2015-01-06 00:52:30 +00:00
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import data.vector data.prod
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open nat vector prod
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variables {A B : Type}
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2015-02-26 00:20:44 +00:00
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definition unzip : Π {n}, vector (A × B) n → vector A n × vector B n
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| unzip nil := (nil, nil)
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| unzip ((a, b) :: t) := (a :: pr₁ (unzip t), b :: pr₂ (unzip t))
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2015-01-06 00:52:30 +00:00
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theorem unzip_nil : unzip nil = (@nil A, @nil B) :=
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rfl
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theorem unzip_cons {n : nat} (a : A) (b : B) (t : vector (A × B) n) :
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unzip ((a, b) :: t) = (a :: pr₁ (unzip t), b :: pr₂ (unzip t)) :=
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rfl
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