proposition: Lemma cvgr_norm_le {T} {F : set_system T} {FF : Filter F} (f : T -> V) (y : V) : f @ F --> y -> forall u, `|y| < u -> \forall t \near F, `|f t| <= u.
proof: Proof. by move=> fy u yu; near do apply/ltW; apply: cvgr_norm_lt yu. 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