proposition: Lemma ex_bound {T : Type} {K : numFieldType} {V : pseudoMetricNormedZmodType K} (f : T -> V) (F : set_system T) {PF : ProperFilter F}: bounded_near f F <-> exists M, F [set x | `|f x| <= M].
proof: Proof. by rewrite boundedE ex_dom_bound dominated_by1. 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