-- Module: Mathlib.RepresentationTheory.Action
Goal:
G : Type v
inst : Monoid G
X Y Z : Action (Type w) G
k : Type u
inst_1 : CommSemiring k
h :
  ∀ (x : X.V) (y : Y.V) (z : Z.V),
    Eq (α :=
      Finsupp.{w, u}
        (MonoidalCategoryStruct.tensorObj (𝒞 := Action.instCategory) X
            (MonoidalCategoryStruct.tensorObj (𝒞 := Action.instCategory) Y Z)).V
        k)
      (((((TensorProduct.AlgebraTensorModule.curry
                            (TensorProduct.AlgebraTensorModule.curry
                              (toLinearMap
                                (comp
                                  (comp (linearizeMap (Iso.hom (α_ X Y Z)))
                                    (μ (MonoidalCategoryStruct.tensorObj (𝒞 := Action.instCategory) X Y) Z))
                                  (rTensor (linearize k G Z) (μ X Y))))) ∘ₗ
                          Finsupp.lsingle x :
                        k →ₗ[k]
                          Finsupp.{w, u} Y.V k →ₗ[k]
                            Finsupp.{w, u} Z.V k →ₗ[k]
                              Finsupp.{w, u}
                                (MonoidalCategoryStruct.tensorObj (𝒞 := Action.instCategory) X
                                    (MonoidalCategoryStruct.tensorObj (𝒞 := Action.instCategory) Y Z)).V
                                k) :
                      (a : k) → (Y.V →₀ k) →ₗ[k] (Z.V →₀ k) →ₗ[k] (X ⊗ Y ⊗ Z).V →₀ k)
                    1 ∘ₗ
                  Finsupp.lsingle y :
                (a : k) → (Z.V →₀ k) →ₗ[k] (X ⊗ Y ⊗ Z).V →₀ k)
              1 ∘ₗ
            Finsupp.lsingle z :
          (a : k) → (X ⊗ Y ⊗ Z).V →₀ k)
        1)
      (((((TensorProduct.AlgebraTensorModule.curry
                            (TensorProduct.AlgebraTensorModule.curry
                              (toLinearMap
                                (comp
                                  (comp (μ X (MonoidalCategoryStruct.tensorObj (𝒞 := Action.instCategory) Y Z))
                                    (lTensor (linearize k G X) (μ Y Z)))
                                  (↑(assoc (linearize k G X) (linearize k G Y) (linearize k G Z)) :
                                    (((linearize k G X).tprod (linearize k G Y)).tprod
                                          (linearize k G Z)).IntertwiningMap
                                      ((linearize k G X).tprod ((linearize k G Y).tprod (linearize k G Z))))))) ∘ₗ
                          Finsupp.lsingle x :
                        k →ₗ[k]
                          Finsupp.{w, u} Y.V k →ₗ[k]
                            Finsupp.{w, u} Z.V k →ₗ[k]
                              Finsupp.{w, u}
                                (MonoidalCategoryStruct.tensorObj (𝒞 := Action.instCategory) X
                                    (MonoidalCategoryStruct.tensorObj (𝒞 := Action.instCategory) Y Z)).V
                                k) :
                      (a : k) → (Y.V →₀ k) →ₗ[k] (Z.V →₀ k) →ₗ[k] (X ⊗ Y ⊗ Z).V →₀ k)
                    1 ∘ₗ
                  Finsupp.lsingle y :
                (a : k) → (Z.V →₀ k) →ₗ[k] (X ⊗ Y ⊗ Z).V →₀ k)
              1 ∘ₗ
            Finsupp.lsingle z :
          (a : k) → (X ⊗ Y ⊗ Z).V →₀ k)
        1)
⊢ Eq (α :=
    IntertwiningMap (V :=
      TensorProduct k (TensorProduct k (Finsupp.{w, u} X.V k) (Finsupp.{w, u} Y.V k)) (Finsupp.{w, u} Z.V k))
      (tprod (tprod (linearize k G X) (linearize k G Y)) (linearize k G Z))
      (linearize k G
        (MonoidalCategoryStruct.tensorObj (𝒞 := Action.instCategory) X
          (MonoidalCategoryStruct.tensorObj (𝒞 := Action.instCategory) Y Z))))
    (comp
      (comp (linearizeMap (Iso.hom (α_ X Y Z))) (μ (MonoidalCategoryStruct.tensorObj (𝒞 := Action.instCategory) X Y) Z))
      (rTensor (linearize k G Z) (μ X Y)))
    (comp
      (comp (μ X (MonoidalCategoryStruct.tensorObj (𝒞 := Action.instCategory) Y Z)) (lTensor (linearize k G X) (μ Y Z)))
      (↑(assoc (linearize k G X) (linearize k G Y) (linearize k G Z)) :
        (((linearize k G X).tprod (linearize k G Y)).tprod (linearize k G Z)).IntertwiningMap
          ((linearize k G X).tprod ((linearize k G Y).tprod (linearize k G Z)))))

Tactic:
ext x y z : 9