16 lines
538 B
Text
16 lines
538 B
Text
open nat
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inductive vector (A : Type) : nat → Type :=
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| nil {} : vector A zero
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| cons : Π {n}, A → vector A n → vector A (succ n)
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infixr `::` := vector.cons
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definition swap {A : Type} : Π {n}, vector A (succ (succ n)) → vector A (succ (succ n))
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| swap (a :: b :: vs) := b :: a :: vs
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-- Remark: in the current approach for HoTT, the equation
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-- swap (a :: b :: v) = b :: a :: v
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-- holds definitionally only when the index is a closed term.
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example (a b : num) (v : vector num 5) : swap (a :: b :: v) = b :: a :: v :=
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rfl
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