-- Module: Mathlib.Algebra.Category.ModuleCat.Presheaf.Monoidal
Goal:
C : Type u_1
inst : Category.{v_1, u_1} C
R : CategoryTheory.Functor.{v_1, u, u_1, u + 1} Cᵒᵖ CommRingCat
M₁ M₂ M₃ :
  PresheafOfModules
    (R ⋙
      forget₂ CommRingCat (FC := fun (R S : CommRingCat.{u}) ↦ (↑R : Type u) →+* (↑S : Type u)) (CC :=
        CommRingCat.carrier) RingCat (FD := fun (R S : RingCat.{u}) ↦ (↑R : Type u) →+* (↑S : Type u)) (CD :=
        RingCat.carrier))
x x_1 : Cᵒᵖ
x_2 : x ⟶ x_1
m₁ : (↑(M₁.obj x) : Type u)
m₂ : (↑(M₂.obj x) : Type u)
m₃ : (↑(M₃.obj x) : Type u)
⊢ Eq (α :=
    (↑(Functor.obj
          (ModuleCat.restrictScalars
            (RingCat.Hom.hom
              (CategoryTheory.Functor.map
                (R ⋙
                  forget₂ CommRingCat (FC := fun (R S : CommRingCat.{u}) ↦ (↑R : Type u) →+* (↑S : Type u)) (CC :=
                    CommRingCat.carrier) RingCat (FD := fun (R S : RingCat.{u}) ↦ (↑R : Type u) →+* (↑S : Type u))
                    (CD := RingCat.carrier))
                x_2)))
          ((Monoidal.tensorObj M₁ (Monoidal.tensorObj M₂ M₃)).obj x_1)) :
      Type u))
    ((ConcreteCategory.hom (FC :=
            fun
              (x1 x2 :
                ModuleCat
                  (↑(Functor.obj
                        (R ⋙
                          forget₂ CommRingCat (FC := fun (R S : CommRingCat.{u}) ↦ (↑R : Type u) →+* (↑S : Type u))
                            (CC := CommRingCat.carrier) RingCat (FD := fun (R S : RingCat.{u}) ↦
                            (↑R : Type u) →+* (↑S : Type u)) (CD := RingCat.carrier))
                        x) :
                    Type u)) ↦
            LinearMap (R :=
              (↑(Functor.obj
                    (R ⋙
                      forget₂ CommRingCat (FC := fun (R S : CommRingCat.{u}) ↦ (↑R : Type u) →+* (↑S : Type u)) (CC :=
                        CommRingCat.carrier) RingCat (FD := fun (R S : RingCat.{u}) ↦ (↑R : Type u) →+* (↑S : Type u))
                        (CD := RingCat.carrier))
                    x) :
                Type u))
              (RingHom.id
                (↑(Functor.obj
                      (R ⋙
                        forget₂ CommRingCat (FC := fun (R S : CommRingCat.{u}) ↦ (↑R : Type u) →+* (↑S : Type u)) (CC :=
                          CommRingCat.carrier) RingCat (FD := fun (R S : RingCat.{u}) ↦ (↑R : Type u) →+* (↑S : Type u))
                          (CD := RingCat.carrier))
                      x) :
                  Type u))
              (↑x1 : Type u) (↑x2 : Type u))
            (CC := ModuleCat.carrier) (Y :=
            Functor.obj
              (ModuleCat.restrictScalars
                (RingCat.Hom.hom
                  (CategoryTheory.Functor.map
                    (R ⋙
                      forget₂ CommRingCat (FC := fun (R S : CommRingCat.{u}) ↦ (↑R : Type u) →+* (↑S : Type u)) (CC :=
                        CommRingCat.carrier) RingCat (FD := fun (R S : RingCat.{u}) ↦ (↑R : Type u) →+* (↑S : Type u))
                        (CD := RingCat.carrier))
                    x_2)))
              ((Monoidal.tensorObj M₁ (Monoidal.tensorObj M₂ M₃)).obj x_1))
            ((Monoidal.tensorObj (Monoidal.tensorObj M₁ M₂) M₃).map x_2 ≫
              CategoryTheory.Functor.map
                (ModuleCat.restrictScalars
                  (RingCat.Hom.hom
                    (CategoryTheory.Functor.map
                      (R ⋙
                        forget₂ CommRingCat (FC := fun (R S : CommRingCat.{u}) ↦ (↑R : Type u) →+* (↑S : Type u)) (CC :=
                          CommRingCat.carrier) RingCat (FD := fun (R S : RingCat.{u}) ↦ (↑R : Type u) →+* (↑S : Type u))
                          (CD := RingCat.carrier))
                      x_2)))
                (Iso.hom
                  ((fun (x : Cᵒᵖ) ↦
                      (α_ (M₁.obj x) (M₂.obj x) (M₃.obj x) :
                        MonoidalCategoryStruct.tensorObj (𝒞 :=
                            ModuleCat.moduleCategory
                              (↑(Functor.obj
                                    (R ⋙
                                      forget₂ CommRingCat (FC := fun (R S : CommRingCat.{u}) ↦
                                        (↑R : Type u) →+* (↑S : Type u)) (CC := CommRingCat.carrier) RingCat (FD :=
                                        fun (R S : RingCat.{u}) ↦ (↑R : Type u) →+* (↑S : Type u)) (CD :=
                                        RingCat.carrier))
                                    x) :
                                Type u))
                            (MonoidalCategoryStruct.tensorObj (𝒞 :=
                              ModuleCat.moduleCategory
                                (↑(Functor.obj
                                      (R ⋙
                                        forget₂ CommRingCat (FC := fun (R S : CommRingCat.{u}) ↦
                                          (↑R : Type u) →+* (↑S : Type u)) (CC := CommRingCat.carrier) RingCat (FD :=
                                          fun (R S : RingCat.{u}) ↦ (↑R : Type u) →+* (↑S : Type u)) (CD :=
                                          RingCat.carrier))
                                      x) :
                                  Type u))
                              (M₁.obj x) (M₂.obj x))
                            (M₃.obj x) ≅
                          MonoidalCategoryStruct.tensorObj (𝒞 :=
                            ModuleCat.moduleCategory
                              (↑(Functor.obj
                                    (R ⋙
                                      forget₂ CommRingCat (FC := fun (R S : CommRingCat.{u}) ↦
                                        (↑R : Type u) →+* (↑S : Type u)) (CC := CommRingCat.carrier) RingCat (FD :=
                                        fun (R S : RingCat.{u}) ↦ (↑R : Type u) →+* (↑S : Type u)) (CD :=
                                        RingCat.carrier))
                                    x) :
                                Type u))
                            (M₁.obj x)
                            (MonoidalCategoryStruct.tensorObj (𝒞 :=
                              ModuleCat.moduleCategory
                                (↑(Functor.obj
                                      (R ⋙
                                        forget₂ CommRingCat (FC := fun (R S : CommRingCat.{u}) ↦
                                          (↑R : Type u) →+* (↑S : Type u)) (CC := CommRingCat.carrier) RingCat (FD :=
                                          fun (R S : RingCat.{u}) ↦ (↑R : Type u) →+* (↑S : Type u)) (CD :=
                                          RingCat.carrier))
                                      x) :
                                  Type u))
                              (M₂.obj x) (M₃.obj x))))
                    x_1))) :
          (a : (↑((M₁.obj x ⊗ M₂.obj x) ⊗ M₃.obj x) : Type u)) →
            (↑((ModuleCat.restrictScalars (RingCat.Hom.hom ((R ⋙ forget₂ CommRingCat RingCat).map x_2))).obj
                  ((Monoidal.tensorObj M₁ (Monoidal.tensorObj M₂ M₃)).obj x_1)) :
              Type u))
        (m₁ ⊗ₜ[(↑(Functor.obj
                  (R ⋙
                    forget₂ CommRingCat (FC := fun (R S : CommRingCat.{u}) ↦ (↑R : Type u) →+* (↑S : Type u)) (CC :=
                      CommRingCat.carrier) RingCat (FD := fun (R S : RingCat.{u}) ↦ (↑R : Type u) →+* (↑S : Type u))
                      (CD := RingCat.carrier))
                  x) :
              Type u)]
            m₂ ⊗ₜ[(↑(Functor.obj
                (R ⋙
                  forget₂ CommRingCat (FC := fun (R S : CommRingCat.{u}) ↦ (↑R : Type u) →+* (↑S : Type u)) (CC :=
                    CommRingCat.carrier) RingCat (FD := fun (R S : RingCat.{u}) ↦ (↑R : Type u) →+* (↑S : Type u))
                    (CD := RingCat.carrier))
                x) :
            Type u)]
          m₃) :
      (↑(Functor.obj
            (ModuleCat.restrictScalars
              (RingCat.Hom.hom
                (CategoryTheory.Functor.map
                  (R ⋙
                    forget₂ CommRingCat (FC := fun (R S : CommRingCat.{u}) ↦ (↑R : Type u) →+* (↑S : Type u)) (CC :=
                      CommRingCat.carrier) RingCat (FD := fun (R S : RingCat.{u}) ↦ (↑R : Type u) →+* (↑S : Type u))
                      (CD := RingCat.carrier))
                  x_2)))
            ((Monoidal.tensorObj M₁ (Monoidal.tensorObj M₂ M₃)).obj x_1)) :
        Type u))
    ((ConcreteCategory.hom (FC :=
            fun
              (x1 x2 :
                ModuleCat
                  (↑(Functor.obj
                        (R ⋙
                          forget₂ CommRingCat (FC := fun (R S : CommRingCat.{u}) ↦ (↑R : Type u) →+* (↑S : Type u))
                            (CC := CommRingCat.carrier) RingCat (FD := fun (R S : RingCat.{u}) ↦
                            (↑R : Type u) →+* (↑S : Type u)) (CD := RingCat.carrier))
                        x) :
                    Type u)) ↦
            LinearMap (R :=
              (↑(Functor.obj
                    (R ⋙
                      forget₂ CommRingCat (FC := fun (R S : CommRingCat.{u}) ↦ (↑R : Type u) →+* (↑S : Type u)) (CC :=
                        CommRingCat.carrier) RingCat (FD := fun (R S : RingCat.{u}) ↦ (↑R : Type u) →+* (↑S : Type u))
                        (CD := RingCat.carrier))
                    x) :
                Type u))
              (RingHom.id
                (↑(Functor.obj
                      (R ⋙
                        forget₂ CommRingCat (FC := fun (R S : CommRingCat.{u}) ↦ (↑R : Type u) →+* (↑S : Type u)) (CC :=
                          CommRingCat.carrier) RingCat (FD := fun (R S : RingCat.{u}) ↦ (↑R : Type u) →+* (↑S : Type u))
                          (CD := RingCat.carrier))
                      x) :
                  Type u))
              (↑x1 : Type u) (↑x2 : Type u))
            (CC := ModuleCat.carrier) (X :=
            MonoidalCategoryStruct.tensorObj (𝒞 :=
              ModuleCat.moduleCategory
                (↑(Functor.obj
                      (R ⋙
                        forget₂ CommRingCat (FC := fun (R S : CommRingCat.{u}) ↦ (↑R : Type u) →+* (↑S : Type u)) (CC :=
                          CommRingCat.carrier) RingCat (FD := fun (R S : RingCat.{u}) ↦ (↑R : Type u) →+* (↑S : Type u))
                          (CD := RingCat.carrier))
                      x) :
                  Type u))
              (MonoidalCategoryStruct.tensorObj (𝒞 :=
                ModuleCat.moduleCategory
                  (↑(Functor.obj
                        (R ⋙
                          forget₂ CommRingCat (FC := fun (R S : CommRingCat.{u}) ↦ (↑R : Type u) →+* (↑S : Type u))
                            (CC := CommRingCat.carrier) RingCat (FD := fun (R S : RingCat.{u}) ↦
                            (↑R : Type u) →+* (↑S : Type u)) (CD := RingCat.carrier))
                        x) :
                    Type u))
                (M₁.obj x) (M₂.obj x))
              (M₃.obj x))
            (Iso.hom
                ((fun (x : Cᵒᵖ) ↦
                    (α_ (M₁.obj x) (M₂.obj x) (M₃.obj x) :
                      MonoidalCategoryStruct.tensorObj (𝒞 :=
                          ModuleCat.moduleCategory
                            (↑(Functor.obj
                                  (R ⋙
                                    forget₂ CommRingCat (FC := fun (R S : CommRingCat.{u}) ↦
                                      (↑R : Type u) →+* (↑S : Type u)) (CC := CommRingCat.carrier) RingCat (FD :=
                                      fun (R S : RingCat.{u}) ↦ (↑R : Type u) →+* (↑S : Type u)) (CD :=
                                      RingCat.carrier))
                                  x) :
                              Type u))
                          (MonoidalCategoryStruct.tensorObj (𝒞 :=
                            ModuleCat.moduleCategory
                              (↑(Functor.obj
                                    (R ⋙
                                      forget₂ CommRingCat (FC := fun (R S : CommRingCat.{u}) ↦
                                        (↑R : Type u) →+* (↑S : Type u)) (CC := CommRingCat.carrier) RingCat (FD :=
                                        fun (R S : RingCat.{u}) ↦ (↑R : Type u) →+* (↑S : Type u)) (CD :=
                                        RingCat.carrier))
                                    x) :
                                Type u))
                            (M₁.obj x) (M₂.obj x))
                          (M₃.obj x) ≅
                        MonoidalCategoryStruct.tensorObj (𝒞 :=
                          ModuleCat.moduleCategory
                            (↑(Functor.obj
                                  (R ⋙
                                    forget₂ CommRingCat (FC := fun (R S : CommRingCat.{u}) ↦
                                      (↑R : Type u) →+* (↑S : Type u)) (CC := CommRingCat.carrier) RingCat (FD :=
                                      fun (R S : RingCat.{u}) ↦ (↑R : Type u) →+* (↑S : Type u)) (CD :=
                                      RingCat.carrier))
                                  x) :
                              Type u))
                          (M₁.obj x)
                          (MonoidalCategoryStruct.tensorObj (𝒞 :=
                            ModuleCat.moduleCategory
                              (↑(Functor.obj
                                    (R ⋙
                                      forget₂ CommRingCat (FC := fun (R S : CommRingCat.{u}) ↦
                                        (↑R : Type u) →+* (↑S : Type u)) (CC := CommRingCat.carrier) RingCat (FD :=
                                        fun (R S : RingCat.{u}) ↦ (↑R : Type u) →+* (↑S : Type u)) (CD :=
                                        RingCat.carrier))
                                    x) :
                                Type u))
                            (M₂.obj x) (M₃.obj x))))
                  x) ≫
              (Monoidal.tensorObj M₁ (Monoidal.tensorObj M₂ M₃)).map x_2) :
          (a : (↑((M₁.obj x ⊗ M₂.obj x) ⊗ M₃.obj x) : Type u)) →
            (↑((ModuleCat.restrictScalars (RingCat.Hom.hom ((R ⋙ forget₂ CommRingCat RingCat).map x_2))).obj
                  ((Monoidal.tensorObj M₁ (Monoidal.tensorObj M₂ M₃)).obj x_1)) :
              Type u))
        (m₁ ⊗ₜ[(↑(Functor.obj
                  (R ⋙
                    forget₂ CommRingCat (FC := fun (R S : CommRingCat.{u}) ↦ (↑R : Type u) →+* (↑S : Type u)) (CC :=
                      CommRingCat.carrier) RingCat (FD := fun (R S : RingCat.{u}) ↦ (↑R : Type u) →+* (↑S : Type u))
                      (CD := RingCat.carrier))
                  x) :
              Type u)]
            m₂ ⊗ₜ[(↑(Functor.obj
                (R ⋙
                  forget₂ CommRingCat (FC := fun (R S : CommRingCat.{u}) ↦ (↑R : Type u) →+* (↑S : Type u)) (CC :=
                    CommRingCat.carrier) RingCat (FD := fun (R S : RingCat.{u}) ↦ (↑R : Type u) →+* (↑S : Type u))
                    (CD := RingCat.carrier))
                x) :
            Type u)]
          m₃) :
      (↑(Functor.obj
            (ModuleCat.restrictScalars
              (RingCat.Hom.hom
                (CategoryTheory.Functor.map
                  (R ⋙
                    forget₂ CommRingCat (FC := fun (R S : CommRingCat.{u}) ↦ (↑R : Type u) →+* (↑S : Type u)) (CC :=
                      CommRingCat.carrier) RingCat (FD := fun (R S : RingCat.{u}) ↦ (↑R : Type u) →+* (↑S : Type u))
                      (CD := RingCat.carrier))
                  x_2)))
            ((Monoidal.tensorObj M₁ (Monoidal.tensorObj M₂ M₃)).obj x_1)) :
        Type u))

Tactic:
rfl