2014-10-31 20:15:21 +00:00
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import logic
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inductive Three :=
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zero : Three,
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one : Three,
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two : Three
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namespace Three
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theorem disj (a : Three) : a = zero ∨ a = one ∨ a = two :=
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rec (or.inl rfl) (or.inr (or.inl rfl)) (or.inr (or.inr rfl)) a
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2014-11-01 23:12:23 +00:00
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example (a : Three) : a ≠ zero → a ≠ one → a = two :=
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2014-10-31 20:15:21 +00:00
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rec (λ h₁ h₂, absurd rfl h₁) (λ h₁ h₂, absurd rfl h₂) (λ h₁ h₂, rfl) a
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end Three
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