proposition: Lemma nbhs_norm0P {P : V -> Prop} : (\forall x \near 0, P x) <-> filter_from [set e | 0 < e] (fun e => [set y | `|y| < e]) P.
proof: Proof. rewrite nbhs_normP; split=> -[/= e e0 Pe]; by exists e => // y /=; have /= := Pe y; rewrite distrC subr0. 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