Definition unstratify (n:nat) (p:sinv n) : knot * other -> Prop := fun w =>
    match w with (existT _ nw w',o) =>
      match decompose_nat nw n with
        | inleft (existT _ m Hm) => snd (proj1_sig (floor m (S nw) (eq_rect  n _ p (m + S nw) Hm))) (w',o)
        | inright H => False
      end
    end.

Lemma stratifies_unstratify_more : forall (n m1 m2:nat) (p1:sinv (m1+n)) (p2:sinv (m2+n)), floor m1 n p1 = floor m2 n p2 -> (stratifies (unstratify (m1+n) p1) n (floor m1 n p1) -> stratifies (unstratify (m2+n) p2) n (floor m2 n p2)).