proposition: Lemma continuity_pt_dnbhs f x : Ranalysis1.continuity_pt f x <-> forall eps, 0 < eps -> x^' (fun u => `|f x - f u| < eps).
proof: Proof. rewrite continuity_pt_cvg' (@cvgrPdist_lt _ [the normedModType _ of R^o]). exact. 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