2014-02-02 02:27:14 +00:00
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import tactic
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2014-01-05 20:05:08 +00:00
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definition xor (x y : Bool) : Bool := (not x) = y
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infixr 50 ⊕ : xor
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2014-01-05 19:03:35 +00:00
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print xor true false
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2014-01-05 20:05:08 +00:00
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variable a : Bool
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2014-01-05 19:03:35 +00:00
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print a ⊕ a ⊕ a
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2014-01-06 03:10:21 +00:00
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check @subst
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2014-01-05 20:05:08 +00:00
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theorem EM2 (a : Bool) : a \/ (not a) :=
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2014-02-02 02:27:14 +00:00
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case (fun x : Bool, x \/ (not x)) (by simp) (by simp) a
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2014-01-05 20:05:08 +00:00
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check EM2
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check EM2 a
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2014-02-02 02:27:14 +00:00
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theorem xor_neq (a b : Bool) : (a ⊕ b) ↔ ((¬ a) = b)
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:= refl (a ⊕ b)
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