many changes regarding coercions:

[helm.git] / helm / software / matita / contribs / formal_topology / overlap / relations_to_o-algebra.ma

diff --git a/helm/software/matita/contribs/formal_topology/overlap/relations_to_o-algebra.ma b/helm/software/matita/contribs/formal_topology/overlap/relations_to_o-algebra.ma
index e661fbfd082333a36cfb52a27b0517f3c42c33d8..856a7e0aec012945c32de153c841cae010b7b740 100644 (file)
--- a/helm/software/matita/contribs/formal_topology/overlap/relations_to_o-algebra.ma
+++ b/helm/software/matita/contribs/formal_topology/overlap/relations_to_o-algebra.ma
@@ -108,7 +108,7 @@ lemma orelation_of_relation_preserves_equality:
     apply (. #‡(e‡#)); ]
 qed.
 
-lemma hint: ∀o1,o2:OA. Type_OF_setoid2 (arrows2 ? o1 o2) → carr2 (arrows2 OA o1 o2).
+lemma hint: ∀o1,o2:OA. Type_OF_setoid21 (arrows2 ? o1 o2) → carr2 (arrows2 OA o1 o2).
  intros; apply t;
 qed.
 coercion hint.
@@ -136,12 +136,12 @@ lemma orelation_of_relation_preserves_identity:
   | change with (a1 ∈ a → ∀y.a1 ♮(id1 REL o1) y→y∈a); intros;
     change in f1 with (a1 = y); apply (. f1^-1‡#); apply f;]
 qed.
-
-lemma hint2: ∀S,T. carr2 (arrows2 OA S T) → Type_OF_setoid2 (arrows2 OA S T).
+(*
+lemma hint2: ∀S,T. carr2 (arrows2 OA S T) → Type_OF_setoid21 (arrows2 OA S T).
  intros; apply c;
 qed.
 coercion hint2.
-
+*)
 (* CSC: ???? forse un uncertain mancato *)
 lemma orelation_of_relation_preserves_composition:
  ∀o1,o2,o3:REL.∀F: arrows1 ? o1 o2.∀G: arrows1 ? o2 o3.
@@ -156,9 +156,11 @@ lemma orelation_of_relation_preserves_composition:
     split; [ assumption | exists; [apply w] split; assumption ]
   | cases e; cases x; cases f1; cases x1; clear e x f1 x1; exists; [apply w1 ]
     split; [ exists; [apply w] split; assumption | assumption ]
-  | cases e; cases x; cases f; cases x1; clear e x f x1; exists; [ apply w1 ]
+  | unfold arrows1_OF_ORelation_setoid; 
+    cases e; cases x; cases f; cases x1; clear e x f x1; exists; [ apply w1 ]
     split; [ assumption | exists; [apply w] split; assumption ]
-  | cases e; cases x; cases f1; cases x1; clear e x f1 x1; exists; [apply w1 ]
+  | unfold arrows1_OF_ORelation_setoid in e; 
+    cases e; cases x; cases f1; cases x1; clear e x f1 x1; exists; [apply w1 ]
     split; [ exists; [apply w] split; assumption | assumption ]
   | whd; intros; apply f; exists; [ apply y] split; assumption;
   | cases f1; clear f1; cases x; clear x; apply (f w); assumption;]