helm/matita/tests/paramodulation.ma

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   3 (*      ||M||                                                             *)
   4 (*      ||A||       A project by Andrea Asperti                           *)
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  11 (*        v         GNU General Public License Version 2                  *)
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  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.