20 lines
383 B
Text
20 lines
383 B
Text
mutual def even, odd
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with even : nat → bool
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| 0 := tt
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| (a+1) := odd a
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with odd : nat → bool
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| 0 := ff
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| (a+1) := even a
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example (a : nat) : even (a + 1) = odd a :=
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by simp [even]
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example (a : nat) : odd (a + 1) = even a :=
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by simp [odd]
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lemma even_eq_not_odd : ∀ a, even a = bnot (odd a) :=
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begin
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intro a, induction a,
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simp [even, odd],
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simph [even, odd]
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end
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