∀ {α : Type u_1} {β : Type u_2} {a : α} {b₁ b₂ : β} [inst : GroupWithZero α] [inst_1 : Preorder α] [inst_2 : Preorder β]
  [inst_3 : MulAction α β] [PosSMulStrictMono α β] [PosSMulReflectLT α β], 0 < a → (a⁻¹ • b₁ < b₂ ↔ b₁ < a • b₂)