-- Lean 4 proof step from Mathlib.CategoryTheory.Galois.Decomposition (goal)
Goal:
C : Type u₁
inst : Category.{u₂, u₁} C
inst_1 : GaloisCategory.{u₁, u₂} C
F : Functor.{u₂, w, u₁, w + 1} C FintypeCat
inst_2 : FiberFunctor F
G : Functor.{u₂, w, u₁, w + 1} C FintypeCat
t s : F ⟶ G
h : ∀ (X : C) [IsGalois.{u₁, u₂} X], t.app X = s.app X
X : C
x : (F.obj X).obj
⊢ Eq (α := (fun (X : ObjectProperty.FullSubcategory Finite) ↦ X.obj) (G.obj X))
    ((@ConcreteCategory.hom _ (ObjectProperty.FullSubcategory.category Finite)
            (fun (X Y : ObjectProperty.FullSubcategory Finite) ↦ TypeCat.Fun X.obj Y.obj)
            (fun (X : ObjectProperty.FullSubcategory Finite) ↦ X.obj)
            (fun (X Y : ObjectProperty.FullSubcategory Finite) ↦
              (TypeCat.instFunLikeFun : FunLike (TypeCat.Fun X.obj Y.obj) X.obj Y.obj))
            _ _ _ (t.app X) :
          (a : (fun (X : ObjectProperty.FullSubcategory Finite) ↦ X.obj) (F.obj X)) →
            (fun (X : ObjectProperty.FullSubcategory Finite) ↦ X.obj) (G.obj X))
        x :
      (fun (X : ObjectProperty.FullSubcategory Finite) ↦ X.obj) (G.obj X))
    ((@ConcreteCategory.hom _ (ObjectProperty.FullSubcategory.category Finite)
            (fun (X Y : ObjectProperty.FullSubcategory Finite) ↦ TypeCat.Fun X.obj Y.obj)
            (fun (X : ObjectProperty.FullSubcategory Finite) ↦ X.obj)
            (fun (X Y : ObjectProperty.FullSubcategory Finite) ↦
              (TypeCat.instFunLikeFun : FunLike (TypeCat.Fun X.obj Y.obj) X.obj Y.obj))
            _ _ _ (s.app X) :
          (a : (fun (X : ObjectProperty.FullSubcategory Finite) ↦ X.obj) (F.obj X)) →
            (fun (X : ObjectProperty.FullSubcategory Finite) ↦ X.obj) (G.obj X))
        x :
      (fun (X : ObjectProperty.FullSubcategory Finite) ↦ X.obj) (G.obj X))
have w : ∀ (A : C) (f : A ⟶ X) (a : (F.obj A).obj),
  IsGalois.{u₁, u₂} A →
    Eq (α := (fun (X : ObjectProperty.FullSubcategory Finite) ↦ X.obj) (G.obj X))
      ((@ConcreteCategory.hom _ (ObjectProperty.FullSubcategory.category Finite)
              (fun (X Y : ObjectProperty.FullSubcategory Finite) ↦ TypeCat.Fun X.obj Y.obj)
              (fun (X : ObjectProperty.FullSubcategory Finite) ↦ X.obj)
              (fun (X Y : ObjectProperty.FullSubcategory Finite) ↦
                (TypeCat.instFunLikeFun : FunLike (TypeCat.Fun X.obj Y.obj) X.obj Y.obj))
              _ _ _ (t.app X) :
            (a : (fun (X : ObjectProperty.FullSubcategory Finite) ↦ X.obj) (F.obj X)) →
              (fun (X : ObjectProperty.FullSubcategory Finite) ↦ X.obj) (G.obj X))
          ((@ConcreteCategory.hom _ (ObjectProperty.FullSubcategory.category Finite)
                  (fun (X Y : ObjectProperty.FullSubcategory Finite) ↦ TypeCat.Fun X.obj Y.obj)
                  (fun (X : ObjectProperty.FullSubcategory Finite) ↦ X.obj)
                  (fun (X Y : ObjectProperty.FullSubcategory Finite) ↦
                    (TypeCat.instFunLikeFun : FunLike (TypeCat.Fun X.obj Y.obj) X.obj Y.obj))
                  _ _ _ (F.map f) :
                (a : (fun (X : ObjectProperty.FullSubcategory Finite) ↦ X.obj) (F.obj A)) →
                  (fun (X : ObjectProperty.FullSubcategory Finite) ↦ X.obj) (F.obj X))
              a :
            (fun (X : ObjectProperty.FullSubcategory Finite) ↦ X.obj) (F.obj X)) :
        (fun (X : ObjectProperty.FullSubcategory Finite) ↦ X.obj) (G.obj X))
      ((@ConcreteCategory.hom _ (ObjectProperty.FullSubcategory.category Finite)
              (fun (X Y : ObjectProperty.FullSubcategory Finite) ↦ TypeCat.Fun X.obj Y.obj)
              (fun (X : ObjectProperty.FullSubcategory Finite) ↦ X.obj)
              (fun (X Y : ObjectProperty.FullSubcategory Finite) ↦
                (TypeCat.instFunLikeFun : FunLike (TypeCat.Fun X.obj Y.obj) X.obj Y.obj))
              _ _ _ (s.app X) :
            (a : (fun (X : ObjectProperty.FullSubcategory Finite) ↦ X.obj) (F.obj X)) →
              (fun (X : ObjectProperty.FullSubcategory Finite) ↦ X.obj) (G.obj X))
          ((@ConcreteCategory.hom _ (ObjectProperty.FullSubcategory.category Finite)
                  (fun (X Y : ObjectProperty.FullSubcategory Finite) ↦ TypeCat.Fun X.obj Y.obj)
                  (fun (X : ObjectProperty.FullSubcategory Finite) ↦ X.obj)
                  (fun (X Y : ObjectProperty.FullSubcategory Finite) ↦
                    (TypeCat.instFunLikeFun : FunLike (TypeCat.Fun X.obj Y.obj) X.obj Y.obj))
                  _ _ _ (F.map f) :
                (a : (fun (X : ObjectProperty.FullSubcategory Finite) ↦ X.obj) (F.obj A)) →
                  (fun (X : ObjectProperty.FullSubcategory Finite) ↦ X.obj) (F.obj X))
              a :
            (fun (X : ObjectProperty.FullSubcategory Finite) ↦ X.obj) (F.obj X)) :
        (fun (X : ObjectProperty.FullSubcategory Finite) ↦ X.obj) (G.obj X))
Tactic: obtain ⟨A, f, a, _, rfl⟩ := exists_hom_from_galois_of_fiber F X x
Cleared hypotheses: x