helm/matita/tests/replace.ma

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   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/replace/".
  16 include "coq.ma".
  17 alias id "nat" = "cic:/Coq/Init/Datatypes/nat.ind#xpointer(1/1)".
  18 alias num (instance 0) = "natural number".
  19 alias symbol "eq" (instance 0) = "Coq's leibnitz's equality".
  20 alias symbol "plus" (instance 0) = "Coq's natural plus".
  21 alias symbol "times" (instance 0) = "Coq's natural times".
  22 alias id "mult_n_O" = "cic:/Coq/Init/Peano/mult_n_O.con".
  23 alias id "plus_n_O" = "cic:/Coq/Init/Peano/plus_n_O.con".
  24
  25 theorem t: \forall x:nat. x * (x + 0) = (0 + x) * (x + x * 0).
  26  intro.
  27  replace in \vdash (? ? (? ? %) (? % %)) with x.
  28  reflexivity.
  29  rewrite < (mult_n_O x).
  30  rewrite < (plus_n_O x).
  31  reflexivity.
  32  reflexivity.
  33  auto.
  34 qed.
  35
  36 (* This test tests "replace in match t" where t contains some metavariables *)
  37 theorem t2: 2 + (3 * 4) = (5 + 5) + 2 * 2.
  38  replace in match (5+?) with (6 + 4); [reflexivity | reflexivity].
  39 qed.