some renaming

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

diff --git a/helm/matita/contribs/PREDICATIVE-TOPOLOGY/subset_defs.ma b/helm/matita/contribs/PREDICATIVE-TOPOLOGY/subset_defs.ma
new file mode 100644 (file)
index 0000000..2ae2471
--- /dev/null
+++ b/helm/matita/contribs/PREDICATIVE-TOPOLOGY/subset_defs.ma
@@ -0,0 +1,43 @@
+(**************************************************************************)
+(*       ___                                                              *)
+(*      ||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/subset_defs".
+
+include "domain_defs.ma".
+
+(* SUBSETS
+   - We use predicative subsets coded as propositional functions
+     according to G.Sambin and S.Valentini "Toolbox" 
+*)
+
+definition Subset \def \lambda (D:Domain). D \to Prop.
+
+(* subset inclusion *) 
+definition ssub: \forall D. Subset D \to Subset D \to Prop \def 
+   \lambda D,U1,U2. \forall d. U1 d \to U2 d. 
+
+
+(* subset overlap *) 
+definition sover: \forall D. Subset D \to Subset D \to Prop \def 
+   \lambda D,U1,U2. \forall d. U1 d \to U2 d. 
+
+
+
+(* full subset: "subset top" *)
+definition stop \def \lambda (D:Domain). \lambda (_:D). True.
+
+coercion stop.
+
+(* empty subset: "subset bottom" *)
+definition sbot \def \lambda (D:Domain). \lambda (_:D). False.
\ No newline at end of file