-- Module: Mathlib.CategoryTheory.Sites.Point.Monoidal
Goal:
C : Type u
inst : Category.{v, u} C
J : GrothendieckTopology.{v, u} C
Φ : Point.{w, v, u} J
A : Type u'
inst_1 : Category.{v', u'} A
inst_2 : MonoidalCategory.{v', u'} A
inst_3 : HasColimitsOfSize.{w, w, v', u'} A
P₁ P₂ P₃ : Functor.{v, v', u, u'} Cᵒᵖ A
X : C
x : Φ.fiber.obj X
h :
  Eq (α :=
    tensorObj.{v', u'} (𝒞 := inst_1)
        (tensorObj.{v', u'} (𝒞 := inst_1) (P₁.obj (Opposite.op X)) (P₂.obj (Opposite.op X))) (P₃.obj (Opposite.op X)) ⟶
      tensorObj.{v', u'} (𝒞 := inst_1) (obj Φ.presheafFiber P₁)
        (tensorObj.{v', u'} (𝒞 := inst_1) (obj Φ.presheafFiber P₂) (obj Φ.presheafFiber P₃)))
    (Iso.hom (α_ (P₁.obj (Opposite.op X)) (P₂.obj (Opposite.op X)) (P₃.obj (Opposite.op X))) ≫
      (Φ.toPresheafFiber X x P₁ ⊗ₘ Φ.toPresheafFiber X x P₂ ⊗ₘ Φ.toPresheafFiber X x P₃))
    (CategoryStruct.comp (Y := obj Φ.presheafFiber (tensorObj (𝒞 := category) (tensorObj (𝒞 := category) P₁ P₂) P₃))
      (Φ.toPresheafFiber X x (tensorObj (𝒞 := category) (tensorObj (𝒞 := category) P₁ P₂) P₃))
      (map Φ.presheafFiber (Iso.hom (α_ P₁ P₂ P₃)) ≫
        Φ.presheafFiberDesc
            (fun (X : C) (x : Φ.fiber.obj X) ↦
              Φ.toPresheafFiber X x P₁ ⊗ₘ Φ.toPresheafFiber X x (tensorObj (𝒞 := category) P₂ P₃))
            ⋯ ≫
          obj Φ.presheafFiber P₁ ◁
            Φ.presheafFiberDesc (fun (X : C) (x : Φ.fiber.obj X) ↦ Φ.toPresheafFiber X x P₂ ⊗ₘ Φ.toPresheafFiber X x P₃)
              ⋯))
⊢ CategoryStruct.comp (Y := obj Φ.presheafFiber (tensorObj (𝒞 := category) (tensorObj (𝒞 := category) P₁ P₂) P₃))
      (Φ.toPresheafFiber X x (tensorObj (𝒞 := category) (tensorObj (𝒞 := category) P₁ P₂) P₃))
      (Φ.presheafFiberDesc
          (fun (X : C) (x : Φ.fiber.obj X) ↦
            Φ.toPresheafFiber X x (tensorObj (𝒞 := category) P₁ P₂) ⊗ₘ Φ.toPresheafFiber X x P₃)
          ⋯ ≫
        Φ.presheafFiberDesc (fun (X : C) (x : Φ.fiber.obj X) ↦ Φ.toPresheafFiber X x P₁ ⊗ₘ Φ.toPresheafFiber X x P₂) ⋯ ▷
            obj Φ.presheafFiber P₃ ≫
          Iso.hom (α_ (obj Φ.presheafFiber P₁) (obj Φ.presheafFiber P₂) (obj Φ.presheafFiber P₃))) =
    CategoryStruct.comp (Y := obj Φ.presheafFiber (tensorObj (𝒞 := category) (tensorObj (𝒞 := category) P₁ P₂) P₃))
      (Φ.toPresheafFiber X x (tensorObj (𝒞 := category) (tensorObj (𝒞 := category) P₁ P₂) P₃))
      (map Φ.presheafFiber (Iso.hom (α_ P₁ P₂ P₃)) ≫
        Φ.presheafFiberDesc
            (fun (X : C) (x : Φ.fiber.obj X) ↦
              Φ.toPresheafFiber X x P₁ ⊗ₘ Φ.toPresheafFiber X x (tensorObj (𝒞 := category) P₂ P₃))
            ⋯ ≫
          obj Φ.presheafFiber P₁ ◁
            Φ.presheafFiberDesc (fun (X : C) (x : Φ.fiber.obj X) ↦ Φ.toPresheafFiber X x P₂ ⊗ₘ Φ.toPresheafFiber X x P₃)
              ⋯)

Tactic:
conv_lhs =>
      simp only [toPresheafFiber_presheafFiberDesc_assoc, tensorHom_def'_assoc,
        ← comp_whiskerRight_assoc, toPresheafFiber_presheafFiberDesc]
      rw [← tensorHom_def'_assoc, associator_naturality]

Premises used: CategoryTheory.GrothendieckTopology.Point.toPresheafFiber_presheafFiberDesc, CategoryTheory.MonoidalCategory.tensorHom_def'_assoc, CategoryTheory.MonoidalCategory.comp_whiskerRight_assoc, CategoryTheory.MonoidalCategory.associator_naturality, CategoryTheory.GrothendieckTopology.Point.toPresheafFiber_presheafFiberDesc_assoc