∀ {α : Type u} {β : Type v} {M : Type w} [inst : DecidableEq β] [inst_1 : Fintype α] [inst_2 : Fintype β] (f : α → β)
  {w : α → M} {b : M} [inst_3 : AddCommMonoid M] [inst_4 : LinearOrder M] [IsOrderedCancelAddMonoid M],
  Fintype.card β • b < ∑ x, w x → ∃ y, b < ∑ x with f x = y, w x