From 4ead19b19835213b82e451ee6fd2ed026ed3f4a5 Mon Sep 17 00:00:00 2001
From: Enrico Tassi <enrico.tassi@inria.fr>
Date: Wed, 17 Dec 2008 17:52:18 +0000
Subject: [PATCH] foo overlap

---
 .../formal_topology/overlap/o-concrete_spaces.ma   |  4 ++--
 .../formal_topology/overlap/o-saturations.ma       | 14 +++-----------
 2 files changed, 5 insertions(+), 13 deletions(-)

diff --git a/helm/software/matita/contribs/formal_topology/overlap/o-concrete_spaces.ma b/helm/software/matita/contribs/formal_topology/overlap/o-concrete_spaces.ma
index 135dae3c9..7292b4ecb 100644
--- a/helm/software/matita/contribs/formal_topology/overlap/o-concrete_spaces.ma
+++ b/helm/software/matita/contribs/formal_topology/overlap/o-concrete_spaces.ma
@@ -20,9 +20,9 @@ coercion xxx.
 
 record concrete_space : Type ≝
  { bp:> BP;
-   downarrow: form bp → oa_P (form bp);
+   downarrow: unary_morphism (oa_P (form bp)) (oa_P (form bp));
    downarrow_is_sat: is_saturation ? downarrow;
-   converges: ∀q1,q2:form bp.
+   converges: ∀q1,q2.
      or_f_minus ?? (⊩) q1 ∧ or_f_minus ?? (⊩) q2 = 
      or_f_minus ?? (⊩) ((downarrow q1) ∧ (downarrow q2));
    all_covered: (*⨍^-_bp*) or_f_minus ?? (⊩) (oa_one (form bp)) = oa_one (concr bp);
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 9b68972b4..22c8fbdea 100644
--- 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.
-- 
2.39.2