helm/matita/tests/elim.ma

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   2 (*       ___                                                                *)
   3 (*      ||M||                                                             *)
   4 (*      ||A||       A project by Andrea Asperti                           *)
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  10 (*       \ /        This file is distributed under the terms of the       *)
  11 (*        v         GNU General Public License Version 2                  *)
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  13 (**************************************************************************)
  14
  15 set "baseuri" "cic:/matita/tests/elim".
  16
  17 inductive stupidtype: Set \def
  18   | Base : stupidtype
  19   | Next : stupidtype \to stupidtype
  20   | Pair : stupidtype \to stupidtype \to stupidtype.
  21
  22 alias symbol "eq" (instance 0) = "leibnitz's equality".
  23 alias symbol "exists" (instance 0) = "exists".
  24 alias symbol "or" (instance 0) = "logical or".
  25 alias num (instance 0) = "natural number".
  26 alias id "True" = "cic:/Coq/Init/Logic/True.ind#xpointer(1/1)".
  27 alias id "refl_equal" = "cic:/Coq/Init/Logic/eq.ind#xpointer(1/1/1)".
  28
  29 theorem serious:
  30   \forall a:stupidtype.
  31     a = Base
  32   \lor
  33     (\exists b:stupidtype.a = Next b)
  34   \lor
  35     (\exists c,d:stupidtype.a = Pair c d).
  36 intros.
  37 elim a.
  38 clear a.left.left.
  39   reflexivity.
  40 clear H.clear H1.clear a.right.
  41   exists.exact e2.exists.exact e1.reflexivity.
  42 clear H.clear a.left.right.
  43   exists.exact e3.reflexivity.
  44 qed.
  45
  46 theorem t: 0=0 \to stupidtype.
  47  intros; constructor 1.
  48 qed.
  49
  50 (* In this test "elim t" should open a new goal 0=0 and put it in the *)
  51 (* goallist so that the THEN tactical closes it using reflexivity.    *)
  52 theorem foo: let ax \def refl_equal ? 0 in t ax = t ax.
  53  elim t; reflexivity.
  54 qed.