proposition: Lemma sub_boundedr (T : Type) (K : numFieldType) (V : pseudoMetricNormedZmodType K) (F G : set_system T) : F `=>` G -> (@bounded_near T K V)^~ G `<=` bounded_near^~ F.
proof: Proof. by move=> FG f; rewrite /bounded_near; apply: filterS=> M; apply: FG. 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