proposition: Lemma nbhsC (x : T) (P : set T) : ~ (forall eps : {posnum R}, ~ (ball x eps%:num `<=` ~` P)) -> nbhs x (~` P).
proof: Proof. by move=> /ex_ball_sig [e] ?; apply/nbhs_ballP; exists e%:num => /=. 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