proposition: Lemma nbhs_pt_comp (P : R -> Prop) (f : R -> R) (x : R) : nbhs (f x) P -> continuity_pt f x -> \near x, P (f x).
proof: Proof. by move=> Lf /continuity_pt_cvg; apply. Qed.
imports: Rdefinitions Raxioms RIneq Rbasic_fun Zwf Epsilon FunctionalExtensionality Ranalysis1 Rsqrt_def Rtrigo1 Reals mathcomp(all_ssreflect ssralg poly mxpoly ssrnum) HB(structures) mathcomp(boolp classical_sets) reals signed topology