proposition: Lemma fine_fcvg a : F --> a%:E -> fine @ F --> a.
proof: Proof. move=> /(_ _)/= Fa; apply/cvgrPdist_lt=> // _/posnumP[e]; rewrite near_simpl. by apply: Fa; apply/nbhs_EFin => /=; apply: (@cvgr_dist_lt _ _ _ (nbhs a)). 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