proposition: Lemma cvg_at_left_within : f x @[x --> x^'-] --> f x -> f x @[x --> within (fun u => u <= x) (nbhs x)] --> f x.
proof: Proof. move=> fxr U Ux; rewrite ?near_simpl ?near_withinE; near=> z; rewrite le_eqVlt. by move/predU1P => [->|]; [exact: nbhs_singleton | near: z; exact: fxr]. Unshelve. all: by end_near. 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