proposition: Lemma cvg_EFin a : (\near F, f F \is a fin_num) -> fine \o f @ F --> a -> f @ F --> a%:E.
proof: Proof. move=> Ffin Fa P/= /nbhs_EFin /Fa; rewrite !near_simpl. by apply: filterS2 Ffin => x /fineK->. 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