19 lines
489 B
Text
19 lines
489 B
Text
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inductive vec (A : Type) : nat → Type
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| nil {} : vec 0
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| cons : Π {n}, A → vec n → vec (n+1)
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open vec
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variables {A : Type}
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variables f : A → A → A
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definition map_head_1 : ∀ {n}, vec A n → vec A n → vec A n
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| .0 nil nil := nil
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| .(n+1) (@cons .A n a va) (cons b vb) := cons (f a b) va
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example : map_head_1 f nil nil = nil :=
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rfl
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example (a b : A) (n : nat) (va vb : vec A n) : map_head_1 f (cons a va) (cons b vb) = cons (f a b) va :=
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rfl
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