Section stratifies.
Variable Q:knot * other -> T.
Variable HQ:hered Q.
Fixpoint stratifies (n:nat) : sinv n -> Prop :=
match n as n' return sinv n' -> Prop with
| 0 => fun _ => True
| S n' => fun (p:sinv (S n')) =>
stratifies n' (fst (proj1_sig p)) /\
forall (k:F_sinv n') (o:other), snd (proj1_sig p) (k,o) = Q (existT F_sinv n' k,o)
end.
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 }.