eq over SET1 and SET no longer used

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

diff --git a/helm/software/matita/contribs/formal_topology/overlap/o-algebra.ma b/helm/software/matita/contribs/formal_topology/overlap/o-algebra.ma
index 533bff3ddd2e191a8305fe229210261033d29fce..10f50358103e04fce97ba83db0c3340c6de9f63f 100644 (file)
--- a/helm/software/matita/contribs/formal_topology/overlap/o-algebra.ma
+++ b/helm/software/matita/contribs/formal_topology/overlap/o-algebra.ma
@@ -13,7 +13,6 @@
 (**************************************************************************)
 
 include "categories.ma".
-include "logic/cprop_connectives.ma". 
 
 inductive bool : Type0 := true : bool | false : bool.
 
@@ -76,7 +75,7 @@ record OAlgebra : Type2 := {
   (* ⇔ deve essere =, l'esiste debole *)
   oa_join_split:
       ∀I:SET.∀p.∀q:arrows2 SET1 I oa_P.
-       oa_overlap p (oa_join I q) ⇔ ∃i:I.oa_overlap p (q i);
+       oa_overlap p (oa_join I q) ⇔ ∃i:carr I.oa_overlap p (q i);
   (*oa_base : setoid;
   1) enum non e' il nome giusto perche' non e' suriettiva
   2) manca (vedere altro capitolo) la "suriettivita'" come immagine di insiemi di oa_base
@@ -134,9 +133,7 @@ intros; split;
   intro x; simplify; cases x; simplify; assumption;]
 qed.
 
-notation "hovbox(a ∧ b)" left associative with precedence 35
-for @{ 'oa_meet_bin $a $b }.
-interpretation "o-algebra binary meet" 'oa_meet_bin a b = 
+interpretation "o-algebra binary meet" 'and a b = 
   (fun21 ___ (binary_meet _) a b).
 
 coercion Type1_OF_OAlgebra nocomposites.
@@ -171,7 +168,7 @@ definition hint5: OAlgebra → objs2 SET1.
 qed.
 coercion hint5.
 
-record ORelation (P,Q : OAlgebra) : Type ≝ {
+record ORelation (P,Q : OAlgebra) : Type2 ≝ {
   or_f_ : P ⇒ Q;
   or_f_minus_star_ : P ⇒ Q;
   or_f_star_ : Q ⇒ P;
@@ -188,14 +185,14 @@ constructor 1;
 | constructor 1;
    (* tenere solo una uguaglianza e usare la proposizione 9.9 per
       le altre (unicita' degli aggiunti e del simmetrico) *)
-   [ apply (λp,q. And4 (eq2 ? (or_f_minus_star_ ?? p) (or_f_minus_star_ ?? q)) 
+   [ apply (λp,q. And42 (eq2 ? (or_f_minus_star_ ?? p) (or_f_minus_star_ ?? q)) 
              (eq2 ? (or_f_minus_ ?? p) (or_f_minus_ ?? q)) 
              (eq2 ? (or_f_ ?? p) (or_f_ ?? q)) 
              (eq2 ? (or_f_star_ ?? p) (or_f_star_ ?? q))); 
    | whd; simplify; intros; repeat split; intros; apply refl2;
-   | whd; simplify; intros; cases H; clear H; split; 
+   | whd; simplify; intros; cases a; clear a; split; 
      intro a; apply sym1; generalize in match a;assumption;
-   | whd; simplify; intros; cases H; cases H1; clear H H1; split; intro a;
+   | whd; simplify; intros; cases a; cases a1; clear a a1; split; intro a;
      [ apply (.= (e a)); apply e4;
      | apply (.= (e1 a)); apply e5;
      | apply (.= (e2 a)); apply e6;
@@ -345,3 +342,8 @@ lemma objs2_SET1_OF_OA: OA → objs2 SET1.
  intro; whd; apply (setoid1_of_OA t);
 qed.
 coercion objs2_SET1_OF_OA.
+
+lemma Type_OF_category2_OF_SET1_OF_OA: OA → Type_OF_category2 SET1.
+ intro; apply (oa_P t);
+qed.
+coercion Type_OF_category2_OF_SET1_OF_OA.