proposition: Lemma closed_ball_itv (R : realFieldType) (x r : R) : 0 < r -> (closed_ball x r = `[x - r, x + r]%classic)%R.
proof: Proof. by move=> r0; apply/seteqP; split => y; rewrite closed_ballE// /closed_ball_ /= in_itv/= 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