proposition: Lemma is_cvg_norm f : cvg (f @ F) -> cvg ((Num.norm \o f : T -> K) @ F).
proof: Proof. by have := cvgP _ (cvg_norm _); apply. 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