proposition: Lemma lb_le_inf E x : nonempty E -> (lbound E) x -> x <= inf E.
proof: Proof. by move=> /(nonemptyN E) En0 /lb_ubN /(sup_le_ub En0); rewrite lerNr. Qed.
imports: HB(structures) mathcomp(all_ssreflect all_algebra) mathcomp(mathcomp_extra boolp classical_sets set_interval) Setoid