proposition: Lemma norm_cvg0P f : `|f x| @[x --> F] --> 0 <-> f @ F --> 0.
proof: Proof. split; last by move=> /cvg_norm; rewrite normr0. move=> f0; apply/cvgr0Pnorm_lt => e e_gt0. by near do rewrite -normr_id; apply: cvgr0_norm_lt. Unshelve. all: by end_near. 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