helm/matita/tests/change.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                  *)
  12 (*                                                                        *)
  13 (**************************************************************************)
  14
  15 set "baseuri" "cic:/matita/tests/change/".
  16 include "coq.ma".
  17 alias num (instance 0) = "natural number".
  18 alias symbol "eq" (instance 0) = "Coq's leibnitz's equality".
  19 alias symbol "plus" (instance 0) = "Coq's natural plus".
  20 alias id "nat" = "cic:/Coq/Init/Datatypes/nat.ind#xpointer(1/1)".
  21
  22 theorem stupid:
  23   \forall a:nat.
  24   a = 5 \to
  25   (3 + 2) = a.
  26 intros.
  27 change in \vdash (? ? % ?) with 5.
  28 rewrite < H in \vdash (? ? % ?).
  29 reflexivity.
  30 qed.
  31
  32 (* tests changing a term under a binder *)
  33 alias id "True" = "cic:/Coq/Init/Logic/True.ind#xpointer(1/1)".
  34 theorem t: (\forall x:nat. x=x) \to True.
  35  intro H.
  36  change in match x in H : (\forall _.%) with (0+x).
  37  change in H: (\forall _.(? ? ? (? % ?))) with 0.
  38  constructor 1.
  39 qed.
  40