(* Proof of lem_comprehension_lr                                           *)
intros; elim (axs_comprehension F a v0); intros; exact (H0 H).
Qed.
(* End of proof of lem_comprehension_lr                                    *)

Lemma lem_comprehension_rl :
forall (F : E -> Prop) (a v0 : E), In v0 a /\ F v0 -> In v0 (subset F a).