32 lines
790 B
Text
32 lines
790 B
Text
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import data.vector
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open nat vector
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check lt.base
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set_option pp.implicit true
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definition add : nat → nat → nat,
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add zero b := b,
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add (succ a) b := succ (add a b)
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definition map {A B C : Type} (f : A → B → C) : Π {n}, vector A n → vector B n → vector C n,
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map nil nil := nil,
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map (a :: va) (b :: vb) := f a b :: map va vb
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definition fib : nat → nat,
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fib 0 := 1,
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fib 1 := 1,
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fib (a+2) := (fib a ↓ lt.step (lt.base a)) + (fib (a+1) ↓ lt.base (a+1))
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[wf] lt.wf
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definition half : nat → nat,
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half 0 := 0,
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half 1 := 0,
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half (x+2) := half x + 1
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variables {A B : Type}
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inductive image_of (f : A → B) : B → Type :=
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mk : Π a, image_of f (f a)
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definition inv {f : A → B} : Π b, image_of f b → A,
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inv ⌞f a⌟ (image_of.mk f a) := a
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