proposition: Lemma fct_entourage : entourage = entourage_ fct_ball.
proof: Proof. rewrite predeqE => A; split; last first. by move=> [_/posnumP[e] sbeA]; exists [set xy | ball xy.1 e%:num xy.2]. move=> [P]; rewrite -entourage_ballE => -[_/posnumP[e] sbeP] sPA. by exists e%:num => //= fg fg_e; apply: sPA => t; apply: sbeP; apply: fg_e. Qed.
imports: HB(structures) mathcomp(all_ssreflect all_algebra finmap generic_quotient) mathcomp(boolp classical_sets functions) mathcomp(cardinality mathcomp_extra fsbigop) reals signed