proposition: Lemma ncvg_abs0 u : ncvg (fun n => `|u n|) 0%:E -> ncvg u 0%:E.
proof: Proof. move=> cu; elim/nbh_finW => e /= gt0_e; case: (cu (B 0 e)). by move=> K {}cu; exists K=> n /cu; rewrite !inE !subr0 eclamp_id // normr_id. Qed.
imports: mathcomp(all_ssreflect all_algebra) mathcomp.bigenough.bigenough mathcomp.classical(boolp classical_sets functions) mathcomp.classical(mathcomp_extra) xfinmap ereal reals discrete topology