proposition: Lemma cvg_limn_einf_sup u l : u @ \oo --> l -> (limn_einf u = l) * (limn_esup u = l).
proof: Proof. move=> ul; rewrite limn_esup_lim limn_einf_lim; split. - by apply/cvg_lim => //; exact/cvg_einfs. - by apply/cvg_lim => //; exact/cvg_esups. Qed.
imports: mathcomp(all_ssreflect ssralg ssrint ssrnum matrix) mathcomp(interval rat) mathcomp(mathcomp_extra boolp classical_sets functions) mathcomp(set_interval) reals ereal signed topology normedtype landau