(* Proof of lem_and_fact                                                   *)
intros; tauto.
Qed.
(* End of proof of lem_and_fact                                            *)

Lemma lem_and_dist :
forall P0 P1 P2 : Prop, P0 /\ P2 \/ P1 /\ P2 -> (P0 \/ P1) /\ P2.