proposition: Lemma ap_imp_Min_less_Max : a [#] b -> Min a b [<] Max a b.
proof: Proof. intro Hap; elim (ap_imp_less _ _ _ Hap); (intro H; [ eapply leEq_less_trans; [ idtac | eapply less_leEq_trans; [ apply H | idtac ] ] ]). apply Min_leEq_lft. apply rht_leEq_Max. apply Min_leEq_rht. apply lft_leEq_Max. Qed.
imports: CoRN.reals.Q_in_CReals Coq.QArith.Qabs CoRN.reals.CauchySeq