-- Lean 4 proof step from Mathlib.CategoryTheory.Monoidal.Closed.Ideal (goal)
Goal:
C : Type u₁
D : Type u₂
inst : Category.{v₁, u₁} C
inst_1 : Category.{v₁, u₂} D
i : Functor.{v₁, v₁, u₂, u₁} D C
inst_2 : CartesianMonoidalCategory.{v₁, u₁} C
inst_3 : Reflective i
inst_4 : MonoidalClosed.{v₁, u₁} C
inst_5 : CartesianMonoidalCategory.{v₁, u₂} D
inst_6 : ExponentialIdeal i
inst_7 : BraidedCategory.{v₁, u₁} C
A B : C
⊢ Eq (α :=
    (reflector i).obj (tensorObj.{v₁, u₁} (𝒞 := inst) A B) ⟶
      tensorObj.{v₁, u₂} (𝒞 := inst_1) ((reflector i).obj A) ((reflector i).obj B))
    ((Equiv.symm (bijection i A B (tensorObj.{v₁, u₂} (𝒞 := inst_1) ((reflector i).obj A) ((reflector i).obj B))) :
          (a : (reflector i).obj A ⊗ (reflector i).obj B ⟶ (reflector i).obj A ⊗ (reflector i).obj B) →
            (reflector i).obj (A ⊗ B) ⟶ (reflector i).obj A ⊗ (reflector i).obj B)
        (𝟙 (tensorObj.{v₁, u₂} (𝒞 := inst_1) ((reflector i).obj A) ((reflector i).obj B))) :
      (reflector i).obj (tensorObj.{v₁, u₁} (𝒞 := inst) A B) ⟶
        tensorObj.{v₁, u₂} (𝒞 := inst_1) ((reflector i).obj A) ((reflector i).obj B))
    (prodComparison (reflector i) A B :
      (reflector i).obj (tensorObj.{v₁, u₁} (𝒞 := inst) A B) ⟶
        tensorObj.{v₁, u₂} (𝒞 := inst_1) ((reflector i).obj A) ((reflector i).obj B))
have simp : Eq (α :=
  (reflector i).obj (tensorObj.{v₁, u₁} (𝒞 := inst) A B) ⟶
    tensorObj.{v₁, u₂} (𝒞 := inst_1) ((reflector i).obj A) ((reflector i).obj B))
  ((Equiv.symm
          (Adjunction.homEquiv (reflectorAdjunction i) (tensorObj.{v₁, u₁} (𝒞 := inst) A B)
            (tensorObj.{v₁, u₂} (𝒞 := inst_1) ((reflector i).obj A) ((reflector i).obj B))) :
        (a : A ⊗ B ⟶ i.obj ((reflector i).obj A ⊗ (reflector i).obj B)) →
          (reflector i).obj (A ⊗ B) ⟶ (reflector i).obj A ⊗ (reflector i).obj B)
      (Iso.hom (β_ A B) ≫
        (Equiv.symm
              (Adjunction.homEquiv (ihom.adjunction B) A
                (i.obj (tensorObj.{v₁, u₂} (𝒞 := inst_1) ((reflector i).obj A) ((reflector i).obj B)))) :
            (a : A ⟶ B ⟹ i.obj ((reflector i).obj A ⊗ (reflector i).obj B)) →
              B ⊗ A ⟶ i.obj ((reflector i).obj A ⊗ (reflector i).obj B))
          (CategoryStruct.comp (Y := i.obj ((reflector i).obj A))
            (NatTrans.app (Adjunction.unit (reflectorAdjunction i)) A)
            ((Adjunction.homEquiv (ihom.adjunction B) (i.obj ((reflector i).obj A))
                  (i.obj (tensorObj.{v₁, u₂} (𝒞 := inst_1) ((reflector i).obj A) ((reflector i).obj B))) :
                (a : B ⊗ i.obj ((reflector i).obj A) ⟶ i.obj ((reflector i).obj A ⊗ (reflector i).obj B)) →
                  i.obj ((reflector i).obj A) ⟶ B ⟹ i.obj ((reflector i).obj A ⊗ (reflector i).obj B))
              (Iso.hom (β_ B (i.obj ((reflector i).obj A))) ≫
                (Equiv.symm
                      (Adjunction.homEquiv (ihom.adjunction (i.obj ((reflector i).obj A))) B
                        (i.obj (tensorObj.{v₁, u₂} (𝒞 := inst_1) ((reflector i).obj A) ((reflector i).obj B)))) :
                    (a : B ⟶ i.obj ((reflector i).obj A) ⟹ i.obj ((reflector i).obj A ⊗ (reflector i).obj B)) →
                      i.obj ((reflector i).obj A) ⊗ B ⟶ i.obj ((reflector i).obj A ⊗ (reflector i).obj B))
                  (CategoryStruct.comp (Y := i.obj ((reflector i).obj B))
                    (NatTrans.app (Adjunction.unit (reflectorAdjunction i)) B)
                    ((Adjunction.homEquiv (ihom.adjunction (i.obj ((reflector i).obj A))) (i.obj ((reflector i).obj B))
                          (i.obj (tensorObj.{v₁, u₂} (𝒞 := inst_1) ((reflector i).obj A) ((reflector i).obj B))) :
                        (a :
                            i.obj ((reflector i).obj A) ⊗ i.obj ((reflector i).obj B) ⟶
                              i.obj ((reflector i).obj A ⊗ (reflector i).obj B)) →
                          i.obj ((reflector i).obj B) ⟶
                            i.obj ((reflector i).obj A) ⟹ i.obj ((reflector i).obj A ⊗ (reflector i).obj B))
                      (Iso.inv (prodComparisonIso i ((reflector i).obj A) ((reflector i).obj B))))))))) :
    (reflector i).obj (tensorObj.{v₁, u₁} (𝒞 := inst) A B) ⟶
      tensorObj.{v₁, u₂} (𝒞 := inst_1) ((reflector i).obj A) ((reflector i).obj B))
  (prodComparison (reflector i) A B :
    (reflector i).obj (tensorObj.{v₁, u₁} (𝒞 := inst) A B) ⟶
      tensorObj.{v₁, u₂} (𝒞 := inst_1) ((reflector i).obj A) ((reflector i).obj B))
Tactic: simp only [bijection, Equiv.trans_def, curriedTensor_obj_obj, Equiv.symm_trans_apply,
    Equiv.symm_symm, Functor.FullyFaithful.homEquiv_apply, Functor.map_id, Iso.homCongr_symm,
    Iso.symm_symm_eq, Iso.refl_symm, Iso.homCongr_apply, Iso.refl_hom, Category.comp_id,
    unitCompPartialBijective_symm_apply, Functor.id_obj, Functor.comp_obj, Iso.symm_inv]