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4 (* ||A|| A project by Andrea Asperti *)
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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".
30 (\exists b:stupidtype.a = Next b)
32 (\exists c,d:stupidtype.a = Pair c d).
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.