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

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)).