proposition: Lemma lim_lime_inf f a (l : R) : f r @[r --> a] --> l%:E -> lime_inf f a = l%:E.
proof: Proof. move=> h; apply/eqP; rewrite eq_le. by rewrite lim_lime_inf'// andbT (le_trans (lime_inf_sup _ _))// lim_lime_sup'. 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)