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 unstratify_Q : forall n (p:sinv n) Q, stratifies Q n p -> forall (k:knot) o, projT1 k < n -> (unstratify n p (k,o) <-> Q (k,o)).