proposition: Lemma cvgr0_norm_le {T} {F : set_system T} {FF : Filter F} (f : T -> V) : f @ F --> 0 -> forall eps, eps > 0 -> \forall t \near F, `|f t| <= eps.
proof: Proof. by move=> ? ? ?; near do rewrite ltW//; 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