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[helm.git] / helm / matita / tests / unfold.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                  *)
+(*                                                                        *)
+(**************************************************************************)
+
+set "baseuri" "cic:/matita/unfold".
+
+include "legacy/coq.ma".
+
+alias symbol "plus" (instance 0) = "Coq's natural plus".
+definition myplus \def \lambda x,y. x+y.
+
+alias id "S" = "cic:/Coq/Init/Datatypes/nat.ind#xpointer(1/1/2)".
+lemma lem: \forall n. S (n + n) = (S n) + n.
+ intro; reflexivity.
+qed.
+
+theorem trivial: \forall n. S (myplus n n) = myplus (S n) n.
+ unfold myplus in \vdash (\forall _.(? ? ? %)).
+ intro.
+ unfold myplus.
+ rewrite > lem.
+ reflexivity.
+qed.
+
+(* This test needs to parse "uno" in the context of the hypothesis H,
+   not in the context of the goal. *)
+alias id "O" = "cic:/Coq/Init/Datatypes/nat.ind#xpointer(1/1/1)".
+theorem t: let uno \def S O in uno + uno = S uno \to uno=uno.
+ intros. unfold uno in H.
+ reflexivity.
+qed.