-- Lean 4 proof step from Mathlib.CategoryTheory.Monoidal.Types.Coyoneda (goal)
Goal:
C : Type u
inst : Category.{v, u} C
inst_1 : MonoidalCategory.{v, u} C
X : C
⊢ Eq (α :=
    tensorObj (𝒞 := types) (Functor.obj (Functor.obj coyoneda (op (tensorUnit.{v, u} C (𝒞 := inst)))) X)
        ((𝟙_ (Type v)) (𝒞 := types)) ⟶
      Functor.obj (Functor.obj coyoneda (op (tensorUnit.{v, u} C (𝒞 := inst)))) X)
    (Iso.hom (ρ_ (Functor.obj (Functor.obj coyoneda (op (tensorUnit.{v, u} C (𝒞 := inst)))) X)))
    (CategoryStruct.comp (Y :=
      tensorObj (𝒞 := types) (Functor.obj (Functor.obj coyoneda (op (tensorUnit.{v, u} C (𝒞 := inst)))) X)
        (Functor.obj (Functor.obj coyoneda (op (tensorUnit.{v, u} C (𝒞 := inst)))) (tensorUnit.{v, u} C (𝒞 := inst))))
      (𝟙 (Functor.obj (Functor.obj coyoneda (op (tensorUnit.{v, u} C (𝒞 := inst)))) X) ⊗ₘ
        ↾fun (x : (𝟙_ (Type v)) (𝒞 := types)) ↦ 𝟙 (unop (op (tensorUnit.{v, u} C (𝒞 := inst)))))
      (CategoryStruct.comp (Y :=
        Functor.obj (Functor.obj coyoneda (op (tensorUnit.{v, u} C (𝒞 := inst))))
          (tensorObj.{v, u} (𝒞 := inst) X (tensorUnit.{v, u} C (𝒞 := inst))))
        ((fun (X Y : C) ↦
            (↾fun
                  (p :
                    tensorObj (𝒞 := types) (Functor.obj (Functor.obj coyoneda (op (tensorUnit.{v, u} C (𝒞 := inst)))) X)
                      (Functor.obj (Functor.obj coyoneda (op (tensorUnit.{v, u} C (𝒞 := inst)))) Y)) ↦
                Iso.inv (λ_ (tensorUnit.{v, u} C (𝒞 := inst))) ≫ (p.1 ⊗ₘ p.2) :
              tensorObj (𝒞 := types) (Functor.obj (Functor.obj coyoneda (op (tensorUnit.{v, u} C (𝒞 := inst)))) X)
                  (Functor.obj (Functor.obj coyoneda (op (tensorUnit.{v, u} C (𝒞 := inst)))) Y) ⟶
                Functor.obj (Functor.obj coyoneda (op (tensorUnit.{v, u} C (𝒞 := inst))))
                  (tensorObj.{v, u} (𝒞 := inst) X Y)))
          X (tensorUnit.{v, u} C (𝒞 := inst)))
        (Functor.map (Functor.obj coyoneda (op (tensorUnit.{v, u} C (𝒞 := inst)))) (Iso.hom (ρ_ X)))))
have h : ∀ (f : Functor.obj (Functor.obj coyoneda (op (tensorUnit.{v, u} C (𝒞 := inst)))) X),
  TypeCat.Fun.toFun
      (ConcreteCategory.hom (FC := TypeCat.Fun)
        (Iso.hom (ρ_ (Functor.obj (Functor.obj coyoneda (op (tensorUnit.{v, u} C (𝒞 := inst)))) X))))
      (f, PUnit.unit) =
    TypeCat.Fun.toFun
      (ConcreteCategory.hom (FC := TypeCat.Fun)
        (CategoryStruct.comp (Y :=
          tensorObj (𝒞 := types) (Functor.obj (Functor.obj coyoneda (op (tensorUnit.{v, u} C (𝒞 := inst)))) X)
            (Functor.obj (Functor.obj coyoneda (op (tensorUnit.{v, u} C (𝒞 := inst))))
              (tensorUnit.{v, u} C (𝒞 := inst))))
          (𝟙 (Functor.obj (Functor.obj coyoneda (op (tensorUnit.{v, u} C (𝒞 := inst)))) X) ⊗ₘ
            ↾fun (x : (𝟙_ (Type v)) (𝒞 := types)) ↦ 𝟙 (unop (op (tensorUnit.{v, u} C (𝒞 := inst)))))
          (CategoryStruct.comp (Y :=
            Functor.obj (Functor.obj coyoneda (op (tensorUnit.{v, u} C (𝒞 := inst))))
              (tensorObj.{v, u} (𝒞 := inst) X (tensorUnit.{v, u} C (𝒞 := inst))))
            ((fun (X Y : C) ↦
                (↾fun
                      (p :
                        tensorObj (𝒞 := types)
                          (Functor.obj (Functor.obj coyoneda (op (tensorUnit.{v, u} C (𝒞 := inst)))) X)
                          (Functor.obj (Functor.obj coyoneda (op (tensorUnit.{v, u} C (𝒞 := inst)))) Y)) ↦
                    Iso.inv (λ_ (tensorUnit.{v, u} C (𝒞 := inst))) ≫ (p.1 ⊗ₘ p.2) :
                  tensorObj (𝒞 := types) (Functor.obj (Functor.obj coyoneda (op (tensorUnit.{v, u} C (𝒞 := inst)))) X)
                      (Functor.obj (Functor.obj coyoneda (op (tensorUnit.{v, u} C (𝒞 := inst)))) Y) ⟶
                    Functor.obj (Functor.obj coyoneda (op (tensorUnit.{v, u} C (𝒞 := inst))))
                      (tensorObj.{v, u} (𝒞 := inst) X Y)))
              X (tensorUnit.{v, u} C (𝒞 := inst)))
            (Functor.map (Functor.obj coyoneda (op (tensorUnit.{v, u} C (𝒞 := inst)))) (Iso.hom (ρ_ X))))))
      (f, PUnit.unit)
Tactic: ext ⟨f, ⟨⟩⟩