proposition: Lemma ereal_inf_le S x : (exists2 y, S y & y <= x) -> ereal_inf S <= x.
proof: Proof. by move=> [y Sy]; apply: le_trans; exact: ereal_inf_lb. 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