helm/software/matita/tests/paramodulation.ma

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   3 (*      ||M||                                                             *)
   4 (*      ||A||       A project by Andrea Asperti                           *)
   5 (*      ||T||                                                             *)
   6 (*      ||I||       Developers:                                           *)
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  10 (*       \ /        This file is distributed under the terms of the       *)
  11 (*        v         GNU General Public License Version 2                  *)
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  13 (**************************************************************************)
  14
  15 set "baseuri" "cic:/matita/tests/paramodulation".
  16 include "../legacy/coq.ma".
  17 alias id "nat" = "cic:/Coq/Init/Datatypes/nat.ind#xpointer(1/1)".
  18 alias symbol "eq" (instance 0) = "Coq's leibnitz's equality".
  19 alias symbol "plus" (instance 0) = "Coq's natural plus".
  20 alias num (instance 0) = "natural number".
  21 alias symbol "times" (instance 0) = "Coq's natural times".
  22
  23 theorem para1:
  24   \forall n,m,n1,m1:nat.
  25     n=m \to n1 = m1 \to (n + n1) = (m + m1).
  26 intros. auto paramodulation.
  27 qed.
  28
  29 theorem para2:
  30   \forall n:nat. n + n = 2 * n.
  31 intros. auto paramodulation.
  32 qed.