intros P Q H' a b H'0; elim H'0; auto.
intros; apply Rstar_0; auto.
intros x y z H'1 H'2 H'3.
apply Rstar_n with (y := y); auto.
apply inP_reduce with (Q := Q); auto.
Qed.

(* Specifications: *)
Theorem inP_reducestar :
forall P Q : list (poly A0 eqA ltM),
(forall a : list (Term A n),
inPolySet A A0 eqA n ltM a Q -> inPolySet A A0 eqA n ltM a P) ->
forall a b : list (Term A n),
reducestar A A0 A1 eqA invA minusA multA divA eqA_dec n ltM ltM_dec Q a b ->
reduceplus A A0 A1 eqA invA minusA multA divA eqA_dec n ltM ltM_dec P a b.