proposition: Lemma lime_sup_inf_at_left f a l : lime_sup f a = l%:E -> lime_inf f a = l%:E -> f x @[x --> a^'-] --> l%:E.
proof: Proof. move=> supfal inffal; apply/cvg_at_leftNP/lime_sup_inf_at_right. - by rewrite /lime_sup -limf_esup_dnbhsN. - by rewrite /lime_inf /lime_sup -(limf_esup_dnbhsN (-%E \o f)) limf_esupN oppeK. Qed.
imports: mathcomp(all_ssreflect ssralg ssrint ssrnum finmap) mathcomp(matrix interval zmodp vector fieldext falgebra) mathcomp(mathcomp_extra boolp classical_sets functions) mathcomp(cardinality) ereal reals signed topology prodnormedzmodule normedtype derive sequences real_interval HB(structures)