proposition: Lemma ereal_supremums_set0_ninfty : supremums (@set0 (\bar R)) -oo.
proof: Proof. by split; [exact/ubP | apply/lbP=> y _; rewrite leNye]. 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