proposition: Lemma fine_cvgP a : f @ F --> a%:E <-> (\near F, f F \is a fin_num) /\ fine \o f @ F --> a.
proof: Proof. by split;[split;[exact: (@cvg_is_fine a)|exact: fine_cvg]|case; apply: cvg_EFin]. 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