proposition: Lemma lb_ereal_inf S M : lbound S M -> M <= ereal_inf S.
proof: Proof. move=> SM; rewrite /ereal_inf leeNr; apply ub_ereal_sup => x [y Sy <-{x}]. by rewrite leeNl oppeK; apply SM. Qed.
imports: HB(structures) mathcomp(all_ssreflect all_algebra finmap) mathcomp(mathcomp_extra boolp classical_sets functions) mathcomp(fsbigop cardinality set_interval) reals signed topology constructive_ereal