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4 (* ||A|| A project by Andrea Asperti *)
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7 (* ||T|| The HELM team. *)
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15 set "baseuri" "cic:/matita/tests/elim".
17 inductive stupidtype: Set \def
19 | Next : stupidtype \to stupidtype
20 | Pair : stupidtype \to stupidtype \to stupidtype.
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)".
33 (\exists b:stupidtype.a = Next b)
35 (\exists c,d:stupidtype.a = Pair c d).
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.
46 theorem t: 0=0 \to stupidtype.
47 intros; constructor 1.
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.