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import Data.Vect partition_condition : (f : elem -> Bool) -> (v : Vect n elem) -> Type partition_condition {n} f v = case partition f v of ((z1 ** pt), (z2 ** pf)) => z1 + z2 = n total partition_length : (f : elem -> Bool) -> (v : Vect n elem) -> partition_condition f v partition_length f [] = Refl partition_length f (x :: xs) with (partition_length f xs) | IH with (partition f xs) | ((p ** vt), (q ** vf)) with (f x) | False = rewrite sym (plusSuccRightSucc p q) in rewrite IH in Refl | True = rewrite IH in Refl |