-- Module: Mathlib.Algebra.Category.HopfAlgCat.Monoidal
Goal:
R : Type u
inst : CommRing R
x x_1 x_2 : HopfAlgCat R
x_3 : x_1 ⟶ x_2
x_4 :
  (Functor.obj
      (forget₂ (HopfAlgCat R) (FC := fun (x1 x2 : HopfAlgCat R) ↦ x1.carrier →ₐc[R] x2.carrier) (CC := carrier)
        (BialgCat R) (FD := fun (x1 x2 : BialgCat R) ↦ x1.carrier →ₐc[R] x2.carrier) (CD := BialgCat.carrier))
      (tensorObj (𝒞 := category) x x_1)).carrier
⊢ Eq (α :=
    (Functor.obj
        (forget₂ (HopfAlgCat R) (FC := fun (x1 x2 : HopfAlgCat R) ↦ x1.carrier →ₐc[R] x2.carrier) (CC := carrier)
          (BialgCat R) (FD := fun (x1 x2 : BialgCat R) ↦ x1.carrier →ₐc[R] x2.carrier) (CD := BialgCat.carrier))
        (tensorObj (𝒞 := category) x x_2)).carrier)
    ((BialgCat.Hom.toBialgHom
            (CategoryTheory.Functor.map
              (forget₂ (HopfAlgCat R) (FC := fun (x1 x2 : HopfAlgCat R) ↦ x1.carrier →ₐc[R] x2.carrier) (CC := carrier)
                (BialgCat R) (FD := fun (x1 x2 : BialgCat R) ↦ x1.carrier →ₐc[R] x2.carrier) (CD := BialgCat.carrier))
              (x ◁ x_3)) :
          (a : ((forget₂ (HopfAlgCat R) (BialgCat R)).obj (x ⊗ x_1)).carrier) →
            ((forget₂ (HopfAlgCat R) (BialgCat R)).obj (x ⊗ x_2)).carrier)
        x_4 :
      (Functor.obj
          (forget₂ (HopfAlgCat R) (FC := fun (x1 x2 : HopfAlgCat R) ↦ x1.carrier →ₐc[R] x2.carrier) (CC := carrier)
            (BialgCat R) (FD := fun (x1 x2 : BialgCat R) ↦ x1.carrier →ₐc[R] x2.carrier) (CD := BialgCat.carrier))
          (tensorObj (𝒞 := category) x x_2)).carrier)
    ((BialgCat.Hom.toBialgHom
            (Iso.inv
                (Iso.refl
                  (tensorObj (𝒞 := BialgCat.category)
                    (Functor.obj
                      (forget₂ (HopfAlgCat R) (FC := fun (x1 x2 : HopfAlgCat R) ↦ x1.carrier →ₐc[R] x2.carrier) (CC :=
                        carrier) (BialgCat R) (FD := fun (x1 x2 : BialgCat R) ↦ x1.carrier →ₐc[R] x2.carrier) (CD :=
                        BialgCat.carrier))
                      x)
                    (Functor.obj
                      (forget₂ (HopfAlgCat R) (FC := fun (x1 x2 : HopfAlgCat R) ↦ x1.carrier →ₐc[R] x2.carrier) (CC :=
                        carrier) (BialgCat R) (FD := fun (x1 x2 : BialgCat R) ↦ x1.carrier →ₐc[R] x2.carrier) (CD :=
                        BialgCat.carrier))
                      x_1))) ≫
              Functor.obj
                    (forget₂ (HopfAlgCat R) (FC := fun (x1 x2 : HopfAlgCat R) ↦ x1.carrier →ₐc[R] x2.carrier) (CC :=
                      carrier) (BialgCat R) (FD := fun (x1 x2 : BialgCat R) ↦ x1.carrier →ₐc[R] x2.carrier) (CD :=
                      BialgCat.carrier))
                    x ◁
                  CategoryTheory.Functor.map
                    (forget₂ (HopfAlgCat R) (FC := fun (x1 x2 : HopfAlgCat R) ↦ x1.carrier →ₐc[R] x2.carrier) (CC :=
                      carrier) (BialgCat R) (FD := fun (x1 x2 : BialgCat R) ↦ x1.carrier →ₐc[R] x2.carrier) (CD :=
                      BialgCat.carrier))
                    x_3 ≫
                Iso.hom
                  (Iso.refl
                    (tensorObj (𝒞 := BialgCat.category)
                      (Functor.obj
                        (forget₂ (HopfAlgCat R) (FC := fun (x1 x2 : HopfAlgCat R) ↦ x1.carrier →ₐc[R] x2.carrier) (CC :=
                          carrier) (BialgCat R) (FD := fun (x1 x2 : BialgCat R) ↦ x1.carrier →ₐc[R] x2.carrier) (CD :=
                          BialgCat.carrier))
                        x)
                      (Functor.obj
                        (forget₂ (HopfAlgCat R) (FC := fun (x1 x2 : HopfAlgCat R) ↦ x1.carrier →ₐc[R] x2.carrier) (CC :=
                          carrier) (BialgCat R) (FD := fun (x1 x2 : BialgCat R) ↦ x1.carrier →ₐc[R] x2.carrier) (CD :=
                          BialgCat.carrier))
                        x_2)))) :
          (a : ((forget₂ (HopfAlgCat R) (BialgCat R)).obj (x ⊗ x_1)).carrier) →
            ((forget₂ (HopfAlgCat R) (BialgCat R)).obj (x ⊗ x_2)).carrier)
        x_4 :
      (Functor.obj
          (forget₂ (HopfAlgCat R) (FC := fun (x1 x2 : HopfAlgCat R) ↦ x1.carrier →ₐc[R] x2.carrier) (CC := carrier)
            (BialgCat R) (FD := fun (x1 x2 : BialgCat R) ↦ x1.carrier →ₐc[R] x2.carrier) (CD := BialgCat.carrier))
          (tensorObj (𝒞 := category) x x_2)).carrier)

Tactic:
rfl