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[helm.git] / matita / tests / dependent_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 ttree : Type → Type :=
+   tempty: ttree nat
+ | tnode : ∀A. ttree A → ttree A → ttree A.
+
+(* CSC: there is an undecidable unification problem here:
+    consider a constructor k : \forall x. f x -> i (g x)
+    The head of the outtype of the injection MutCase should be (f ?1)
+    such that (f ?1) unifies with (g d) [ where d is the Rel that binds
+    the corresponding right parameter in the outtype ]
+    Coq dodges the problem by generating an equality between sigma-types
+    (that state the existence of a ?1 such that ...) *)
+theorem injection_test3:
+ ∀t,t'. tnode nat t tempty = tnode nat t' tempty → t = t'.
+ intros.
+ destruct H.
+ reflexivity.
+qed.
+
+theorem injection_test3:
+ ∀t,t'.
+  tnode nat (tnode nat t t') tempty = tnode nat (tnode nat t' tempty) tempty →
+   t = t'.
+ intros;
+ destruct H;
+ assumption.
+qed.