{C : Type u₁} →
  [inst : CategoryTheory.Category.{v₁, u₁} C] →
    {J : CategoryTheory.GrothendieckTopology C} →
      {R₀ : CategoryTheory.Functor Cᵒᵖ RingCat} →
        {R : CategoryTheory.Sheaf J RingCat} →
          {α : R₀ ⟶ R.val} →
            {M₀ : PresheafOfModules R₀} →
              {A : CategoryTheory.Sheaf J AddCommGrpCat} →
                {φ : M₀.presheaf ⟶ A.val} →
                  {X : Cᵒᵖ} →
                    {r : ↑(R.val.obj X)} →
                      {m : ↑(A.val.obj X)} →
                        (x : ↑(A.val.obj X)) →
                          (∀ ⦃Y : Cᵒᵖ⦄ (f : X ⟶ Y) (r₀ : ↑(R₀.obj Y)),
                              (CategoryTheory.ConcreteCategory.hom (α.app Y)) r₀ =
                                  (CategoryTheory.ConcreteCategory.hom (R.val.map f)) r →
                                ∀ (m₀ : ↑(M₀.obj Y)),
                                  (CategoryTheory.ConcreteCategory.hom (φ.app Y)) m₀ =
                                      (CategoryTheory.ConcreteCategory.hom (A.val.map f)) m →
                                    (CategoryTheory.ConcreteCategory.hom (A.val.map f)) x =
                                      (CategoryTheory.ConcreteCategory.hom (φ.app Y)) (r₀ • m₀)) →
                            PresheafOfModules.Sheafify.SMulCandidate α φ r m