proposition: Lemma lime_infE f a : lime_inf f a = ereal_sup [set inf_ball f a e | e in `]0, +oo[ ]%R.
proof: Proof. by rewrite /lime_inf lime_supE /ereal_inf oppeK image_comp. 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)