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[helm.git] / matita / tests / inversion2.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".
+
+inductive nat : Set \def
+   O : nat
+ | S : nat \to nat.
+
+
+inductive le (n:nat) : nat \to Prop \def
+   leO : le n n
+ | leS : \forall m. le n m \to le n (S m).
+ 
+theorem le_inv2:
+ \forall n,m.
+  \forall P: nat -> nat -> Prop.
+   ? -> ? -> le n m -> P n m.
+[7:
+  intros;
+  inversion H;
+  [ apply x
+  | simplify;
+    apply x1
+  ]
+| skip
+| skip
+| skip
+| skip
+| skip
+| skip
+]
+qed.
+
+inductive ledx : nat \to nat \to Prop \def
+   ledxO : \forall n. ledx n n
+ | ledxS : \forall m.\forall n. ledx n m \to ledx n (S m).
+
+
+alias symbol "eq" (instance 0) = "Coq's leibnitz's equality".
+
+theorem test_inversion: \forall n. le n O \to n=O.
+ intros.
+ inversion H.
+ (* cut n=n \to O=O \to n=O.
+  apply Hcut; reflexivity. *)
+  (* elim H. BUG DI UNSHARING *)
+  (*apply (ledx_ind (\lambda x.\lambda y.  n=x \to O=y \to x=y) ? ? ? ? H).*)
+    simplify. intros. reflexivity.    
+    simplify. intros. destruct H3.
+qed.