update in binaries for λδ

[helm.git] / helm / software / matita / library / formal_topology / concrete_spaces.ma

diff --git a/helm/software/matita/library/formal_topology/concrete_spaces.ma b/helm/software/matita/library/formal_topology/concrete_spaces.ma
index d95072cb973a2fa4c65f3ecd60212f84ba71438a..69ff6f13450b519aa0cb68e5b5eae85c58672a4b 100644 (file)
--- a/helm/software/matita/library/formal_topology/concrete_spaces.ma
+++ b/helm/software/matita/library/formal_topology/concrete_spaces.ma
@@ -14,31 +14,24 @@
 
 include "formal_topology/basic_pairs.ma".
 
-record concrete_space : Type ≝
+(* carr1 e' necessario perche' ci sega via la coercion per gli oggetti di REL!
+   (confondendola con la coercion per gli oggetti di SET
+record concrete_space : Type1 ≝
  { bp:> BP;
-   converges: ∀a: concr bp.∀U,V: form bp. a ⊩ U → a ⊩ V → a ⊩ (U ↓ V);
-   all_covered: ∀x: concr bp. x ⊩ form bp
+   converges: ∀a: carr1 (concr bp).∀U,V: carr1 (form bp). a ⊩ U → a ⊩ V → a ⊩ (U ↓ V);
+   all_covered: ∀x: carr1 (concr bp). x ⊩ form bp
  }.
 
-definition bp': concrete_space → basic_pair ≝ λc.bp c.
-
-coercion bp'.
-
-record convergent_relation_pair (CS1,CS2: concrete_space) : Type ≝
+record convergent_relation_pair (CS1,CS2: concrete_space) : Type1 ≝
  { rp:> arrows1 ? CS1 CS2;
    respects_converges:
     ∀b,c.
-     extS ?? rp \sub\c (BPextS CS2 (b ↓ c)) =
-     BPextS CS1 ((extS ?? rp \sub\f b) ↓ (extS ?? rp \sub\f c));
+     minus_image ?? rp \sub\c (BPextS CS2 (b ↓ c)) =
+     BPextS CS1 ((minus_image ?? rp \sub\f b) ↓ (minus_image ?? rp \sub\f c));
    respects_all_covered:
-    extS ?? rp\sub\c (BPextS CS2 (form CS2)) = BPextS CS1 (form CS1)
+    minus_image ?? rp\sub\c (BPextS CS2 (full_subset (form CS2))) = BPextS CS1 (full_subset (form CS1))
  }.
 
-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.
  intros;
  constructor 1;
@@ -51,11 +44,6 @@ definition convergent_relation_space_setoid: concrete_space → concrete_space 
      | intros 3; apply trans1]]
 qed.
 
-definition rp'': ∀CS1,CS2.convergent_relation_space_setoid CS1 CS2 → arrows1 BP CS1 CS2 ≝
- λCS1,CS2,c.rp ?? c.
-
-coercion rp''.
-
 definition convergent_relation_space_composition:
  ∀o1,o2,o3: concrete_space.
   binary_morphism1
@@ -67,23 +55,23 @@ definition convergent_relation_space_composition:
        constructor 1;
         [ apply (fun1 ??? (comp1 BP ???)); [apply (bp o2) |*: apply rp; assumption]
         | intros;
-          change in ⊢ (? ? ? (? ? ? (? ? ? %) ?) ?) with (c \sub \c ∘ c1 \sub \c);
+          change in ⊢ (? ? ? (? ? ? (? ? ? %) ?) ?) with (c1 \sub \c ∘ c \sub \c);
           change in ⊢ (? ? ? ? (? ? ? ? (? ? ? ? ? (? ? ? (? ? ? %) ?) ?)))
-            with (c \sub \f ∘ c1 \sub \f);
+            with (c1 \sub \f ∘ c \sub \f);
           change in ⊢ (? ? ? ? (? ? ? ? (? ? ? ? ? ? (? ? ? (? ? ? %) ?))))
-            with (c \sub \f ∘ c1 \sub \f);
+            with (c1 \sub \f ∘ c \sub \f);
           apply (.= (extS_com ??????));
           apply (.= (†(respects_converges ?????)));
           apply (.= (respects_converges ?????));
           apply (.= (†(((extS_com ??????) \sup -1)‡(extS_com ??????)\sup -1)));
           apply refl1;
-        | change in ⊢ (? ? ? (? ? ? (? ? ? %) ?) ?) with (c \sub \c ∘ c1 \sub \c);
+        | change in ⊢ (? ? ? (? ? ? (? ? ? %) ?) ?) with (c1 \sub \c ∘ c \sub \c);
           apply (.= (extS_com ??????));
           apply (.= (†(respects_all_covered ???)));
           apply (.= respects_all_covered ???);
           apply refl1]
      | intros;
-       change with (a ∘ b = a' ∘ b');
+       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));
@@ -106,15 +94,16 @@ definition CSPA: category1.
        apply refl1]
   | apply convergent_relation_space_composition
   | intros; simplify;
-    change with ((a12 ∘ a23) ∘ a34 = a12 ∘ (a23 ∘ a34));
+    change with (a34 ∘ (a23 ∘ a12) = (a34 ∘ a23) ∘ a12);
     apply (.= ASSOC1);
     apply refl1
   | intros; simplify;
-    change with (id1 ? o1 ∘ a = a);
-    apply (.= id_neutral_left1 ????);
+    change with (a ∘ id1 ? o1 = a);
+    apply (.= id_neutral_right1 ????);
     apply refl1
   | intros; simplify;
-    change with (a ∘ id1 ? o2 = a);
-    apply (.= id_neutral_right1 ????);
+    change with (id1 ? o2 ∘ a = a);
+    apply (.= id_neutral_left1 ????);
     apply refl1]
 qed.
+*)
\ No newline at end of file