proposition: Lemma leEq_imp_Min_is_lft : forall x y : IR, x [<=] y -> Min x y [=] x.
proof: Proof. intros. simpl; unfold MIN. astepr ( [--][--]x). apply un_op_wd_unfolded. apply eq_transitive_unfolded with (Max [--]y [--]x). apply Max_comm. apply leEq_imp_Max_is_rht. apply inv_resp_leEq. assumption. Qed.
imports: CoRN.reals.Q_in_CReals Coq.QArith.Qabs CoRN.reals.CauchySeq