proposition: Lemma closed_ballR_compact (R : realType) (x e : R) : 0 < e -> compact (closed_ball x e).
proof: Proof. move=> e_gt0; have : compact `[x - e, x + e] by apply: segment_compact. by rewrite closed_ballE//; under eq_set do rewrite 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