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1 (**************************************************************************)
2 (*       ___                                                              *)
3 (*      ||M||                                                             *)
4 (*      ||A||       A project by Andrea Asperti                           *)
5 (*      ||T||                                                             *)
6 (*      ||I||       Developers:                                           *)
7 (*      ||T||         The HELM team.                                      *)
8 (*      ||A||         http://helm.cs.unibo.it                             *)
9 (*      \   /                                                             *)
10 (*       \ /        This file is distributed under the terms of the       *)
11 (*        v         GNU General Public License Version 2                  *)
12 (*                                                                        *)
13 (**************************************************************************)
14
15
16 include "coq.ma".
17
18 alias id "O" = "cic:/Coq/Init/Datatypes/nat.ind#xpointer(1/1/1)".
19 alias id "S" = "cic:/Coq/Init/Datatypes/nat.ind#xpointer(1/1/2)".
20 alias id "nat" = "cic:/Coq/Init/Datatypes/nat.ind#xpointer(1/1)".
21 alias symbol "eq" (instance 0) = "Coq's leibnitz's equality".
22 alias symbol "minus" (instance 0) = "Coq's natural minus".
23 alias symbol "plus" (instance 0) = "Coq's natural plus".
24 alias symbol "times" (instance 0) = "Coq's natural times".
25 theorem a : \forall x,y:nat. x*x+(S y) = O - x.
26 intros.
27 auto new depth = 4 width = 3 use_paramod = false.