proposition: Lemma ereal_sup_gt S x : x < ereal_sup S -> exists2 y, S y & x < y.
proof: Proof. rewrite not_exists2P => + g; apply/negP; rewrite -leNgt. by apply: ub_ereal_sup => y Sy; move: (g y) => [//|/negP]; rewrite leNgt. 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