intros Q p H' H'0; auto.
apply reducestar0; auto.
apply Rstar_0; auto.
apply pO_irreducible.
Qed.

Theorem reducestar_in_pO :
forall (Q : list (poly A0 eqA ltM)) (a : Term A n) (p : list (Term A n)),
inPolySet A A0 eqA n ltM p Q ->
~ zeroP (A:=A) A0 eqA (n:=n) a ->
reducestar Q (mults (A:=A) multA (n:=n) a p) (pO A n).