-- Lean 4 proof step from Mathlib.Topology.Sheaves.Presheaf (goal)
Goal:
C : Type u
inst : Category.{v, u} C
inst_1 : Limits.HasColimits.{v, u} C
X Y : TopCat
f : X ⟶ Y
hf :
  IsOpenMap (X := (↑X : Type v)) (Y := (↑Y : Type v))
    (⇑(ConcreteCategory.hom (FC := fun (X Y : TopCat.{v}) ↦ C((↑X : Type v), (↑Y : Type v))) (CC := TopCat.carrier) f) :
      (a : (↑X : Type v)) → (↑Y : Type v))
ℱ 𝒢 : TopCat.Presheaf C Y
u : ℱ ⟶ 𝒢
U : Opens (↑X : Type v)
j : CostructuredArrow (Opens.map f).op (op U)
eq :
  Eq (α := obj (CostructuredArrow.proj (Opens.map f).op (op U) ⋙ ℱ) j ⟶ (obj (pullback C f) 𝒢).obj (op U))
    (CategoryStruct.comp (Y :=
        obj
          (obj (const (CostructuredArrow (Opens.map f).op (op U)))
            (Limits.Cocone.pt (J := CostructuredArrow (Opens.map f).op (op U))
              ((LeftExtension.mk ((Opens.map f).op.leftKanExtension ℱ)
                    ((Opens.map f).op.leftKanExtensionUnit ℱ)).coconeAt
                (op U))))
          j)
        (NatTrans.app
          (Limits.Cocone.ι
            ((LeftExtension.mk ((Opens.map f).op.leftKanExtension ℱ) ((Opens.map f).op.leftKanExtensionUnit ℱ)).coconeAt
              (op U)))
          j)
        (NatTrans.app (CategoryTheory.Functor.map (pullback C f) u) (op U)) :
      obj (CostructuredArrow.proj (Opens.map f).op (op U) ⋙ ℱ) j ⟶ (obj (pullback C f) 𝒢).obj (op U))
    (NatTrans.app (whiskerLeft (CostructuredArrow.proj (Opens.map f).op (op U)) u) j ≫
        NatTrans.app
          (Limits.Cocone.ι
            ((LeftExtension.mk ((Opens.map f).op.leftKanExtension 𝒢) ((Opens.map f).op.leftKanExtensionUnit 𝒢)).coconeAt
              (op U)))
          j :
      obj (CostructuredArrow.proj (Opens.map f).op (op U) ⋙ ℱ) j ⟶
        obj
          (obj (const (CostructuredArrow (Opens.map f).op (op U)))
            (Limits.Cocone.pt (J := CostructuredArrow (Opens.map f).op (op U))
              ((LeftExtension.mk ((Opens.map f).op.leftKanExtension 𝒢)
                    ((Opens.map f).op.leftKanExtensionUnit 𝒢)).coconeAt
                (op U))))
          j)
⊢ Eq (α := obj (CostructuredArrow.proj (Opens.map f).op (op U) ⋙ ℱ) j ⟶ 𝒢.obj (op (hf.functor.obj U)))
    (CategoryStruct.comp (Y :=
      obj
        (obj (const (CostructuredArrow (Opens.map f).op (op U)))
          (Limits.Cocone.pt (J := CostructuredArrow (Opens.map f).op (op U))
            ((LeftExtension.mk ((Opens.map f).op.leftKanExtension ℱ) ((Opens.map f).op.leftKanExtensionUnit ℱ)).coconeAt
              (op U))))
        j)
      (NatTrans.app
        (Limits.Cocone.ι
          ((LeftExtension.mk ((Opens.map f).op.leftKanExtension ℱ) ((Opens.map f).op.leftKanExtensionUnit ℱ)).coconeAt
            (op U)))
        j)
      (NatTrans.app (CategoryTheory.Functor.map (pullback C f) u) (op U) ≫
        Iso.hom
          (Limits.IsColimit.coconePointUniqueUpToIso
            ((Opens.map f).op.isPointwiseLeftKanExtensionLeftKanExtensionUnit 𝒢 (op U))
            (Limits.colimitOfDiagramTerminal
              {
                lift :=
                  fun
                    (s :
                      Limits.Cone (C := CostructuredArrow (Opens.map f).op (op U))
                        (empty (CostructuredArrow (Opens.map f).op (op U)))) ↦
                  CostructuredArrow.homMk (homOfLE ⋯).op ⋯,
                fac := ⋯, uniq := ⋯ }
              (CostructuredArrow.proj (Opens.map f).op (op U) ⋙ 𝒢)))))
    (CategoryStruct.comp (Y :=
      obj
        (obj (const (CostructuredArrow (Opens.map f).op (op U)))
          (Limits.Cocone.pt (J := CostructuredArrow (Opens.map f).op (op U))
            ((LeftExtension.mk ((Opens.map f).op.leftKanExtension ℱ) ((Opens.map f).op.leftKanExtensionUnit ℱ)).coconeAt
              (op U))))
        j)
      (NatTrans.app
        (Limits.Cocone.ι
          ((LeftExtension.mk ((Opens.map f).op.leftKanExtension ℱ) ((Opens.map f).op.leftKanExtensionUnit ℱ)).coconeAt
            (op U)))
        j)
      (CategoryStruct.comp (Y := ℱ.obj (op (hf.functor.obj U)))
        (Iso.hom
            (Limits.IsColimit.coconePointUniqueUpToIso
              ((Opens.map f).op.isPointwiseLeftKanExtensionLeftKanExtensionUnit ℱ (op U))
              (Limits.colimitOfDiagramTerminal
                {
                  lift :=
                    fun
                      (s :
                        Limits.Cone (C := CostructuredArrow (Opens.map f).op (op U))
                          (empty (CostructuredArrow (Opens.map f).op (op U)))) ↦
                    CostructuredArrow.homMk (homOfLE ⋯).op ⋯,
                  fac := ⋯, uniq := ⋯ }
                (CostructuredArrow.proj (Opens.map f).op (op U) ⋙ ℱ))) :
          (obj (pullback C f) ℱ).obj (op U) ⟶ ℱ.obj (op (hf.functor.obj U)))
        (u.app (op (hf.functor.obj U)) : ℱ.obj (op (hf.functor.obj U)) ⟶ 𝒢.obj (op (hf.functor.obj U)))))
have w : Eq (α := obj (CostructuredArrow.proj (Opens.map f).op (op U) ⋙ ℱ) j ⟶ 𝒢.obj (op (hf.functor.obj U)))
  (NatTrans.app (whiskerLeft (CostructuredArrow.proj (Opens.map f).op (op U)) u) j ≫
      NatTrans.app
        (Limits.Cocone.ι
          (Limits.coconeOfDiagramTerminal (X :=
            CostructuredArrow.mk (Y :=
              op
                {
                  carrier :=
                    (⇑(ConcreteCategory.hom (FC := fun (X Y : TopCat.{v}) ↦ C((↑X : Type v), (↑Y : Type v))) (CC :=
                            TopCat.carrier) f) :
                        (a : (↑X : Type v)) → (↑Y : Type v)) ''
                      (↑U : Set (↑X : Type v)),
                  is_open' := sorry })
              (Quiver.Hom.op (homOfLE sorry)))
            {
              lift :=
                fun
                  (s :
                    Limits.Cone (C := CostructuredArrow (Opens.map f).op (op U))
                      (empty (CostructuredArrow (Opens.map f).op (op U)))) ↦
                CostructuredArrow.homMk (homOfLE sorry).op sorry,
              fac := sorry, uniq := sorry }
            (CostructuredArrow.proj (Opens.map f).op (op U) ⋙ 𝒢)))
        j :
    ℱ.obj (obj (CostructuredArrow.proj (Opens.map f).op (op U)) j) ⟶ 𝒢.obj (op (hf.functor.obj U)))
  (CategoryStruct.comp (Y :=
      Limits.Cocone.pt (J := CostructuredArrow (Opens.map f).op (op U)) (F :=
        CostructuredArrow.proj (Opens.map f).op (op U) ⋙ ℱ)
        (Limits.coconeOfDiagramTerminal (X :=
          CostructuredArrow.mk (Y :=
            op
              {
                carrier :=
                  (⇑(ConcreteCategory.hom (FC := fun (X Y : TopCat.{v}) ↦ C((↑X : Type v), (↑Y : Type v))) (CC :=
                          TopCat.carrier) f) :
                      (a : (↑X : Type v)) → (↑Y : Type v)) ''
                    (↑U : Set (↑X : Type v)),
                is_open' := sorry })
            (Quiver.Hom.op (homOfLE sorry)))
          {
            lift :=
              fun
                (s :
                  Limits.Cone (C := CostructuredArrow (Opens.map f).op (op U))
                    (empty (CostructuredArrow (Opens.map f).op (op U)))) ↦
              CostructuredArrow.homMk (homOfLE sorry).op sorry,
            fac := sorry, uniq := sorry }
          (CostructuredArrow.proj (Opens.map f).op (op U) ⋙ ℱ)))
      (NatTrans.app
          (Limits.Cocone.ι
            (Limits.coconeOfDiagramTerminal (X :=
              CostructuredArrow.mk (Y :=
                op
                  {
                    carrier :=
                      (⇑(ConcreteCategory.hom (FC := fun (X Y : TopCat.{v}) ↦ C((↑X : Type v), (↑Y : Type v))) (CC :=
                              TopCat.carrier) f) :
                          (a : (↑X : Type v)) → (↑Y : Type v)) ''
                        (↑U : Set (↑X : Type v)),
                    is_open' := sorry })
                (Quiver.Hom.op (homOfLE sorry)))
              {
                lift :=
                  fun
                    (s :
                      Limits.Cone (C := CostructuredArrow (Opens.map f).op (op U))
                        (empty (CostructuredArrow (Opens.map f).op (op U)))) ↦
                  CostructuredArrow.homMk (homOfLE sorry).op sorry,
                fac := sorry, uniq := sorry }
              (CostructuredArrow.proj (Opens.map f).op (op U) ⋙ ℱ)))
          j :
        obj (CostructuredArrow.proj (Opens.map f).op (op U) ⋙ ℱ) j ⟶
          obj
            (obj (const (CostructuredArrow (Opens.map f).op (op U)))
              (Limits.Cocone.pt (J := CostructuredArrow (Opens.map f).op (op U)) (F :=
                CostructuredArrow.proj (Opens.map f).op (op U) ⋙ ℱ)
                (Limits.coconeOfDiagramTerminal (X :=
                  CostructuredArrow.mk (Y :=
                    op
                      {
                        carrier :=
                          (⇑(ConcreteCategory.hom (FC := fun (X Y : TopCat.{v}) ↦ C((↑X : Type v), (↑Y : Type v)))
                                  (CC := TopCat.carrier) f) :
                              (a : (↑X : Type v)) → (↑Y : Type v)) ''
                            (↑U : Set (↑X : Type v)),
                        is_open' := sorry : Opens (↑Y : Type v) })
                    (Quiver.Hom.op (homOfLE sorry)))
                  {
                    lift :=
                      fun
                        (s :
                          Limits.Cone (C := CostructuredArrow (Opens.map f).op (op U))
                            (empty (CostructuredArrow (Opens.map f).op (op U)))) ↦
                      CostructuredArrow.homMk (homOfLE sorry).op sorry,
                    fac := sorry, uniq := sorry :
                    Limits.IsLimit (C := CostructuredArrow (Opens.map f).op (op U))
                      (Limits.asEmptyCone
                        (CostructuredArrow.mk (Y :=
                          op
                            {
                              carrier :=
                                (⇑(ConcreteCategory.hom (FC := fun (X Y : TopCat.{v}) ↦ C((↑X : Type v), (↑Y : Type v)))
                                        (CC := TopCat.carrier) f) :
                                    (a : (↑X : Type v)) → (↑Y : Type v)) ''
                                  (↑U : Set (↑X : Type v)),
                              is_open' := sorry : Opens (↑Y : Type v) })
                          (Quiver.Hom.op (homOfLE sorry)))) }
                  (CostructuredArrow.proj (Opens.map f).op (op U) ⋙ ℱ))))
            j)
      (u.app (op (hf.functor.obj U))) :
    obj (CostructuredArrow.proj (Opens.map f).op (op U) ⋙ ℱ) j ⟶ 𝒢.obj (op (hf.functor.obj U)))
Tactic: rw [Limits.IsColimit.comp_coconePointUniqueUpToIso_hom_assoc, reassoc_of% eq,
    Limits.IsColimit.comp_coconePointUniqueUpToIso_hom]