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[helm.git] / matita / contribs / LOGIC / Insert / fun.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 "CLE/defs.ma".
+include "Insert/inv.ma".
+
+(* Functional properties ****************************************************)
+(*
+theorem insert_total: \forall S,i,P. i <= P \to \exists Q. Insert S i P Q.
+ intros 4; elim H; clear H i P;
+ decompose; autobatch.
+qed.  
+
+theorem insert_inj: \forall S1,i,P, Q. Insert S1 i P Q \to 
+                    \forall S2. Insert S2 i P Q \to S1 = S2.
+ intros 5; elim H; clear H i P Q;
+ [ lapply linear insert_inv_zero to H1; destruct; autobatch
+ | lapply linear insert_inv_succ to H3; decompose; destruct; autobatch
+ ].
+qed.
+*)