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

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(* Rewriting                                                               *)
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Lemma lem_or_and_conv_l :
forall a b c d : Prop,
a /\ b \/ c /\ d -> (a \/ c) /\ (b \/ c) /\ (a \/ d) /\ (b \/ d).