X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=helm%2Fmatita%2Ftests%2Finversion.ma;h=4f8c4c6d42b6560bd04872e007892776bab10ab0;hb=33a02e0b639217093eb63f30169aaa6ac8c78907;hp=5f173344454084a0f2fd296b9732d4ba2f16729c;hpb=d9394782ed9580f3565eb9b4682d8348aae6349e;p=helm.git

diff --git a/helm/matita/tests/inversion.ma b/helm/matita/tests/inversion.ma
index 5f1733444..4f8c4c6d4 100644
--- a/helm/matita/tests/inversion.ma
+++ b/helm/matita/tests/inversion.ma
@@ -1,4 +1,19 @@
-set "baseuri" "cic:/matita/tests/".
+(**************************************************************************)
+(*       ___                                                              *)
+(*      ||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/tests/inversion/".
+include "coq.ma".
 
 inductive nat : Set \def
    O : nat
@@ -8,17 +23,41 @@ inductive le (n:nat) : nat \to Prop \def
    leO : le n n
  | leS : \forall m. le n m \to le n (S m).
 
-alias symbol "eq" (instance 0) = "leibnitz's equality".
+alias symbol "eq" (instance 0) = "Coq's leibnitz's equality".
 
 theorem test_inversion: \forall n. le n O \to n=O.
  intros.
+ (* inversion begins *)
  cut O=O.
   (* goal 2: 0 = 0 *)
   goal 7. reflexivity.
   (* goal 1 *)
-  generalize Hcut.      (* non attaccata. Dovrebbe dare 0=0 -> n=0 *)
+  generalize in match Hcut.
   apply (le_ind ? (\lambda x. O=x \to n=x) ? ? ? H).
-  intro. reflexivity.
+  (* first goal (left open) *)
+  intro. rewrite < H1.
+  clear Hcut.
+  (* second goal (closed) *)
+  goal 14.
   simplify. intros.
   discriminate H3.
+  (* inversion ends *)
+  reflexivity.
+qed.
+
+(* Piu' semplice e non lascia l'ipotesi inutile Hcut *)
+alias id "refl_equal" = "cic:/Coq/Init/Logic/eq.ind#xpointer(1/1/1)".
+theorem test_inversion2: \forall n. le n O \to n=O.
+ intros.
+ (* inversion begins *)
+ generalize in match (refl_equal nat O).
+ apply (le_ind ? (\lambda x. O=x \to n=x) ? ? ? H).
+ (* first goal (left open) *)
+ intro. rewrite < H1.
+ (* second goal (closed) *)
+ goal 13.
+ simplify. intros.
+ discriminate H3.
+ (* inversion ends *)
+ reflexivity.
 qed.