proposition: Lemma ex_strict_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. rewrite boundedE ex_strict_dom_bound ?strictly_dominated_by1//. by near=> x; rewrite oner_eq0. 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