Some important proofs/definitions were (and are still) commented out and

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

diff --git a/helm/software/matita/contribs/formal_topology/overlap/relations.ma b/helm/software/matita/contribs/formal_topology/overlap/relations.ma
index f7827939d2a5f7d950c276d40ec9b2031f636d0a..b1589a827fbc50717a08be48ec3fc2f2adf3eae2 100644 (file)
--- a/helm/software/matita/contribs/formal_topology/overlap/relations.ma
+++ b/helm/software/matita/contribs/formal_topology/overlap/relations.ma
@@ -240,25 +240,25 @@ definition minus_image: ∀U,V:REL. (U ⇒_\r1 V) × Ω^V ⇒_1 Ω^U.
        apply (if ?? (e ^ -1 ??)); assumption]]
 qed.
 
-(*
 (* minus_image is the same as ext *)
 
 theorem image_id: ∀o,U. image o o (id1 REL o) U = U.
  intros; unfold image; simplify; split; simplify; intros;
   [ change with (a ∈ U);
-    cases H; cases x; change in f with (eq1 ? w a); apply (. f‡#); assumption
+    cases e; cases x; change in f with (eq1 ? w a); apply (. f^-1‡#); assumption
   | change in f with (a ∈ U);
-    exists; [apply a] split; [ change with (a = a); apply refl | assumption]]
+    exists; [apply a] split; [ change with (a = a); apply refl1 | assumption]]
 qed.
 
 theorem minus_star_image_id: ∀o,U. minus_star_image o o (id1 REL o) U = U.
  intros; unfold minus_star_image; simplify; split; simplify; intros;
-  [ change with (a ∈ U); apply H; change with (a=a); apply refl
-  | change in f1 with (eq1 ? x a); apply (. f1 \sup -1‡#); apply f]
+  [ change with (a ∈ U); apply f; change with (a=a); apply refl1
+  | change in f1 with (eq1 ? x a); apply (. f1‡#); apply f]
 qed.
 
+alias symbol "compose" (instance 2) = "category1 composition".
 theorem image_comp: ∀A,B,C,r,s,X. image A C (r ∘ s) X = image B C r (image A B s X).
- intros; unfold image; simplify; split; simplify; intros; cases H; clear H; cases x;
+ intros; unfold image; simplify; split; simplify; intros; cases e; clear e; cases x;
  clear x; [ cases f; clear f; | cases f1; clear f1 ]
  exists; try assumption; cases x; clear x; split; try assumption;
  exists; try assumption; split; assumption.
@@ -268,10 +268,11 @@ theorem minus_star_image_comp:
  ∀A,B,C,r,s,X.
   minus_star_image A C (r ∘ s) X = minus_star_image B C r (minus_star_image A B s X).
  intros; unfold minus_star_image; simplify; split; simplify; intros; whd; intros;
-  [ apply H; exists; try assumption; split; assumption
-  | change with (x ∈ X); cases f; cases x1; apply H; assumption]
+  [ apply f; exists; try assumption; split; assumption
+  | change with (x ∈ X); cases f1; cases x1; apply f; assumption]
 qed.
 
+(*
 (*CSC: unused! *)
 theorem ext_comp:
  ∀o1,o2,o3: REL.