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[helm.git] / matita / tests / injection.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 "coq.ma".
+
+alias id "nat" = "cic:/Coq/Init/Datatypes/nat.ind#xpointer(1/1)".
+alias id "bool" = "cic:/Coq/Init/Datatypes/bool.ind#xpointer(1/1)".
+alias id "S" = "cic:/Coq/Init/Datatypes/nat.ind#xpointer(1/1/2)".
+
+inductive t0 : Type :=
+   k0 : nat → nat → t0
+ | k0' : bool → bool → t0.
+
+theorem injection_test0: ∀n,n',m,m'. k0 n m = k0 n' m' → m = m'.
+ intros;
+ destruct H;
+ reflexivity.
+qed.
+
+inductive t : Type → Type :=
+   k : nat → t nat
+ | k': bool → t bool.
+ 
+theorem injection_test1: ∀n,n'. k n = k n' → n = n'.
+ intros;
+ destruct H;
+ reflexivity.
+qed.
+
+inductive tt (A:Type) : Type -> Type :=
+   k1: nat → nat → tt A nat
+ | k2: bool → bool → tt A bool.
+ 
+theorem injection_test2: ∀n,n',m,m'. k1 bool n n' = k1 bool m m' → n' = m'.
+ intros;
+ destruct H;
+ reflexivity.
+qed.
+
+inductive ttree : Type → Type :=
+   tempty: ttree nat
+ | tnode : ∀A. ttree A → ttree A → ttree A.
+
+theorem injection_test4:
+ ∀n,n',m,m'. k1 bool (S n) (S (S m)) = k1 bool (S n') (S (S (S m'))) → m = S m'.
+ intros;
+ destruct H;
+ reflexivity.
+qed.