Definition stratify (n:nat) : { x:sinv n | stratifies n x }.
End stratifies.

Lemma decompose_nat : forall (x y:nat), { m:nat & y = (m + S x) } + { ge x y }.
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.