Section ListDenoteConj.
Context {A : Type}.
Variables (f : A -> Prop) (g : Prop -> Prop -> Prop) (b : Prop).
Variable (gconj : forall x y, g x y -> y).
Proof with auto.
induction l; simpl... apply prop_ext; split; tauto.
apply prop_ext; split; simpl; rewrite IHl; tauto.
Qed.

Lemma listd_flat_map_and h l
(H : forall a b', and (f a) b' -> listd f and b' (h a)) :
listd f and b l -> listd f and b (flat_map h l).