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import Data.Vect data Insert : elem -> Vect n elem -> Vect (S n) elem -> Type where IHere : Insert x xs (x :: xs) ILater : Insert x xs ys -> Insert x (m :: xs) (m :: ys) total insert_append : (as : Vect n elem) -> (x : elem) -> (bs : Vect m elem) -> Insert x (as ++ bs) (rewrite plusSuccRightSucc n m in as ++ x :: bs) insert_append [] x bs = IHere insert_append {n = S k} {m} (a :: as) x bs = let IH = insert_append as x bs in ILater {m = a} {x = x} {xs = as ++ bs} {ys = rewrite plusSuccRightSucc k m in as ++ x :: bs} (?cvt) |