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[helm.git] / helm / matita / library / datatypes / constructors.ma

diff --git a/helm/matita/library/datatypes/constructors.ma b/helm/matita/library/datatypes/constructors.ma
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+(**************************************************************************)
+(*       ___                                                               *)
+(*      ||M||                                                             *)
+(*      ||A||       A project by Andrea Asperti                           *)
+(*      ||T||                                                             *)
+(*      ||I||       Developers:                                           *)
+(*      ||T||       A.Asperti, C.Sacerdoti Coen,                          *)
+(*      ||A||       E.Tassi, S.Zacchiroli                                 *)
+(*      \   /                                                             *)
+(*       \ /        This file is distributed under the terms of the       *)
+(*        v         GNU Lesser General Public License Version 2.1         *)
+(*                                                                        *)
+(**************************************************************************)
+
+set "baseuri" "cic:/matita/datatypes/constructors/".
+include "logic/equality.ma".
+
+inductive void : Set \def.
+
+inductive Prod (A,B:Set) : Set \def
+pair : A \to B \to Prod A B.
+
+definition fst \def \lambda A,B:Set.\lambda p: Prod A B.
+match p with
+[(pair a b) \Rightarrow a]. 
+
+definition snd \def \lambda A,B:Set.\lambda p: Prod A B.
+match p with
+[(pair a b) \Rightarrow b].
+
+theorem eq_pair_fst_snd: \forall A,B:Set.\forall p: Prod A B.
+p = pair A B (fst A B p) (snd A B p).
+intros.elim p.simplify.reflexivity.
+qed.
+
+inductive Sum (A,B:Set) : Set \def
+  inl : A \to Sum A B
+| inr : B \to Sum A B.