∀ {R : Type u_1} {X : Type u_2} [inst : PseudoMetricSpace R] [inst_1 : Mul R] [BoundedMul R] {f g : X → R},
  (∃ C, ∀ (x y : X), dist (f x) (f y) ≤ C) →
    (∃ C, ∀ (x y : X), dist (g x) (g y) ≤ C) → ∃ C, ∀ (x y : X), dist ((f * g) x) ((f * g) y) ≤ C