Definition unstratify (n:nat) (p:sinv n) : predicate := 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 _ p (m + S nw) Hm)) (w', e)
        | inright H => T_bot
      end
    end.Definition proof_irr_nat := eq_proofs_unicity dec_eq_nat.

Lemma stratify_unstratify : forall n, stratify n oo unstratify n = id (sinv n).