Created
October 6, 2016 19:02
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Theorem foo : [(n : nat) -> (x : =(zero; succ(n); nat)) -> =(zero; succ(n); nat)] { | |
intro; aux {auto}; | |
intro; aux {auto}; | |
hypothesis #2 ||| works just fine here | |
}. | |
Operator is-zero : (0). | |
[is-zero(n)] =def= [natrec(n; unit; _._. void)]. | |
Theorem succ-not-zero : [(n : nat) -> =(succ(n); zero; nat) -> void] { | |
auto; | |
assert [is-zero(succ(n))]; | |
aux { | |
unfold <is-zero>; | |
subst [=(succ(n); zero; nat)] [h. natrec(h; _; _._. _)]; auto; | |
aux { hypothesis #2 }; ||| fails with seemingly identical sequent here | |
reduce; auto | |
}; | |
unfold <is-zero>; reduce; auto | |
}. |
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