proposition: Lemma gauge_ent A : gauge A -> entourage A.
proof: Proof. case=> n; elim: n A; first by move=> ? _ /filterS; apply; apply: filterI. by move=> n ? A _ /filterS; apply; apply: filterI; have ? := iter_split_ent n. Qed.
imports: HB(structures) mathcomp(all_ssreflect all_algebra finmap generic_quotient) mathcomp(boolp classical_sets functions) mathcomp(cardinality mathcomp_extra fsbigop) reals signed