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.
Proof with auto.
induction l; simpl... intros [B C]. specialize (H a _ (conj B (IHl C))).
solve [rewrite listd_app; auto].
Qed.
Proof with simpl; try solve[exfalso; auto]; auto. induction l... Qed.

Lemma listd_In_inv_prop a l : listd f and True l -> In a l -> f a.