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[helm.git] / matita / tests / paramodulation / group.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 "eq" = "cic:/Coq/Init/Logic/eq.ind#xpointer(1/1)".
+alias id "eq_ind" = "cic:/Coq/Init/Logic/eq_ind.con".
+alias id "eq_ind_r" = "cic:/Coq/Init/Logic/eq_ind_r.con".
+alias id "sym_eq" = "cic:/Coq/Init/Logic/sym_eq.con".
+
+
+theorem self:
+  \forall A:Set.
+  \forall f,g:A \to A.
+  \forall H:(\forall x,y:A. x = y).
+  \forall H:(\forall x,y,z:A. f x = y).
+  \forall x,y:A. x=y.
+intros.autobatch paramodulation.
+qed.
+
+theorem GRP049_simple:
+  \forall A:Set.
+  \forall inv: A \to A.
+  \forall mult: A \to A \to A.
+  \forall H: (\forall x,y,z:A.mult z (inv (mult (inv (mult (inv (mult z y)) x)) (inv (mult y (mult (inv y) y))))) = x).
+  \forall a,b:A. mult (inv a) a = mult (inv b) b.
+intros.autobatch paramodulation; exact a.
+qed.
+
+theorem GRP049 :
+  \forall A:Set.
+  \forall inv: A \to A.
+  \forall mult: A \to A \to A.
+  \forall H: (\forall x,y,z:A.mult z (inv (mult (inv (mult (inv (mult z y)) x)) (inv (mult y (mult (inv y) y))))) = x).
+  \forall a,b:A. mult a (inv a)= mult b (inv b).
+intros.autobatch paramodulation timeout = 600;exact a.
+qed.