moved formal_topology into library"

[helm.git] / helm / software / matita / contribs / formal_topology / overlap / apply_functor.ma

diff --git a/helm/software/matita/contribs/formal_topology/overlap/apply_functor.ma b/helm/software/matita/contribs/formal_topology/overlap/apply_functor.ma
deleted file mode 100644 (file)
index 81cf6d8..0000000
--- a/helm/software/matita/contribs/formal_topology/overlap/apply_functor.ma
+++ /dev/null
@@ -1,122 +0,0 @@
-(**************************************************************************)
-(*       ___                                                              *)
-(*      ||M||                                                             *)
-(*      ||A||       A project by Andrea Asperti                           *)
-(*      ||T||                                                             *)
-(*      ||I||       Developers:                                           *)
-(*      ||T||         The HELM team.                                      *)
-(*      ||A||         http://helm.cs.unibo.it                             *)
-(*      \   /                                                             *)
-(*       \ /        This file is distributed under the terms of the       *)
-(*        v         GNU General Public License Version 2                  *)
-(*                                                                        *)
-(**************************************************************************)
-
-include "categories.ma".
-include "notation.ma".
-
-record Fo (C1,C2:CAT2) (F:arrows3 CAT2 C1 C2) : Type2 ≝ {
-  F2: C2;
-  F1: C1;
-  FP: map_objs2 ?? F F1 =_\ID F2
-}.
-
-notation "ℱ\sub 1 x" non associative with precedence 60 for @{'F1 $x}.
-notation > "ℱ_1" non associative with precedence 90 for @{F1 ???}.
-interpretation "F1" 'F1 x = (F1 ??? x). 
-
-notation "ℱ\sub 2 x" non associative with precedence 60 for @{'F2 $x}.
-notation > "ℱ_2" non associative with precedence 90 for @{F2 ???}.
-interpretation "F2" 'F2 x = (F2 ??? x). 
-
-lemma REW : ∀C1,C2: CAT2.∀F:arrows3 CAT2 C1 C2.∀X,Y:Fo ?? F.
-  arrows2 C2 (F (ℱ_1 X)) (F (ℱ_1 Y)) → 
-  arrows2 C2 (ℱ_2 X) (ℱ_2 Y).           
-intros 5; cases X; cases Y; clear X Y; 
-cases H; cases H1; intros; assumption;
-qed.           
-
-record Fm_c (C1,C2:CAT2) (F:arrows3 CAT2 C1 C2) (X,Y:Fo ?? F) : Type2 ≝ {
-  Fm2: arrows2 C2 (F2 ??? X) (F2 ??? Y);
-  Fm1: arrows2 C1 (F1 ??? X) (F1 ??? Y);
-  FmP: REW ?? F X Y (map_arrows2 ?? F ?? Fm1) = Fm2
-}.
-
-notation "ℳ\sub 1 x" non associative with precedence 60 for @{'Fm1 $x}.
-notation > "ℳ_1" non associative with precedence 90 for @{Fm1 ?????}.
-interpretation "Fm1" 'Fm1 x = (Fm1 ????? x). 
-
-notation "ℳ\sub 2 x" non associative with precedence 60 for @{'Fm2 $x}.
-notation > "ℳ_2" non associative with precedence 90 for @{Fm2 ?????}.
-interpretation "Fm2" 'Fm2 x = (Fm2 ????? x). 
-
-definition Fm : 
- ∀C1,C2: CAT2.∀F:arrows3 CAT2 C1 C2.
-   Fo ?? F → Fo ?? F → setoid2. 
-intros (C1 C2 F X Y); constructor 1; [apply (Fm_c C1 C2 F X Y)]
-constructor 1; [apply (λf,g.Fm2 ????? f =_2 Fm2 ????? g);]
-[ intro; apply refl2;
-| intros 3; apply sym2; assumption;
-| intros 5; apply (trans2 ?? ??? x1 x2);]
-qed.
-
-definition F_id : 
- ∀C1,C2: CAT2.∀F:arrows3 CAT2 C1 C2.∀o.Fm ?? F o o.
-intros; constructor 1; 
-   [ apply (id2 C2 (F2 ??? o));
-   | apply (id2 C1 (F1 ??? o));
-   | cases o; cases H; simplify; apply (respects_id2 ?? F);]
-qed.
-
-definition F_comp : 
-  ∀C1,C2: CAT2.∀F:arrows3 CAT2 C1 C2.∀o1,o2,o3.
-    (Fm ?? F o1 o2) × (Fm ?? F o2 o3) ⇒_2 (Fm ?? F o1 o3).
-intros; constructor 1;
-[ intros (f g); constructor 1;
-    [ apply (comp2 C2 ??? (ℳ_2 f) (ℳ_2 g));
-    | apply (comp2 C1 ??? (ℳ_1 f) (ℳ_1 g));
-    | apply hide; cases o1 in f; cases o2 in g; cases o3; clear o1 o2 o3;
-      cases H; cases H1; cases H2; intros 2; cases c; cases c1; clear c c1;
-      simplify; apply (.= (respects_comp2:?)); apply (e1‡e);]
-| intros 6; change with ((ℳ_2 b ∘ ℳ_2 a) = (ℳ_2 b' ∘ ℳ_2 a'));
-  change in e1 with (ℳ_2 b = ℳ_2 b');
-  change in e with (ℳ_2 a = ℳ_2 a');
-  apply (e‡e1);]
-qed.
-
-
-definition Apply : ∀C1,C2: CAT2.arrows3 CAT2 C1 C2 → CAT2.
-intros (C1 C2 F);
-constructor 1; 
-[ apply (Fo ?? F);
-| apply (Fm ?? F); 
-| apply F_id; 
-| apply F_comp;
-| intros; apply (comp_assoc2 C2 ???? (ℳ_2 a12) (ℳ_2 a23) (ℳ_2 a34));
-| intros; apply (id_neutral_right2 C2 ?? (ℳ_2 a));
-| intros; apply (id_neutral_left2 C2 ?? (ℳ_2 a));]
-qed.
-
-definition faithful ≝  
-   λC1,C2.λF:arrows3 CAT2 C1 C2.∀S,T.∀f,g:arrows2 C1 S T.
-     map_arrows2 ?? F ?? f = map_arrows2 ?? F ?? g → f=g.
-
-definition Ylppa : ∀C1,C2: CAT2.∀F:arrows3 CAT2 C1 C2.
-  faithful ?? F →  let rC2 ≝ Apply ?? F in arrows3 CAT2 rC2 C1.
-intros; constructor 1;
-[ intro; apply (ℱ_1 o);
-| intros; constructor 1; 
-  [ intros; apply (ℳ_1 c);
-  | apply hide; intros; apply f;  change in e with (ℳ_2 a = ℳ_2 a');
-    lapply (FmP ????? a) as H1; lapply (FmP ????? a') as H2;
-    cut (REW ????? (map_arrows2 ?? F ?? (ℳ_1 a)) = 
-         REW ????? (map_arrows2 ?? F ?? (ℳ_1 a')));[2:
-      apply (.= H1); apply (.= e); apply (H2^-1);]
-    clear H1 H2 e; cases S in a a' Hcut; cases T;
-    cases H; cases H1; simplify; intros; assumption;]
-| intro; apply rule #;
-| intros; simplify; apply rule #;]
-qed.
-
-
-