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

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