proposition: Lemma nbhs_pt_comp (P : R -> Prop) (f : R -> R) (x : R) : nbhs (f x) P -> Ranalysis1.continuity_pt f x -> \near x, P (f x).
proof: Proof. by move=> Lf /continuity_pt_cvg; apply. 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