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