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

Tactic:
rfl