simpl in |- *.
intros P R H'; try assumption.
apply OBuch_Stable_f; auto.
rewrite H'.
case (pbuchf (pair P (genOCPf P))); simpl in |- *; auto.
Qed.

Theorem pbuchf_Inv :
forall P R : list (poly A0 eqA ltM),
R = strip _ (pbuchf (P, genOCPf P)) ->
forall a b : poly A0 eqA ltM, In a R -> In b R -> reds a b R.