intros P a b H' H'0.
apply pbuchf_Inv with (P := P); auto.
Qed.

Theorem reds_SpolyQ :
forall (P : list (poly A0 eqA ltM)) (a b : poly A0 eqA ltM),
reds a b P ->
Spoly_1 A A0 A1 eqA invA minusA multA divA eqA_dec n ltM ltM_dec P
(s2p A A0 eqA n ltM a) (s2p A A0 eqA n ltM b).