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[helm.git] / matita / contribs / dama / dama / constructive_connectives.ma

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+(**************************************************************************)
+(*       ___                                                              *)
+(*      ||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                  *)
+(*                                                                        *)
+(**************************************************************************)
+
+include "logic/connectives.ma".
+
+inductive Or (A,B:Type) : Type ≝
+   Left : A → Or A B
+ | Right : B → Or A B.
+
+interpretation "constructive or" 'or x y =
+  (cic:/matita/constructive_connectives/Or.ind#xpointer(1/1) x y).
+
+inductive And (A,B:Type) : Type ≝
+ | Conj : A → B → And A B.
+ 
+interpretation "constructive and" 'and x y =
+  (cic:/matita/constructive_connectives/And.ind#xpointer(1/1) x y).
+
+inductive exT (A:Type) (P:A→Type) : Type ≝
+  ex_introT: ∀w:A. P w → exT A P.
+
+inductive ex (A:Type) (P:A→Prop) : Type ≝
+  ex_intro: ∀w:A. P w → ex A P.
+
+(*
+notation < "hvbox(Σ ident i opt (: ty) break . p)"
+  right associative with precedence 20
+for @{ 'sigma ${default
+  @{\lambda ${ident i} : $ty. $p)}
+  @{\lambda ${ident i} . $p}}}.
+*)
+
+interpretation "constructive exists" 'exists \eta.x =
+  (cic:/matita/constructive_connectives/ex.ind#xpointer(1/1) _ x).
+interpretation "constructive exists (Type)" 'exists \eta.x =
+  (cic:/matita/constructive_connectives/exT.ind#xpointer(1/1) _ x).
+
+alias id "False" = "cic:/matita/logic/connectives/False.ind#xpointer(1/1)".
+definition Not ≝ λx:Type.x → False.
+
+interpretation "constructive not" 'not x = 
+  (cic:/matita/constructive_connectives/Not.con x).