Definition proof_irr_nat := eq_proofs_unicity dec_eq_nat.Program Definition unstratify (n:nat) : Mor (projT2 (sinv n)) predS :=
    Build_Mor _ _ (fun p =>
      Build_Mor _ _ (fun w =>
      match w with (existT nw w',e) =>
        match decompose_nat nw n with
          | inleft (existT m Hm) => snd (floor m (S nw) (eq_rect n (fun x => projT1 (sinv x)) p (m + S nw) Hm)) (w', e)
          | inright H => T_bot
        end
      end) _) _.

Lemma stratify_unstratify_more : forall n m1 m2 p1 p2, @equiv _ (projT2 (sinv n)) (floor m1 n p1) (floor m2 n p2) -> @equiv _ (projT2 (sinv n)) (stratify n (unstratify (m1+n) p1)) (stratify n (unstratify (m2+n) p2)).