proposition: Lemma nbhsC_ball (x : T) (P : set T) : nbhs x (~` P) -> {d : {posnum R} | ball x d%:num `<=` ~` P}.
proof: Proof. move=> /nbhs_ballP xNP; apply: ex_ball_sig. by have [_ /posnumP[e] eP /(_ _ eP)] := xNP. Qed.
imports: HB(structures) mathcomp(all_ssreflect ssralg ssrint ssrnum finmap matrix) mathcomp(rat interval zmodp vector fieldext falgebra) mathcomp(mathcomp_extra boolp classical_sets functions) mathcomp(cardinality set_interval Rstruct) ereal reals signed topology prodnormedzmodule