14 lines
430 B
Text
14 lines
430 B
Text
open nat
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theorem ex1 (n : nat) : bit0 n ≠ 1 :=
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nat.cases_on n
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(show 0 ≠ 1, from ne.symm nat.one_ne_zero)
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(λ m h1,
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have h2 : succ (succ (m + m)) = 1, from nat.succ_add m m ▸ h1,
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nat.no_confusion h2 (λ h3, absurd h3 (nat.succ_ne_zero (m + m))))
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theorem ex2 (n : nat) : succ n ≠ 0 :=
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λ h, nat.no_confusion h
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theorem ex3 (n : nat) : succ (succ n) ≠ 1 :=
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λ h, nat.no_confusion h (λ h, nat.no_confusion h)
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