From f104e539b06bf5695f4d526d5217a581f5a9c5f5 Mon Sep 17 00:00:00 2001
From: Ferruccio Guidi <ferruccio.guidi@unibo.it>
Date: Mon, 28 Nov 2005 19:42:52 +0000
Subject: [PATCH] coa continued

---
 .../contribs/PREDICATIVE-TOPOLOGY/coa_defs.ma | 17 +++++++-
 .../PREDICATIVE-TOPOLOGY/coa_props.ma         | 19 +++++++++
 .../PREDICATIVE-TOPOLOGY/domain_data.ma       | 40 +++++++++++++++++++
 3 files changed, 75 insertions(+), 1 deletion(-)
 create mode 100644 helm/matita/contribs/PREDICATIVE-TOPOLOGY/coa_props.ma
 create mode 100644 helm/matita/contribs/PREDICATIVE-TOPOLOGY/domain_data.ma

diff --git a/helm/matita/contribs/PREDICATIVE-TOPOLOGY/coa_defs.ma b/helm/matita/contribs/PREDICATIVE-TOPOLOGY/coa_defs.ma
index 6d4ea68af..4600b0ecc 100644
--- a/helm/matita/contribs/PREDICATIVE-TOPOLOGY/coa_defs.ma
+++ b/helm/matita/contribs/PREDICATIVE-TOPOLOGY/coa_defs.ma
@@ -15,7 +15,7 @@
 set "baseuri" "cic:/matita/PREDICATIVE-TOPOLOGY/coa_defs".
 
 include "iff.ma".
-include "domain_defs.ma".
+include "domain_data.ma".
 
 (* COMPLETE OVERLAP ALGEBRAS 
 *)
@@ -37,6 +37,21 @@ record COA: Type \def {
 }.
 
 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;
diff --git a/helm/matita/contribs/PREDICATIVE-TOPOLOGY/coa_props.ma b/helm/matita/contribs/PREDICATIVE-TOPOLOGY/coa_props.ma
new file mode 100644
index 000000000..a25f8c79a
--- /dev/null
+++ b/helm/matita/contribs/PREDICATIVE-TOPOLOGY/coa_props.ma
@@ -0,0 +1,19 @@
+(**************************************************************************)
+(*       ___                                                              *)
+(*      ||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_props".
+
+include "coa_defs.ma".
+
+theorem zero_le: \forall (P:COA). \forall (p:P). le ? (zero P) p.
diff --git a/helm/matita/contribs/PREDICATIVE-TOPOLOGY/domain_data.ma b/helm/matita/contribs/PREDICATIVE-TOPOLOGY/domain_data.ma
new file mode 100644
index 000000000..ed0afab4f
--- /dev/null
+++ b/helm/matita/contribs/PREDICATIVE-TOPOLOGY/domain_data.ma
@@ -0,0 +1,40 @@
+(**************************************************************************)
+(*       ___                                                              *)
+(*      ||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/domain_data".
+
+include "../../library/datatypes/constructors.ma".
+include "../../library/datatypes/bool.ma".
+include "domain_defs.ma".
+
+(* QUANTIFICATION DOMAINS
+   - Here we define some useful domains based on data types
+*)
+
+definition DBool : Domain \def
+   mk_Domain (mk_Class bool (true_f ?) (eq ?)).
+
+definition dbool_ixfam : \forall (C:Class). C \to C \to (DBool \to C) \def
+   \lambda C,c0,c1,b.
+   match b in bool with 
+      [ false \Rightarrow c0
+      | true \Rightarrow c1
+      ].
+
+definition DVoid : Domain \def
+   mk_Domain (mk_Class void (true_f ?) (eq ?)).
+
+definition dvoid_ixfam : \forall (C:Class). (DVoid \to C) \def
+   \lambda C,v.
+   match v in void with [].
-- 
2.39.2