm/software/matita/contribs/formal_topology/overlap/o-basic_pairs.ma b/helm/software/matita/contribs/formal_topology/overlap/o-basic_pairs.ma index 6476c4aeb..b6d6e1b3d 100644 --- a/helm/software/matita/contribs/formal_topology/overlap/o-basic_pairs.ma +++ b/helm/software/matita/contribs/formal_topology/overlap/o-basic_pairs.ma @@ -21,6 +21,7 @@ record Obasic_pair: Type2 ≝ Orel: arrows2 ? Oconcr Oform }. +(* FIX *) interpretation "basic pair relation indexed" 'Vdash2 x y c = (Orel c x y). interpretation "basic pair relation (non applied)" 'Vdash c = (Orel c). @@ -35,7 +36,8 @@ record Orelation_pair (BP1,BP2: Obasic_pair): Type2 ≝ Oform_rel: arrows2 ? (Oform BP1) (Oform BP2); Ocommute: ⊩ ∘ Oconcr_rel = Oform_rel ∘ ⊩ }. - + +(* FIX *) interpretation "concrete relation" 'concr_rel r = (Oconcr_rel __ r). interpretation "formal relation" 'form_rel r = (Oform_rel __ r). -- 2.39.2