∀ {ι : Type u_1} {α : Type u_2} {β : Type u_3} [inst : Semiring α] [inst_1 : LinearOrder α] [IsStrictOrderedRing α]
  [ExistsAddOfLE α] [inst_4 : AddCommMonoid β] [inst_5 : LinearOrder β] [IsOrderedCancelAddMonoid β]
  [inst_7 : Module α β] [PosSMulStrictMono α β] {σ : Equiv.Perm ι} {f : ι → α} {g : ι → β} [inst_9 : Fintype ι],
  Antivary f g → (∑ i, f i • g i < ∑ i, f i • g (σ i) ↔ ¬Antivary f (g ∘ ⇑σ))