intros A R xs bs cs H'.
apply monGRBarAux with (l := xs ++ cs); auto.
Qed.
Hint Resolve monGRBar.
Section lems.
Variable trm : Set.
Variable tdiv : trm -> trm -> Prop.
Definition Bad (M : list trm) := GoodR trm tdiv M -> False.

Lemma tdivExists_trmHd_lem :
forall (F : list trm) (f : trm),
(forall g : trm, In g F -> ~ tdiv g f) ->
ExistsL trm (fun g : trm => tdiv g f) F -> False.