helm/matita/tests/elim.ma

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   2 (*       ___                                                              *)
   3 (*      ||M||                                                             *)
   4 (*      ||A||       A project by Andrea Asperti                           *)
   5 (*      ||T||                                                             *)
   6 (*      ||I||       Developers:                                           *)
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   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/elim".
  16 include "coq.ma".
  17
  18 inductive stupidtype: Set \def
  19   | Base : stupidtype
  20   | Next : stupidtype \to stupidtype
  21   | Pair : stupidtype \to stupidtype \to stupidtype.
  22
  23 alias symbol "eq" (instance 0) = "Coq's leibnitz's equality".
  24 alias symbol "exists" (instance 0) = "Coq's exists".
  25 alias symbol "or" (instance 0) = "Coq's logical or".
  26 alias num (instance 0) = "natural number".
  27 alias id "True" = "cic:/Coq/Init/Logic/True.ind#xpointer(1/1)".
  28 alias id "refl_equal" = "cic:/Coq/Init/Logic/eq.ind#xpointer(1/1/1)".
  29
  30 theorem serious:
  31   \forall a:stupidtype.
  32     a = Base
  33   \lor
  34     (\exists b:stupidtype.a = Next b)
  35   \lor
  36     (\exists c,d:stupidtype.a = Pair c d).
  37 intros.
  38 elim a.
  39 clear a.left.left.
  40   reflexivity.
  41 clear H.clear H1.clear a.right.
  42   exists.exact s.exists.exact s1.reflexivity.
  43 clear H.clear a.left.right.
  44   exists.exact s.reflexivity.
  45 qed.
  46
  47 theorem t: 0=0 \to stupidtype.
  48  intros; constructor 1.
  49 qed.
  50
  51 (* In this test "elim t" should open a new goal 0=0 and put it in the *)
  52 (* goallist so that the THEN tactical closes it using reflexivity.    *)
  53 theorem foo: let ax \def refl_equal ? 0 in t ax = t ax.
  54  elim t; reflexivity.
  55 qed.