21 lines
496 B
Text
21 lines
496 B
Text
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inductive Vec.{u} (α : Type u) : Nat → Type u
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| nil : Vec α 0
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| cons : α → {n : Nat} → Vec α n → Vec α (n+1)
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open Vec
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universes u
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variable {α : Type u}
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variable (f : α → α → α)
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def mapHead1 : {n : Nat} → Vec α n → Vec α n → Vec α n
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| _, nil, nil => nil
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| _, cons a va, cons b bv => cons (f a b) va
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theorem ex1 : mapHead1 f nil nil = nil :=
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rfl
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theorem ex2 (a b : α) (n : Nat) (va vb : Vec α n) : mapHead1 f (cons a va) (cons b vb) = cons (f a b) va :=
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rfl
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