proposition: Lemma nbhs_ball_normE : @nbhs_ball_ K R R (ball_ Num.norm) = nbhs_ (entourage_ (ball_ Num.norm)).
proof: Proof. rewrite /nbhs_ entourage_E predeq2E => x A; split. move=> [e egt0 sbeA]. by exists [set xy | ball_ Num.norm xy.1 e xy.2] => //; exists e. by move=> [E [e egt0 sbeE] sEA]; exists e => // ??; apply/sEA/sbeE. Qed.
imports: HB(structures) mathcomp(all_ssreflect all_algebra finmap generic_quotient) mathcomp(boolp classical_sets functions) mathcomp(cardinality mathcomp_extra fsbigop) reals signed