proposition: Lemma cvge_sub0 f (k : \bar R) : k \is a fin_num -> (fun x => f x - k) @ F --> 0 <-> f @ F --> k.
proof: Proof. move=> kfin; split. move=> /cvgeD-/(_ (cst k) _ isT (cvg_cst _)). by rewrite add0e; under eq_fun => x do rewrite subeK//. move: k kfin => [k _ fk| |]//; rewrite -(@subee _ k%:E)//. by apply: cvgeB => //; exact: cvg_cst. 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