intros aP R Q H'; elim H'; simpl in |- *; auto.
intros a aP0 Q0 R0 H'0 H'1 H'2; try assumption.
apply
incl_tran
with
(m := nf A A0 A1 eqA plusA invA minusA multA divA cs eqA_dec n ltM
ltM_dec os a aP0 :: aP0); simpl in |- *;
auto.
apply incl_addEnd1; auto.
Qed.

(* Specifications: *)
Theorem ObuchPred :
forall aP R Q : list (poly A0 eqA ltM),
OBuch aP Q R ->
forall a : poly A0 eqA ltM,
In a aP -> red A A0 A1 eqA invA minusA multA divA eqA_dec n ltM ltM_dec a R.