23 lines
579 B
Text
23 lines
579 B
Text
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import data.vector
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open nat vector
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variable {A : Type}
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definition rev : Π {n : nat}, vector A n → vector A n
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| ⌞0⌟ [] := []
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| ⌞n+1⌟ (x :: xs) := concat (rev xs) x
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theorem rev_concat : Π {n : nat} (xs : vector A n) (a : A), rev (concat xs a) = a :: rev xs
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| 0 [] a := rfl
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| (n+1) (x :: xs) a :=
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begin
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unfold [concat, rev], rewrite rev_concat
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end
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theorem rev_rev : Π {n : nat} (xs : vector A n), rev (rev xs) = xs
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| 0 [] := rfl
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| (n+1) (x :: xs) :=
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begin
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unfold rev at {1}, krewrite rev_concat, rewrite rev_rev
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end
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