intros P Q H' a b H'0; elim H'0; auto.
intros a0 b0 nZb p q r H'1 H'2 H'3; auto.
apply reducetop with (b := b0) (nZb := nZb) (q := q); auto.
Qed.

(* Specifications: *)
Theorem inP_reduceplus :
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),
reduceplus 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.