removed no longer used METAs

[helm.git] / helm / matita / contribs / PREDICATIVE-TOPOLOGY / coa_defs.ma

diff --git a/helm/matita/contribs/PREDICATIVE-TOPOLOGY/coa_defs.ma b/helm/matita/contribs/PREDICATIVE-TOPOLOGY/coa_defs.ma
index 6d4ea68af22c95f1c6d026270bf014c9b370988e..c840fbdaf7cddc972b4f3cdade571c5b2aa84dd4 100644 (file)
--- a/helm/matita/contribs/PREDICATIVE-TOPOLOGY/coa_defs.ma
+++ b/helm/matita/contribs/PREDICATIVE-TOPOLOGY/coa_defs.ma
@@ -15,16 +15,16 @@
 set "baseuri" "cic:/matita/PREDICATIVE-TOPOLOGY/coa_defs".
 
 include "iff.ma".
-include "domain_defs.ma".
+include "domain_data.ma".
 
 (* COMPLETE OVERLAP ALGEBRAS 
 *)
 
 record COA: Type \def {
-   coa: Class;                                   (* carrier *)
+   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 *)
+        sup: \forall (D:Domain). (D \to coa) \to coa; (* supremum *)
         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; 
@@ -36,9 +36,26 @@ record COA: Type \def {
         density: \forall p,q. (\forall r. ov p r \to ov q r) \to le p q
 }.
 
-coercion coa.
+definition zero: \forall (P:COA). P \def
+   \lambda (P:COA). inf P ? (dvoid_ixfam P).
+
+definition one: \forall (P:COA). P \def
+   \lambda (P:COA). sup P ? (dvoid_ixfam P).
+
+definition binf: \forall (P:COA). P \to P \to P \def
+   \lambda (P:COA). \lambda p0,p1.
+   inf P ? (dbool_ixfam P p0 p1).
+
+definition bsup: \forall (P:COA). P \to P \to P \def
+   \lambda (P:COA). \lambda p0,p1.
+   sup P ? (dbool_ixfam P p0 p1).
+
 (*                          
    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
+*)
+
+inductive pippo : Prop \def
+   | Pippo: let x \def zero in zero = x \to pippo.
+   
\ No newline at end of file