More reorganization.

[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 22c8fbdeaf7fe9e583a17a4d5230aa7a89b93545..0511edd34095c9f1b99fcc3fd06f3f8728ab4b57 100644 (file)
--- a/helm/software/matita/contribs/formal_topology/overlap/o-saturations.ma
+++ b/helm/software/matita/contribs/formal_topology/overlap/o-saturations.ma
@@ -16,28 +16,28 @@ include "o-algebra.ma".
 
 alias symbol "eq" = "setoid1 eq".
 definition is_saturation ≝
- λC:OA.λA:unary_morphism (oa_P C) (oa_P C).
+ λC:OA.λA:unary_morphism1 C C.
   ∀U,V. (U ≤ A V) = (A U ≤ A V).
 
 definition is_reduction ≝
- λC:OA.λJ:unary_morphism (oa_P C) (oa_P C).
+ λC:OA.λJ:unary_morphism1 C C.
     ∀U,V. (J U ≤ V) = (J U ≤ J V).
 
 theorem saturation_expansive: ∀C,A. is_saturation C A → ∀U. U ≤ A U.
- intros; apply (fi ?? (H ??)); apply (oa_leq_refl C).
+ intros; apply (fi ?? (i ??)); apply (oa_leq_refl C).
 qed.
 
 theorem saturation_monotone:
  ∀C,A. is_saturation C A →
   ∀U,V. U ≤ V → A U ≤ A V.
- intros; apply (if ?? (H ??)); apply (oa_leq_trans C);
+ intros; apply (if ?? (i ??)); apply (oa_leq_trans C);
   [apply V|3: apply saturation_expansive ]
  assumption.
 qed.
 
 theorem saturation_idempotent: ∀C,A. is_saturation C A → ∀U. 
- eq (oa_P C) (A (A U)) (A U).
+ eq1 C (A (A U)) (A U).
  intros; apply (oa_leq_antisym C);
-  [ apply (if ?? (H (A U) U)); apply (oa_leq_refl C).
+  [ apply (if ?? (i (A U) U)); apply (oa_leq_refl C).
   | apply saturation_expansive; assumption]
-qed.
+qed.
\ No newline at end of file