coimplication (continued)

complete overlap algebras (started)

diff --git a/helm/matita/contribs/PREDICATIVE-TOPOLOGY/coa_defs.ma b/helm/matita/contribs/PREDICATIVE-TOPOLOGY/coa_defs.ma
new file mode 100644 (file)
index 0000000..6d4ea68
--- /dev/null
+++ b/helm/matita/contribs/PREDICATIVE-TOPOLOGY/coa_defs.ma
@@ -0,0 +1,44 @@
+(**************************************************************************)
+(*       ___                                                              *)
+(*      ||M||                                                             *)
+(*      ||A||       A project by Andrea Asperti                           *)
+(*      ||T||                                                             *)
+(*      ||I||       Developers:                                           *)
+(*      ||T||         The HELM team.                                      *)
+(*      ||A||         http://helm.cs.unibo.it                             *)
+(*      \   /                                                             *)
+(*       \ /        This file is distributed under the terms of the       *)
+(*        v         GNU General Public License Version 2                  *)
+(*                                                                        *)
+(**************************************************************************)
+
+set "baseuri" "cic:/matita/PREDICATIVE-TOPOLOGY/coa_defs".
+
+include "iff.ma".
+include "domain_defs.ma".
+
+(* COMPLETE OVERLAP ALGEBRAS 
+*)
+
+record COA: Type \def {
+   coa: Class;                                   (* carrier *)
+        le: coa \to coa \to Prop;                     (* inclusion *)
+        ov: coa \to coa \to Prop;                     (* overlap *)
+        sup: \forall (D:Domain). (D \to coa) \to coa; (* suprimum *)
+        inf: \forall (D:Domain). (D \to coa) \to coa; (* infimum *)
+        le_refl: \forall p. le p p;
+        le_trans: \forall p,r. le p r \to \forall q. le r q \to le p q; 
+        le_antysym: \forall q,p. le q p \to le p q \to ceq ? p q;
+        ov_sym: \forall q,p. ov q p \to ov p q;
+        sup_le: \forall D,ps,q. le (sup D ps) q \liff \iforall d. le (ps d) q;
+        inf_le: \forall D,p,qs. le p (inf D qs) \liff \iforall d. le p (qs d);
+        sup_ov: \forall D,ps,q. ov (sup D ps) q \liff \iexists d. ov (ps d) q;
+        density: \forall p,q. (\forall r. ov p r \to ov q r) \to le p q
+}.
+
+coercion coa.
+(*                          
+   inf_ov: forall p q, ov p q -> ov p (inf QDBool (bool_family _ p q))
+        properness: ov zero zero -> False;
+        distributivity: forall I p q, id _ (inf QDBool (bool_family _ (sup I p) q)) (sup I (fun i => (inf QDBool (bool_family _ (p i) q))));
+*)
\ No newline at end of file

diff --git a/helm/matita/contribs/PREDICATIVE-TOPOLOGY/iff.ma b/helm/matita/contribs/PREDICATIVE-TOPOLOGY/iff.ma
index e6475c5fdafcadb59a37891950c839e6a9e6e0a2..9a9491923f889afb28808116a23eb121fa77473c 100644 (file)
--- a/helm/matita/contribs/PREDICATIVE-TOPOLOGY/iff.ma
+++ b/helm/matita/contribs/PREDICATIVE-TOPOLOGY/iff.ma
@@ -14,12 +14,18 @@
 
 set "baseuri" "cic:/matita/logic/iff".
 
+include "../../library/logic/connectives.ma".
+
 definition Iff : Prop \to Prop \to Prop \def
    \lambda A,B. (A \to B) \land (B \to A).
    
  (*CSC: the URI must disappear: there is a bug now *)
 interpretation "logical iff" 'iff x y = (cic:/matita/logic/iff/Iff.con x y).
 
-notation < "hvbox(a break \liff b)" 
+notation > "hvbox(a break \liff b)" 
+  left associative with precedence 25
+for @{ 'iff $a $b }.
+
+notation < "hvbox(a break \leftrightarrow b)" 
   left associative with precedence 25
 for @{ 'iff $a $b }.