-- Lean 4 proof step from Mathlib.Topology.Sheaves.CommRingCat (goal)
Goal:
X_1 : TopCat
R : TopCommRingCat
X : TopCommRingCat
⊢ Eq.{u + 2} (α :=
    Quiver.Hom (V := TopCatᵒᵖ ⥤ CommRingCat)
      { obj := fun (X_2 : TopCatᵒᵖ) ↦ continuousFunctions X_2 X,
        map := fun {x x_1 : TopCatᵒᵖ} (f : x ⟶ x_1) ↦ continuousFunctions.pullback f X, map_id := ⋯, map_comp := ⋯ }
      { obj := fun (X_2 : TopCatᵒᵖ) ↦ continuousFunctions X_2 X,
        map := fun {x x_1 : TopCatᵒᵖ} (f : x ⟶ x_1) ↦ continuousFunctions.pullback f X, map_id := ⋯, map_comp := ⋯ })
    { app := fun (X_2 : TopCatᵒᵖ) ↦ continuousFunctions.map X_2 (𝟙 X), naturality := ⋯ }
    (𝟙
      { obj := fun (X_2 : TopCatᵒᵖ) ↦ continuousFunctions X_2 X,
        map := fun {x x_1 : TopCatᵒᵖ} (f : x ⟶ x_1) ↦ continuousFunctions.pullback f X, map_id := ⋯, map_comp := ⋯ })
have w : ∀ (x : TopCatᵒᵖ)
  (x_1 :
    (↑(Functor.obj
          { obj := fun (X_2 : TopCatᵒᵖ) ↦ continuousFunctions X_2 X,
            map := fun {x x_1 : TopCatᵒᵖ} (f : x ⟶ x_1) ↦ continuousFunctions.pullback f X, map_id := sorry, map_comp := sorry }
          x) :
      Type u)),
  Eq (α :=
    (↑(Functor.obj
          { obj := fun (X_2 : TopCatᵒᵖ) ↦ continuousFunctions X_2 X,
            map := fun {x x_2 : TopCatᵒᵖ} (f : x ⟶ x_2) ↦ continuousFunctions.pullback f X, map_id := sorry, map_comp := sorry }
          x) :
      Type u))
    ((CommRingCat.Hom.hom
            (NatTrans.app { app := fun (X_2 : TopCatᵒᵖ) ↦ continuousFunctions.map X_2 (𝟙 X), naturality := sorry } x) :
          (a :
              (↑({ obj := fun (X_2 : TopCatᵒᵖ) ↦ continuousFunctions X_2 X,
                        map := fun {x x_2 : TopCatᵒᵖ} (f : x ⟶ x_2) ↦ continuousFunctions.pullback f X, map_id := sorry,
                        map_comp := sorry }.obj
                    x) :
                Type u)) →
            (↑({ obj := fun (X_2 : TopCatᵒᵖ) ↦ continuousFunctions X_2 X,
                      map := fun {x x_2 : TopCatᵒᵖ} (f : x ⟶ x_2) ↦ continuousFunctions.pullback f X, map_id := sorry,
                      map_comp := sorry }.obj
                  x) :
              Type u))
        x_1 :
      (↑(Functor.obj
            { obj := fun (X_2 : TopCatᵒᵖ) ↦ continuousFunctions X_2 X,
              map := fun {x x_2 : TopCatᵒᵖ} (f : x ⟶ x_2) ↦ continuousFunctions.pullback f X, map_id := sorry,
              map_comp := sorry }
            x) :
        Type u))
    ((CommRingCat.Hom.hom
            (NatTrans.app
              (𝟙
                { obj := fun (X_2 : TopCatᵒᵖ) ↦ continuousFunctions X_2 X,
                  map := fun {x x_2 : TopCatᵒᵖ} (f : x ⟶ x_2) ↦ continuousFunctions.pullback f X, map_id := sorry,
                  map_comp := sorry })
              x) :
          (a :
              (↑({ obj := fun (X_2 : TopCatᵒᵖ) ↦ continuousFunctions X_2 X,
                        map := fun {x x_2 : TopCatᵒᵖ} (f : x ⟶ x_2) ↦ continuousFunctions.pullback f X, map_id := sorry,
                        map_comp := sorry }.obj
                    x) :
                Type u)) →
            (↑({ obj := fun (X_2 : TopCatᵒᵖ) ↦ continuousFunctions X_2 X,
                      map := fun {x x_2 : TopCatᵒᵖ} (f : x ⟶ x_2) ↦ continuousFunctions.pullback f X, map_id := sorry,
                      map_comp := sorry }.obj
                  x) :
              Type u))
        x_1 :
      (↑(Functor.obj
            { obj := fun (X_2 : TopCatᵒᵖ) ↦ continuousFunctions X_2 X,
              map := fun {x x_2 : TopCatᵒᵖ} (f : x ⟶ x_2) ↦ continuousFunctions.pullback f X, map_id := sorry,
              map_comp := sorry }
            x) :
        Type u))
Tactic: ext