2015-08-12 22:05:14 +00:00
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import data.examples.vector
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2015-01-05 01:57:25 +00:00
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open nat vector
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2015-02-26 00:20:44 +00:00
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definition diag {A : Type} : Π {n}, vector (vector A n) n → vector A n
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| diag nil := nil
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| diag ((a :: va) :: vs) := a :: diag (map tail vs)
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2015-01-05 01:57:25 +00:00
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theorem diag_nil (A : Type) : diag (@nil (vector A 0)) = nil :=
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rfl
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theorem diag_succ {A : Type} {n : nat} (a : A) (va : vector A n) (vs : vector (vector A (succ n)) n) :
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diag ((a :: va) :: vs) = a :: diag (map tail vs) :=
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rfl
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