helm/matita/tests/apply.ma

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   3 (*      ||M||                                                             *)
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  11 (*        v         GNU General Public License Version 2                  *)
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  13 (**************************************************************************)
  14
  15 (* test _with_ the WHD on the apply argument *)
  16 set "baseuri" "cic:/matita/tests/apply/".
  17 include "coq.ma".
  18
  19 alias id "not" = "cic:/Coq/Init/Logic/not.con".
  20 alias id "False" = "cic:/Coq/Init/Logic/False.ind#xpointer(1/1)".
  21
  22 theorem b:
  23   \forall x:Prop.
  24   (not x) \to x \to False.
  25 intros.
  26 apply H.
  27 assumption.
  28 qed.
  29
  30 (* test _without_ the WHD on the apply argument *)
  31
  32 alias symbol "eq" (instance 0) = "Coq's leibnitz's equality".
  33
  34 theorem a:
  35   \forall A:Set.
  36   \forall x: A.
  37   not (x=x) \to not (x=x).
  38 intros.
  39 apply H.
  40 qed.