proposition: Lemma limf_einfE f F : limf_einf f F = ereal_sup [set ereal_inf (f @` V) | V in F].
proof: Proof. rewrite /limf_einf limf_esupE /ereal_inf oppeK -[in RHS]image_comp /=. congr (ereal_sup [set _ | _ in [set ereal_sup _ | _ in _]]). by under eq_fun do rewrite -image_comp. 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