helm/matita/tests/elim.ma

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   3 (*      ||M||                                                             *)
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  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
  26 theorem serious:
  27   \forall a:stupidtype.
  28     a = Base
  29   \lor
  30     (\exists b:stupidtype.a = Next b)
  31   \lor
  32     (\exists c,d:stupidtype.a = Pair c d).
  33 intros.
  34 elim a.
  35 clear a.left.left.
  36   reflexivity.
  37 clear H.clear H1.clear a.right.
  38   exists.exact e2.exists.exact e1.reflexivity.
  39 clear H.clear a.left.right.
  40   exists.exact e3.reflexivity.
  41 qed.