proposition: Lemma ex_strict_bound_gt0 {T : Type} {K : numFieldType} {V : pseudoMetricNormedZmodType K} (f : T -> V) (F : set_system T) {PF : Filter F}: bounded_near f F -> exists2 M, M > 0 & F [set x | `|f x| < M].
proof: Proof. move=> /pinfty_ex_gt0[M M_gt0 FM]; exists (M + 1); rewrite ?addr_gt0//. by apply: filterS FM => x /le_lt_trans/= ->//; rewrite ltrDl. 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