X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=helm%2Fsoftware%2Fmatita%2Fcontribs%2Fformal_topology%2Foverlap%2Fapply_functor.ma;h=789988194f6ade4c616334b96bf5157b77a71912;hb=3e5c359c75874748cfed8a9046031b62396e0e6d;hp=7b10b4b9fc98f05bd0736344545809630c9f89c4;hpb=427bbecb65191dc43037c8d62dbdebeccf7c1c29;p=helm.git

diff --git a/helm/software/matita/contribs/formal_topology/overlap/apply_functor.ma b/helm/software/matita/contribs/formal_topology/overlap/apply_functor.ma
index 7b10b4b9f..789988194 100644
--- a/helm/software/matita/contribs/formal_topology/overlap/apply_functor.ma
+++ b/helm/software/matita/contribs/formal_topology/overlap/apply_functor.ma
@@ -23,11 +23,11 @@ record Fo (C1,C2:CAT2) (F:arrows3 CAT2 C1 C2) : Type2 ≝ {
 
 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). 
+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). 
+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)) → 
@@ -44,11 +44,11 @@ record Fm_c (C1,C2:CAT2) (F:arrows3 CAT2 C1 C2) (X,Y:Fo ?? F) : Type2 ≝ {
 
 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). 
+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). 
+interpretation "Fm2" 'Fm2 x = (Fm2 ????? x). 
 
 definition Fm : 
  ∀C1,C2: CAT2.∀F:arrows3 CAT2 C1 C2.
@@ -96,3 +96,27 @@ constructor 1;
 | 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.
+
+
+