proposition: Lemma at_right_in_segment (x : R) (P : set R) : (\forall e \near 0^'+, {in `[x - e, x + e], forall x, P x}) <-> (\near x, P x).
proof: Proof. rewrite nbhsr0P -propeqE; apply: eq_near => y /=. by rewrite -propeqE; apply: eq_forall => z; rewrite ler_distlC. 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