Many universe inconsistency avoided here and there.

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

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 c3221a7d99a0068e52b17781c8be2aa01ece8afd..0bd8715a67550692dbc7fbdc702e8ecbdff15f86 100644 (file)
--- a/helm/software/matita/contribs/formal_topology/overlap/o-concrete_spaces.ma
+++ b/helm/software/matita/contribs/formal_topology/overlap/o-concrete_spaces.ma
@@ -47,7 +47,8 @@ lemma xxx : ∀x.carr x → carr1 (setoid1_of_setoid x). intros; assumption; qed
 coercion xxx nocomposites.
 
 lemma down_p : ∀S,I:SET.∀u:S⇒S.∀c:arrows1 SET I S.∀a:I.∀a':I.a=a'→u (c a)=u (c a').
-intros; unfold uncurry_arrows; apply (†(†H));
+intros; unfold uncurry_arrows; change in c with (I ⇒ S);
+apply (†(†H));
 qed.
 
 alias symbol "eq" = "setoid eq".
@@ -118,13 +119,6 @@ definition rp'': ∀CS1,CS2.convergent_relation_space_setoid CS1 CS2 → arrows1
 
 coercion rp''.
 
-definition prop_1_SET : 
- ∀A,B:SET.∀w:arrows1 SET A B.∀a,b:A.eq1 ? a b→eq1 ? (w a) (w b).
-intros; apply (prop_1 A B w a b H);
-qed.
-
-interpretation "SET dagger" 'prop1 h = (prop_1_SET _ _ _ _ _ h).
-
 definition convergent_relation_space_composition:
  ∀o1,o2,o3: concrete_space.
   binary_morphism1
@@ -134,17 +128,17 @@ definition convergent_relation_space_composition:
  intros; constructor 1;
      [ intros; whd in c c1 ⊢ %;
        constructor 1;
-        [ apply (fun1 ??? (comp1 BP ???)); [apply (bp o2) |*: apply rp; assumption]
-        | intros;  
+        [ apply (c1 ∘ c);
+        | intros;
           change in ⊢ (? ? ? % ?) with (c\sub\c⎻ (c1\sub\c⎻ (Ext⎽o3 (b↓c2))));
+          unfold uncurry_arrows;
           alias symbol "trans" = "trans1".
           apply (.= († (respects_converges : ?)));
-          apply (.= (respects_converges : ?));
-          apply refl1;
+          apply (respects_converges ?? c (c1\sub\f⎻ b) (c1\sub\f⎻ c2));
         | change in ⊢ (? ? ? % ?) with (c\sub\c⎻ (c1\sub\c⎻ (Ext⎽o3 (oa_one (form o3)))));
+          unfold uncurry_arrows;
           apply (.= (†(respects_all_covered :?)));
-          apply (.= (respects_all_covered :?));
-          apply refl1]
+          apply rule (respects_all_covered ?? c);]
      | intros;
        change with (b ∘ a = b' ∘ a'); 
        change in H with (rp'' ?? a = rp'' ?? a');
@@ -158,25 +152,16 @@ definition CSPA: category1.
   | apply convergent_relation_space_setoid
   | intro; constructor 1;
      [ apply id1
-     | intros;
-       unfold id; simplify;
-       apply (.= (equalset_extS_id_X_X ??));
-       apply (.= (†((equalset_extS_id_X_X ??)\sup -1‡
-                    (equalset_extS_id_X_X ??)\sup -1)));
-       apply refl1;
-     | apply (.= (equalset_extS_id_X_X ??));
-       apply refl1]
+     | intros; apply refl1;
+     | apply refl1]
   | apply convergent_relation_space_composition
   | intros; simplify;
     change with (a34 ∘ (a23 ∘ a12) = (a34 ∘ a23) ∘ a12);
-    apply (.= ASSOC1);
-    apply refl1
+    apply ASSOC1;
   | intros; simplify;
     change with (a ∘ id1 ? o1 = a);
-    apply (.= id_neutral_right1 ????);
-    apply refl1
+    apply (id_neutral_right1 : ?);
   | intros; simplify;
     change with (id1 ? o2 ∘ a = a);
-    apply (.= id_neutral_left1 ????);
-    apply refl1]
+    apply (id_neutral_left1 : ?);]
 qed.