-- Lean 4 proof step from Mathlib.Condensed.Discrete.Colimit (goal)
Goal:
X : LightProfiniteᵒᵖ ⥤ Type u
inst : PreservesFiniteProducts X
hX : (S : LightProfinite.{u}) → IsColimit (X.mapCocone (coconeRightOpOfCone S.asLimitCone))
S : LightProfiniteᵒᵖ
Y : FintypeCatᵒᵖ
right : Discrete PUnit.{1}
g : toLightProfinite.op.obj Y ⟶ obj (fromPUnit S) right
f :
  LocallyConstant
    (↑((toLightProfinite.obj (Opposite.unop Y)).toTop (P := fun (X : TopCat.{u}) ↦
          TotallyDisconnectedSpace.{u} (↑X : Type u) ∧ SecondCountableTopology.{u} (↑X : Type u))) :
      Type u)
    (X.obj
      (Opposite.op
        (CompHausLike.of
          (fun (X : TopCat.{u}) ↦
            TotallyDisconnectedSpace.{u} (↑X : Type u) ∧ SecondCountableTopology.{u} (↑X : Type u))
          PUnit.{u + 1})))
⊢ TypeCat.Fun.toFun
      (ConcreteCategory.hom (FC := TypeCat.Fun)
        ((↾fun (f : LocallyConstant (Opposite.unop Y).obj (X.obj (Opposite.op (LightProfinite.of PUnit.{u + 1})))) ↦
            (⇑f : (a : (Opposite.unop Y).obj) → X.obj (Opposite.op (LightProfinite.of PUnit.{u + 1})))) ≫
          Iso.inv (isoFinYonedaComponents X (toLightProfinite.obj (Opposite.unop Y)))))
      f =
    TypeCat.Fun.toFun
      (ConcreteCategory.hom (FC := TypeCat.Fun)
        (NatTrans.app
          (counitApp (P := fun (X : TopCat.{u}) ↦
            TotallyDisconnectedSpace.{u} (↑X : Type u) ∧ SecondCountableTopology.{u} (↑X : Type u)) X)
          (Opposite.op (toLightProfinite.obj (Opposite.unop Y)))))
      f
have w : ∀
  (a :
    Function.Fiber (Y :=
      (↑((toLightProfinite.obj (Opposite.unop Y)).toTop (P := fun (X : TopCat.{u}) ↦
            TotallyDisconnectedSpace.{u} (↑X : Type u) ∧ SecondCountableTopology.{u} (↑X : Type u))) :
        Type u))
      (Z :=
      X.obj
        (Opposite.op
          (CompHausLike.of
            (fun (X : TopCat.{u}) ↦
              TotallyDisconnectedSpace.{u} (↑X : Type u) ∧ SecondCountableTopology.{u} (↑X : Type u))
            PUnit.{u + 1})))
      (⇑f :
        (a : (↑(toLightProfinite.obj (Opposite.unop Y)).toTop : Type u)) →
          X.obj
            (Opposite.op
              (CompHausLike.of
                (fun (X : TopCat) ↦ TotallyDisconnectedSpace (↑X : Type u) ∧ SecondCountableTopology (↑X : Type u))
                PUnit.{u + 1})))),
  Eq (α :=
    (fun (X : Type u) ↦ X)
      (X.obj
        (Opposite.op
          (fiber (P := fun (X : TopCat.{u}) ↦
            TotallyDisconnectedSpace.{u} (↑X : Type u) ∧ SecondCountableTopology.{u} (↑X : Type u)) f a))))
    ((ConcreteCategory.hom (FC := TypeCat.Fun)
            (X.map
              (Quiver.Hom.op
                (sigmaIncl (P := fun (X : TopCat.{u}) ↦
                  TotallyDisconnectedSpace.{u} (↑X : Type u) ∧ SecondCountableTopology.{u} (↑X : Type u)) f a))) :
          (a_1 : (fun (X : Type u) ↦ X) (X.obj (Opposite.op (toLightProfinite.obj (Opposite.unop Y))))) →
            (fun (X : Type u) ↦ X) (X.obj (Opposite.op (fiber f a))))
        (TypeCat.Fun.toFun
          (ConcreteCategory.hom (FC := TypeCat.Fun)
            ((↾fun (f : LocallyConstant (Opposite.unop Y).obj (X.obj (Opposite.op (LightProfinite.of PUnit.{u + 1})))) ↦
                (⇑f : (a : (Opposite.unop Y).obj) → X.obj (Opposite.op (LightProfinite.of PUnit.{u + 1})))) ≫
              Iso.inv (isoFinYonedaComponents X (toLightProfinite.obj (Opposite.unop Y)))))
          f) :
      (fun (X : Type u) ↦ X)
        (X.obj
          (Opposite.op
            (fiber (P := fun (X : TopCat.{u}) ↦
              TotallyDisconnectedSpace.{u} (↑X : Type u) ∧ SecondCountableTopology.{u} (↑X : Type u)) f a))))
    ((ConcreteCategory.hom (FC := TypeCat.Fun)
            (X.map
              (Quiver.Hom.op
                (sigmaIncl (P := fun (X : TopCat.{u}) ↦
                  TotallyDisconnectedSpace.{u} (↑X : Type u) ∧ SecondCountableTopology.{u} (↑X : Type u)) f a))) :
          (a_1 : (fun (X : Type u) ↦ X) (X.obj (Opposite.op (toLightProfinite.obj (Opposite.unop Y))))) →
            (fun (X : Type u) ↦ X) (X.obj (Opposite.op (fiber f a))))
        (TypeCat.Fun.toFun
          (ConcreteCategory.hom (FC := TypeCat.Fun)
            (NatTrans.app
              (counitApp (P := fun (X : TopCat.{u}) ↦
                TotallyDisconnectedSpace.{u} (↑X : Type u) ∧ SecondCountableTopology.{u} (↑X : Type u)) X)
              (Opposite.op (toLightProfinite.obj (Opposite.unop Y)))))
          f) :
      (fun (X : Type u) ↦ X)
        (X.obj
          (Opposite.op
            (fiber (P := fun (X : TopCat.{u}) ↦
              TotallyDisconnectedSpace.{u} (↑X : Type u) ∧ SecondCountableTopology.{u} (↑X : Type u)) f a))))
Tactic: apply presheaf_ext.{u, u} (X := X) (Y := X) (f := f)