proposition: Lemma bounded_locally (T : topologicalType) (R : numFieldType) (V : normedModType R) (A : set T) (f : T -> V) : [bounded f x | x in A] -> [locally [bounded f x | x in A]].
proof: Proof. by move=> /sub_boundedr AB x Ax; apply: AB; apply: within_nbhsW. 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