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[helm.git] / helm / software / matita / library / formal_topology / relations.ma

diff --git a/helm/software/matita/library/formal_topology/relations.ma b/helm/software/matita/library/formal_topology/relations.ma
index 72e12aa9dc500009518aebf7fb7038f629821771..5e2274047031ecc5cc02f2fc12c07f4b0d7d47de 100644 (file)
--- a/helm/software/matita/library/formal_topology/relations.ma
+++ b/helm/software/matita/library/formal_topology/relations.ma
@@ -108,12 +108,12 @@ qed.
 interpretation "subset comprehension" 'comprehension s p =
  (comprehension s (mk_unary_morphism __ p _)).
 
-definition ext: ∀X,S:REL. ∀r: arrows1 ? X S. S ⇒ Ω \sup X.
- apply (λX,S,r.mk_unary_morphism ?? (λf.{x ∈ X | x ♮r f}) ?);
+definition ext: ∀X,S:REL. binary_morphism1 (arrows1 ? X S) S (Ω \sup X).
+ apply (λX,S.mk_binary_morphism1 ??? (λr:arrows1 ? X S.λf:S.{x ∈ X | x ♮r f}) ?);
   [ intros; simplify; apply (.= (H‡#)); apply refl1
-  | intros; simplify; split; intros; simplify; intros;
-     [ apply (. #‡(#‡H)); assumption
-     | apply (. #‡(#‡H\sup -1)); assumption]]
+  | intros; simplify; split; intros; simplify; intros; cases f; split; try assumption;
+     [ apply (. (#‡H1)); whd in H; apply (if ?? (H ??)); assumption
+     | apply (. (#‡H1\sup -1)); whd in H; apply (fi ?? (H ??));assumption]]
 qed.
 
 definition extS: ∀X,S:REL. ∀r: arrows1 ? X S. Ω \sup S ⇒ Ω \sup X.
@@ -154,7 +154,7 @@ lemma equalset_extS_id_X_X: ∀o:REL.∀X.extS ?? (id1 ? o) X = X.
         | change with (a = a); apply refl]]]
 qed.
 
-lemma extS_com: ∀o1,o2,o3,c1,c2,S. extS o1 o3 (c1 ∘ c2) S = extS o1 o2 c1 (extS o2 o3 c2 S).
+lemma extS_com: ∀o1,o2,o3,c1,c2,S. extS o1 o3 (c2 ∘ c1) S = extS o1 o2 c1 (extS o2 o3 c2 S).
  intros; unfold extS; simplify; split; intros; simplify; intros;
   [ cases f (H1 H2); cases H2 (w H3); clear f H2; split; [assumption]
     cases H3 (H4 H5); cases H5 (w1 H6); clear H3 H5; cases H6 (H7 H8); clear H6;