foo overlap

[helm.git] / helm / software / matita / contribs / formal_topology / overlap / o-saturations.ma

diff --git a/helm/software/matita/contribs/formal_topology/overlap/o-saturations.ma b/helm/software/matita/contribs/formal_topology/overlap/o-saturations.ma
index 9b68972b42cd7aadf23784edd3129e3730706cb3..22c8fbdeaf7fe9e583a17a4d5230aa7a89b93545 100644 (file)
--- a/helm/software/matita/contribs/formal_topology/overlap/o-saturations.ma
+++ b/helm/software/matita/contribs/formal_topology/overlap/o-saturations.ma
@@ -14,21 +14,13 @@
 
 include "o-algebra.ma".
 
-definition hint1: OA → Type ≝ λc:OA.carr (oa_P c).
-coercion hint1.
-
-definition hint2: ∀C.hint1 C → carr1 ((λx.x) (setoid1_of_setoid (oa_P C))).
-intros; assumption;
-qed.
-coercion hint2. 
-
 alias symbol "eq" = "setoid1 eq".
 definition is_saturation ≝
- λC:OA.λA:C → C.
+ λC:OA.λA:unary_morphism (oa_P C) (oa_P C).
   ∀U,V. (U ≤ A V) = (A U ≤ A V).
 
 definition is_reduction ≝
- λC:OA.λJ:C → C.
+ λC:OA.λJ:unary_morphism (oa_P C) (oa_P C).
     ∀U,V. (J U ≤ V) = (J U ≤ J V).
 
 theorem saturation_expansive: ∀C,A. is_saturation C A → ∀U. U ≤ A U.
@@ -37,7 +29,7 @@ qed.
 
 theorem saturation_monotone:
  ∀C,A. is_saturation C A →
-  ∀U,V:C. U ≤ V → A U ≤ A V.
+  ∀U,V. U ≤ V → A U ≤ A V.
  intros; apply (if ?? (H ??)); apply (oa_leq_trans C);
   [apply V|3: apply saturation_expansive ]
  assumption.