-- Module: Mathlib.CategoryTheory.Yoneda
Goal:
C_1 : Type u₁
inst : Category.{v₁, u₁} C_1
C : Type u₁
inst_1 : Category.{v₁, u₁} C
Y Z : C
f : Y ⟶ Z
w :
  ∀ (F : C ⥤ Type v₁) (g : obj (obj (Functor.rightOp coyoneda ⋙ coyoneda) Y) F),
    Eq (α :=
      obj
        (obj
          (evaluation C (Type v₁) ⋙
            obj (whiskeringRight (C ⥤ Type v₁) (Type v₁) (Type (max u₁ v₁))) uliftFunctor.{u₁, v₁})
          Z)
        F)
      (TypeCat.Fun.toFun
        (ConcreteCategory.hom (FC := TypeCat.Fun)
          (NatTrans.app
            (map (Functor.rightOp coyoneda ⋙ coyoneda) f ≫
              Iso.hom
                ((fun (X : C) ↦
                    (NatIso.ofComponents
                        (fun (x : C ⥤ Type v₁) ↦ Equiv.toIso (Equiv.trans coyonedaEquiv (Equiv.symm Equiv.ulift))) ⋯ :
                      Iso (C := (C ⥤ Type v₁) ⥤ Type (max u₁ v₁)) (obj (Functor.rightOp coyoneda ⋙ coyoneda) X)
                        (obj
                          (evaluation C (Type v₁) ⋙
                            obj (whiskeringRight (C ⥤ Type v₁) (Type v₁) (Type (max u₁ v₁))) uliftFunctor.{u₁, v₁})
                          X)))
                  Z))
            F))
        g)
      (TypeCat.Fun.toFun
        (ConcreteCategory.hom (FC := TypeCat.Fun)
          (NatTrans.app
            (Iso.hom
                ((fun (X : C) ↦
                    (NatIso.ofComponents
                        (fun (x : C ⥤ Type v₁) ↦ Equiv.toIso (Equiv.trans coyonedaEquiv (Equiv.symm Equiv.ulift))) ⋯ :
                      Iso (C := (C ⥤ Type v₁) ⥤ Type (max u₁ v₁)) (obj (Functor.rightOp coyoneda ⋙ coyoneda) X)
                        (obj
                          (evaluation C (Type v₁) ⋙
                            obj (whiskeringRight (C ⥤ Type v₁) (Type v₁) (Type (max u₁ v₁))) uliftFunctor.{u₁, v₁})
                          X)))
                  Y) ≫
              map
                (evaluation C (Type v₁) ⋙
                  obj (whiskeringRight (C ⥤ Type v₁) (Type v₁) (Type (max u₁ v₁))) uliftFunctor.{u₁, v₁})
                f)
            F))
        g)
⊢ Eq (α :=
    Quiver.Hom (V := (C ⥤ Type v₁) ⥤ Type (max u₁ v₁)) (obj (Functor.rightOp coyoneda ⋙ coyoneda) Y)
      (obj
        (evaluation C (Type v₁) ⋙
          obj (whiskeringRight (C ⥤ Type v₁) (Type v₁) (Type (max u₁ v₁))) uliftFunctor.{u₁, v₁})
        Z))
    (map (Functor.rightOp coyoneda ⋙ coyoneda) f ≫
      Iso.hom
        ((fun (X : C) ↦
            (NatIso.ofComponents
                (fun (x : C ⥤ Type v₁) ↦ Equiv.toIso (Equiv.trans coyonedaEquiv (Equiv.symm Equiv.ulift))) ⋯ :
              Iso (C := (C ⥤ Type v₁) ⥤ Type (max u₁ v₁)) (obj (Functor.rightOp coyoneda ⋙ coyoneda) X)
                (obj
                  (evaluation C (Type v₁) ⋙
                    obj (whiskeringRight (C ⥤ Type v₁) (Type v₁) (Type (max u₁ v₁))) uliftFunctor.{u₁, v₁})
                  X)))
          Z))
    (Iso.hom
        ((fun (X : C) ↦
            (NatIso.ofComponents
                (fun (x : C ⥤ Type v₁) ↦ Equiv.toIso (Equiv.trans coyonedaEquiv (Equiv.symm Equiv.ulift))) ⋯ :
              Iso (C := (C ⥤ Type v₁) ⥤ Type (max u₁ v₁)) (obj (Functor.rightOp coyoneda ⋙ coyoneda) X)
                (obj
                  (evaluation C (Type v₁) ⋙
                    obj (whiskeringRight (C ⥤ Type v₁) (Type v₁) (Type (max u₁ v₁))) uliftFunctor.{u₁, v₁})
                  X)))
          Y) ≫
      map
        (evaluation C (Type v₁) ⋙
          obj (whiskeringRight (C ⥤ Type v₁) (Type v₁) (Type (max u₁ v₁))) uliftFunctor.{u₁, v₁})
        f)

Tactic:
ext F g