proposition: Lemma ereal_sup_le S x : (exists2 y, S y & x <= y) -> x <= ereal_sup S.
proof: Proof. by move=> [y Sy] /le_trans; apply; exact: ereal_sup_ub. 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