∀ {ι : Type u_1} {α : Type u_2} [inst : AddCommMonoid α] [inst_1 : PartialOrder α] [AddLeftMono α] {s : Multiset ι}
  (f g : ι → α), (∀ i ∈ s, f i ≤ g i) → (Multiset.map f s).sum ≤ (Multiset.map g s).sum