Back to step 1: all files that used to pass now pass again.

[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 78ea321a59857682393a42ed2baca1a4aa6fe0ce..6a9d7794db701429f657746dc1b41dc4922aad58 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
@@ -37,11 +37,6 @@ intros; constructor 1;
  | do 2 unfold FunClass_1_OF_Type_OF_setoid21; intros; apply  (†(†e));]
 qed.
 
-(*
-lemma xxx : ∀x.carr x → carr1 (setoid1_of_setoid x). intros; assumption; qed.
-coercion xxx nocomposites.
-*)
-
 lemma down_p : ∀S:SET1.∀I:SET.∀u:S⇒S.∀c:arrows2 SET1 I S.∀a:I.∀a':I.a=a'→u (c a)=u (c a').
 intros; apply (†(†e));
 qed.
@@ -61,28 +56,30 @@ record concrete_space : Type2 ≝
  }.
 
 interpretation "o-concrete space downarrow" 'downarrow x = 
-  (fun_1 __ (downarrow _) x).
+  (fun11 __ (downarrow _) x).
 
 definition bp': concrete_space → basic_pair ≝ λc.bp c.
 coercion bp'.
 
-lemma setoid_OF_OA : OA → setoid.
-intros; apply (oa_P o);
+definition bp'': concrete_space → objs2 BP.
+ intro; apply (bp' c);
 qed.
-
-coercion setoid_OF_OA.
+coercion bp''.
 
 definition binary_downarrow : 
   ∀C:concrete_space.binary_morphism1 (form C) (form C) (form C).
 intros; constructor 1;
-[ intros; apply (↓ c ∧ ↓ c1);
-| intros; apply ((†H)‡(†H1));]
+[ intros; apply (↓ t ∧ ↓ t1);
+| intros;
+  alias symbol "prop2" = "prop21".
+  alias symbol "prop1" = "prop11".
+  apply ((†e)‡(†e1));]
 qed.
 
-interpretation "concrete_space binary ↓" 'fintersects a b = (fun1 _ _ _ (binary_downarrow _) a b).
+interpretation "concrete_space binary ↓" 'fintersects a b = (fun21 _ _ _ (binary_downarrow _) a b).
 
-record convergent_relation_pair (CS1,CS2: concrete_space) : Type ≝
- { rp:> arrows1 ? CS1 CS2;
+record convergent_relation_pair (CS1,CS2: concrete_space) : Type2 ≝
+ { rp:> arrows2 ? CS1 CS2;
    respects_converges:
     ∀b,c. eq1 ? (rp\sub\c⎻ (Ext⎽CS2 (b ↓ c))) (Ext⎽CS1 (rp\sub\f⎻ b ↓ rp\sub\f⎻ c));
    respects_all_covered:
@@ -92,69 +89,76 @@ record convergent_relation_pair (CS1,CS2: concrete_space) : Type ≝
 
 definition rp' : ∀CS1,CS2. convergent_relation_pair CS1 CS2 → relation_pair CS1 CS2 ≝
  λCS1,CS2,c. rp CS1 CS2 c.
- 
 coercion rp'.
 
-definition convergent_relation_space_setoid: concrete_space → concrete_space → setoid1.
+definition convergent_relation_space_setoid: concrete_space → concrete_space → setoid2.
  intros;
  constructor 1;
   [ apply (convergent_relation_pair c c1)
   | constructor 1;
      [ intros;
        apply (relation_pair_equality c c1 c2 c3);
-     | intros 1; apply refl1;
-     | intros 2; apply sym1; 
-     | intros 3; apply trans1]]
+     | intros 1; apply refl2;
+     | intros 2; apply sym2; 
+     | intros 3; apply trans2]]
 qed.
 
-definition rp'': ∀CS1,CS2.convergent_relation_space_setoid CS1 CS2 → arrows1 BP CS1 CS2 ≝
- λCS1,CS2,c.rp ?? c.
 
+definition rp'': ∀CS1,CS2.carr2 (convergent_relation_space_setoid CS1 CS2) → arrows2 BP CS1 CS2 ≝
+ λCS1,CS2,c.rp ?? c.
 coercion rp''.
 
+definition rp''': ∀CS1,CS2.Type_OF_setoid2 (convergent_relation_space_setoid CS1 CS2) → arrows2 BP CS1 CS2 ≝
+ λCS1,CS2,c.rp ?? c.
+coercion rp'''.
+
+definition rp'''': ∀CS1,CS2.Type_OF_setoid2 (convergent_relation_space_setoid CS1 CS2) → carr2 (arrows2 BP CS1 CS2) ≝
+ λCS1,CS2,c.rp ?? c.
+coercion rp''''.
+
 definition convergent_relation_space_composition:
  ∀o1,o2,o3: concrete_space.
-  binary_morphism1
+  binary_morphism2
    (convergent_relation_space_setoid o1 o2)
    (convergent_relation_space_setoid o2 o3)
    (convergent_relation_space_setoid o1 o3).
  intros; constructor 1;
-     [ intros; whd in c c1 ⊢ %;
+     [ intros; whd in t t1 ⊢ %;
        constructor 1;
-        [ apply (c1 ∘ c);
+        [ apply (t1 ∘ t);
         | intros;
-          change in ⊢ (? ? ? % ?) with (c\sub\c⎻ (c1\sub\c⎻ (Ext⎽o3 (b↓c2))));
-          unfold uncurry_arrows;
+          change in ⊢ (? ? ? % ?) with (t\sub\c⎻ (t1\sub\c⎻ (Ext⎽o3 (b↓c))));
+          unfold FunClass_1_OF_Type_OF_setoid21;
           alias symbol "trans" = "trans1".
           apply (.= († (respects_converges : ?)));
-          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_converges ?? t (t1\sub\f⎻ b) (t1\sub\f⎻ c));
+        | change in ⊢ (? ? ? % ?) with (t\sub\c⎻ (t1\sub\c⎻ (Ext⎽o3 (oa_one (form o3)))));
+          unfold FunClass_1_OF_Type_OF_setoid21;
           apply (.= (†(respects_all_covered :?)));
-          apply rule (respects_all_covered ?? c);]
+          apply rule (respects_all_covered ?? t);]
      | intros;
        change with (b ∘ a = b' ∘ a'); 
-       change in H with (rp'' ?? a = rp'' ?? a');
-       change in H1 with (rp'' ?? b = rp ?? b');
-       apply ( (H‡H1));]
+       change in e with (rp'' ?? a = rp'' ?? a');
+       change in e1 with (rp'' ?? b = rp ?? b');
+       apply (e‡e1);]
 qed.
 
-definition CSPA: category1.
+definition CSPA: category2.
  constructor 1;
   [ apply concrete_space
   | apply convergent_relation_space_setoid
   | intro; constructor 1;
-     [ apply id1
+     [ apply id2
      | intros; apply refl1;
      | apply refl1]
   | apply convergent_relation_space_composition
-  | intros; simplify;
+  | intros; simplify; whd in a12 a23 a34;
     change with (a34 ∘ (a23 ∘ a12) = (a34 ∘ a23) ∘ a12);
-    apply ASSOC1;
+    apply rule ASSOC;
   | intros; simplify;
-    change with (a ∘ id1 ? o1 = a);
-    apply (id_neutral_right1 : ?);
+    change with (a ∘ id2 ? o1 = a);
+    apply (id_neutral_right2 : ?);
   | intros; simplify;
-    change with (id1 ? o2 ∘ a = a);
-    apply (id_neutral_left1 : ?);]
-qed.
+    change with (id2 ? o2 ∘ a = a);
+    apply (id_neutral_left2 : ?);]
+qed.
\ No newline at end of file