X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=helm%2Fsoftware%2Fmatita%2Fcontribs%2Fformal_topology%2Foverlap%2Fo-basic_pairs.ma;h=7e0064e4631429b570248dd4117a88c397521207;hb=26711af9f9afbaf93dbb3a4e1c227d6e884a8ebe;hp=01eac172cebf69cdbdb416efac07d3a082e9b353;hpb=4dfb1305a9c4a7c292f4b1957de1454d46c1ab8a;p=helm.git

diff --git a/helm/software/matita/contribs/formal_topology/overlap/o-basic_pairs.ma b/helm/software/matita/contribs/formal_topology/overlap/o-basic_pairs.ma
index 01eac172c..7e0064e46 100644
--- a/helm/software/matita/contribs/formal_topology/overlap/o-basic_pairs.ma
+++ b/helm/software/matita/contribs/formal_topology/overlap/o-basic_pairs.ma
@@ -13,12 +13,11 @@
 (**************************************************************************)
 
 include "o-algebra.ma".
-include "datatypes/categories.ma".
 
-record basic_pair: Type ≝
+record basic_pair: Type2 ≝
  { concr: OA;
    form: OA;
-   rel: arrows1 ? concr form
+   rel: arrows2 ? concr form
  }.
 
 notation > "x ⊩ y" with precedence 45 for @{'Vdash2 $x $y ?}.
@@ -31,9 +30,9 @@ interpretation "basic pair relation (non applied)" 'Vdash c = (rel c).
 
 alias symbol "eq" = "setoid1 eq".
 alias symbol "compose" = "category1 composition".
-record relation_pair (BP1,BP2: basic_pair): Type ≝
- { concr_rel: arrows1 ? (concr BP1) (concr BP2);
-   form_rel: arrows1 ? (form BP1) (form BP2);
+record relation_pair (BP1,BP2: basic_pair): Type2 ≝
+ { concr_rel: arrows2 ? (concr BP1) (concr BP2);
+   form_rel: arrows2 ? (form BP1) (form BP2);
    commute: ⊩ ∘ concr_rel = form_rel ∘ ⊩
  }.
 
@@ -44,23 +43,24 @@ interpretation "concrete relation" 'concr_rel r = (concr_rel __ r).
 interpretation "formal relation" 'form_rel r = (form_rel __ r). 
 
 definition relation_pair_equality:
- ∀o1,o2. equivalence_relation1 (relation_pair o1 o2).
+ ∀o1,o2. equivalence_relation2 (relation_pair o1 o2).
  intros;
  constructor 1;
   [ apply (λr,r'. ⊩ ∘ r \sub\c = ⊩ ∘ r' \sub\c);
   | simplify;
     intros;
-    apply refl1;
+    apply refl2;
   | simplify;
     intros 2;
-    apply sym1;
+    apply sym2;
   | simplify;
     intros 3;
-    apply trans1;
+    apply trans2;
   ]      
 qed.
 
-definition relation_pair_setoid: basic_pair → basic_pair → setoid1.
+(* qui setoid1 e' giusto: ma non lo e'!!! *)
+definition relation_pair_setoid: basic_pair → basic_pair → setoid2.
  intros;
  constructor 1;
   [ apply (relation_pair b b1)
@@ -73,22 +73,22 @@ lemma eq_to_eq': ∀o1,o2.∀r,r': relation_pair_setoid o1 o2. r=r' → r \sub\f
  apply (.= ((commute ?? r) \sup -1));
  apply (.= H);
  apply (.= (commute ?? r'));
- apply refl1;
+ apply refl2;
 qed.
 
 
 definition id_relation_pair: ∀o:basic_pair. relation_pair o o.
  intro;
  constructor 1;
-  [1,2: apply id1;
-  | lapply (id_neutral_right1 ? (concr o) ? (⊩)) as H;
-    lapply (id_neutral_left1 ?? (form o) (⊩)) as H1;
+  [1,2: apply id2;
+  | lapply (id_neutral_right2 ? (concr o) ? (⊩)) as H;
+    lapply (id_neutral_left2 ?? (form o) (⊩)) as H1;
     apply (.= H);
     apply (H1 \sup -1);]
 qed.
 
 definition relation_pair_composition:
- ∀o1,o2,o3. binary_morphism1 (relation_pair_setoid o1 o2) (relation_pair_setoid o2 o3) (relation_pair_setoid o1 o3).
+ ∀o1,o2,o3. binary_morphism2 (relation_pair_setoid o1 o2) (relation_pair_setoid o2 o3) (relation_pair_setoid o1 o3).
  intros;
  constructor 1;
   [ intros (r r1);
@@ -97,26 +97,26 @@ definition relation_pair_composition:
      | apply (r1 \sub\f ∘ r \sub\f)
      | lapply (commute ?? r) as H;
        lapply (commute ?? r1) as H1;
-       apply (.= ASSOC1);
+       apply rule (.= ASSOC);
        apply (.= #‡H1);
-       apply (.= ASSOC1\sup -1);
+       apply rule (.= ASSOC ^ -1);
        apply (.= H‡#);
-       apply ASSOC1]
+       apply rule ASSOC]
   | intros;
     change with (⊩ ∘ (b\sub\c ∘ a\sub\c) = ⊩ ∘ (b'\sub\c ∘ a'\sub\c));  
-    change in H with (⊩ ∘ a \sub\c = ⊩ ∘ a' \sub\c);
-    change in H1 with (⊩ ∘ b \sub\c = ⊩ ∘ b' \sub\c);
-    apply (.= ASSOC1);
-    apply (.= #‡H1);
+    change in e with (⊩ ∘ a \sub\c = ⊩ ∘ a' \sub\c);
+    change in e1 with (⊩ ∘ b \sub\c = ⊩ ∘ b' \sub\c);
+    apply rule (.= ASSOC);
+    apply (.= #‡e1);
     apply (.= #‡(commute ?? b'));
-    apply (.= ASSOC1 \sup -1);
-    apply (.= H‡#);
-    apply (.= ASSOC1);
+    apply rule (.= ASSOC \sup -1);
+    apply (.= e‡#);
+    apply rule (.= ASSOC);
     apply (.= #‡(commute ?? b')\sup -1);
-    apply (ASSOC1 \sup -1)]
+    apply rule (ASSOC \sup -1)]
 qed.
     
-definition BP: category1.
+definition BP: category2.
  constructor 1;
   [ apply basic_pair
   | apply relation_pair_setoid
@@ -125,13 +125,13 @@ definition BP: category1.
   | intros;
     change with (⊩ ∘ (a34\sub\c ∘ (a23\sub\c ∘ a12\sub\c)) =
                  ⊩ ∘ ((a34\sub\c ∘ a23\sub\c) ∘ a12\sub\c));
-    apply (ASSOC1‡#);
+    apply rule (ASSOC‡#);
   | intros;
     change with (⊩ ∘ (a\sub\c ∘ (id_relation_pair o1)\sub\c) = ⊩ ∘ a\sub\c);
-    apply ((id_neutral_right1 ????)‡#);
+    apply ((id_neutral_right2 ????)‡#);
   | intros;
     change with (⊩ ∘ ((id_relation_pair o2)\sub\c ∘ a\sub\c) = ⊩ ∘ a\sub\c);
-    apply ((id_neutral_left1 ????)‡#);]
+    apply ((id_neutral_left2 ????)‡#);]
 qed.
 
 
@@ -184,4 +184,4 @@ qed.
 
 interpretation "basic pair relation for subsets" 'Vdash2 x y = (fun1 (concr _) __ (relS _) x y).
 interpretation "basic pair relation for subsets (non applied)" 'Vdash = (fun1 ___ (relS _)).
-*)
\ No newline at end of file
+*)