some renaming

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

diff --git a/helm/matita/contribs/PREDICATIVE-TOPOLOGY/domain_defs.ma b/helm/matita/contribs/PREDICATIVE-TOPOLOGY/domain_defs.ma
new file mode 100644 (file)
index 0000000..821002e
--- /dev/null
+++ b/helm/matita/contribs/PREDICATIVE-TOPOLOGY/domain_defs.ma
@@ -0,0 +1,64 @@
+(**************************************************************************)
+(*       ___                                                              *)
+(*      ||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_defs".
+
+include "class_defs.ma".
+
+(* QUANTIFICATION DOMAINS
+   - These are the categories on which we allow quantification
+   - We set up single quantifiers, parametric on the domain, so they
+     already have the properties  that usually are axiomatized inside the 
+     domain structure. This makes domains easier to use
+*)
+
+
+
+record Domain: Type \def {
+   qd: Class
+}.
+
+coercion qd.
+
+
+
+(* internal universal quantification *)
+inductive iall (D:Domain) (P:D \to Prop) : Prop \def
+   | iall_intro: (\forall d:D. cin D d \to P d) \to iall D P.
+
+(*CSC: the URI must disappear: there is a bug now *)
+interpretation "internal for all" 'iall \eta.x =
+  (cic:/matita/PREDICATIVE-TOPOLOGY/domain_defs/iall.ind#xpointer(1/1) _ x).
+
+notation < "hvbox(\iall ident i opt (: ty) break . p)"
+  right associative with precedence 20
+for @{ 'iall ${default
+  @{\lambda ${ident i} : $ty. $p)}
+  @{\lambda ${ident i} . $p}}}.
+
+
+
+(* internal existential quantification *)
+inductive iex (D:Domain) (P:D \to Prop) : Prop \def
+   | iex_intro: \forall d:D. cin D d \land P d \to iex D P.
+
+(*CSC: the URI must disappear: there is a bug now *)
+interpretation "internal exist" 'iexist \eta.x =
+  (cic:/matita/PREDICATIVE-TOPOLOGY/domain_defs/iex.ind#xpointer(1/1) _ x).
+
+notation < "hvbox(\iexist ident i opt (: ty) break . p)"
+  right associative with precedence 20
+for @{ 'iexist ${default
+  @{\lambda ${ident i} : $ty. $p)}
+  @{\lambda ${ident i} . $p}}}.