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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 set "baseuri" "cic:/matita/tests/paramodulation".
16 alias id "nat" = "cic:/Coq/Init/Datatypes/nat.ind#xpointer(1/1)".
17 alias symbol "eq" (instance 0) = "leibnitz's equality".
18 alias symbol "plus" (instance 0) = "natural plus".
19 alias num (instance 0) = "natural number".
20 alias symbol "times" (instance 0) = "natural times".
21
22 theorem para1:
23   \forall n,m,n1,m1:nat.
24     n=m \to n1 = m1 \to (n + n1) = (m + m1).
25 intros. auto.
26 qed.
27
28 theorem para2:
29   \forall n:nat. n + n = 2 * n.
30 intros. auto.
31 qed.