{R : Type u_1} →
  {E₁ : Type u_2} →
    {E₂ : Type u_3} →
      [inst : Semiring R] →
        [inst_1 : AddCommMonoid E₁] →
          [inst_2 : PartialOrder E₁] →
            [inst_3 : AddCommMonoid E₂] →
              [inst_4 : PartialOrder E₂] →
                [inst_5 : Module R E₁] →
                  [inst_6 : Module R E₂] →
                    (toFun : E₁ → E₂) →
                      (∀ (x y : E₁), toFun (x + y) = toFun x + toFun y) →
                        (∀ (m : R) (x : E₁), toFun (m • x) = (RingHom.id R) m • toFun x) → Monotone toFun → E₁ →ₚ[R] E₂