-- Module: Mathlib.Geometry.RingedSpace.PresheafedSpace.Gluing
Goal:
C : Type u
inst : Category.{v, u} C
D : GlueData.{v, u} C
i j k : D.J
U : Opens (↑(↑(pullback (D.f i j) (D.f i k)) : TopCat) : Type v)
w :
  Eq (α := Set (↑(↑(D.V (k, i)) : TopCat) : Type v))
    (Set.preimage (β := (↑(↑(D.V (i, k)) : TopCat) : Type v))
      (⇑(ConcreteCategory.hom (FC := fun (X Y : TopCat.{v}) ↦ C((↑X : Type v), (↑Y : Type v))) (CC := TopCat.carrier)
            (D.t k i).base) :
        (a : (↑(↑(D.V (k, i)) : TopCat) : Type v)) → (↑(↑(D.V (i, k)) : TopCat) : Type v))
      ((⇑(ConcreteCategory.hom (FC := fun (X Y : TopCat.{v}) ↦ C((↑X : Type v), (↑Y : Type v))) (CC := TopCat.carrier)
              (X := (↑(pullback (D.f i j) (D.f i k)) : TopCat)) (Hom.base (pullback.snd (D.f i j) (D.f i k)))) :
          (a : (↑(↑(pullback (D.f i j) (D.f i k)) : TopCat) : Type v)) → (↑(↑(D.V (i, k)) : TopCat) : Type v)) ''
        (↑U : Set (↑(↑(pullback (D.f i j) (D.f i k)) : TopCat) : Type v))))
    (Set.image (α := (↑(↑(pullback (D.f k i) (D.f k j)) : TopCat) : Type v))
      (⇑(ConcreteCategory.hom (FC := fun (X Y : TopCat.{v}) ↦ C((↑X : Type v), (↑Y : Type v))) (CC := TopCat.carrier)
            (X := (↑(pullback (D.f k i) (D.f k j)) : TopCat)) (Hom.base (pullback.fst (D.f k i) (D.f k j)))) :
        (a : (↑(↑(pullback (D.f k i) (D.f k j)) : TopCat) : Type v)) → (↑(↑(D.V (k, i)) : TopCat) : Type v))
      ((⇑(ConcreteCategory.hom (FC := fun (X Y : TopCat.{v}) ↦ C((↑X : Type v), (↑Y : Type v))) (CC := TopCat.carrier)
              (D.t' k i j).base) :
          (a : (↑(↑(pullback (D.f k i) (D.f k j)) : TopCat) : Type v)) →
            (↑(↑(pullback (D.f i j) (D.f i k)) : TopCat) : Type v)) ⁻¹'
        (↑U : Set (↑(↑(pullback (D.f i j) (D.f i k)) : TopCat) : Type v))))
⊢ op
      {
        carrier :=
          Set.preimage (β := (↑(↑(D.V (i, k)) : TopCat) : Type v))
            (⇑(ConcreteCategory.hom (FC := fun (X Y : TopCat.{v}) ↦ C((↑X : Type v), (↑Y : Type v))) (CC :=
                  TopCat.carrier) (D.t k i).base) :
              (a : (↑(↑(D.V (k, i)) : TopCat) : Type v)) → (↑(↑(D.V (i, k)) : TopCat) : Type v))
            ((⇑(ConcreteCategory.hom (FC := fun (X Y : TopCat.{v}) ↦ C((↑X : Type v), (↑Y : Type v))) (CC :=
                    TopCat.carrier) (X := (↑(pullback (D.f i j) (D.f i k)) : TopCat))
                    (Hom.base (pullback.snd (D.f i j) (D.f i k)))) :
                (a : (↑(↑(pullback (D.f i j) (D.f i k)) : TopCat) : Type v)) → (↑(↑(D.V (i, k)) : TopCat) : Type v)) ''
              (↑U : Set (↑(↑(pullback (D.f i j) (D.f i k)) : TopCat) : Type v))),
        is_open' := ⋯ : Opens (↑(↑(D.V (k, i)) : TopCat) : Type v) } =
    op
      {
        carrier :=
          Set.image (α := (↑(↑(pullback (D.f k i) (D.f k j)) : TopCat) : Type v))
            (⇑(ConcreteCategory.hom (FC := fun (X Y : TopCat.{v}) ↦ C((↑X : Type v), (↑Y : Type v))) (CC :=
                  TopCat.carrier) (X := (↑(pullback (D.f k i) (D.f k j)) : TopCat))
                  (Hom.base (pullback.fst (D.f k i) (D.f k j)))) :
              (a : (↑(↑(pullback (D.f k i) (D.f k j)) : TopCat) : Type v)) → (↑(↑(D.V (k, i)) : TopCat) : Type v))
            ((⇑(ConcreteCategory.hom (FC := fun (X Y : TopCat.{v}) ↦ C((↑X : Type v), (↑Y : Type v))) (CC :=
                    TopCat.carrier) (D.t' k i j).base) :
                (a : (↑(↑(pullback (D.f k i) (D.f k j)) : TopCat) : Type v)) →
                  (↑(↑(pullback (D.f i j) (D.f i k)) : TopCat) : Type v)) ⁻¹'
              (↑U : Set (↑(↑(pullback (D.f i j) (D.f i k)) : TopCat) : Type v))),
        is_open' := ⋯ }

Tactic:
congr 2