{R : Type u_1} →
  {E₁ : Type u_2} →
    {E₂ : Type u_3} →
      [inst : Semiring R] →
        [inst_1 : AddCommGroup E₁] →
          [inst_2 : PartialOrder E₁] →
            [IsOrderedAddMonoid E₁] →
              [inst_4 : AddCommGroup E₂] →
                [inst_5 : PartialOrder E₂] →
                  [IsOrderedAddMonoid E₂] →
                    [inst_7 : Module R E₁] →
                      [inst_8 : Module R E₂] → (f : E₁ →ₗ[R] E₂) → (∀ (x : E₁), 0 ≤ x → 0 ≤ f x) → E₁ →ₚ[R] E₂