-- Lean 4 proof step from Mathlib.AlgebraicGeometry.StructureSheaf (goal)
Goal:
R M A : Type u
inst : CommRing R
inst_1 : AddCommGroup M
inst_2 : Module R M
inst_3 : CommRing A
inst_4 : Algebra R A
x : (↑(PrimeSpectrum.Top R) : Type u)
r : R
α : stalk (PresheafOfModules.presheaf (moduleStructurePresheaf R R)) x ≅
  Functor.obj
    (forget₂ CommRingCat (FC := fun (R S : CommRingCat.{u}) ↦ (↑R : Type u) →+* (↑S : Type u)) (CC :=
        CommRingCat.carrier) RingCat (FD := fun (R S : RingCat.{u}) ↦ (↑R : Type u) →+* (↑S : Type u)) (CD :=
        RingCat.carrier) ⋙
      forget₂ RingCat (FC := fun (R S : RingCat.{u}) ↦ (↑R : Type u) →+* (↑S : Type u)) (CC := RingCat.carrier)
        AddCommGrpCat (FD := fun (x1 x2 : AddCommGrpCat.{u}) ↦ (↑x1 : Type u) →+ (↑x2 : Type u)) (CD :=
        AddCommGrpCat.carrier))
    (stalk (structurePresheafInCommRingCat R) x) :=
  Limits.colimit.isoColimitCocone
    {
      cocone :=
        Functor.mapCocone
          (forget₂ CommRingCat (FC := fun (R S : CommRingCat.{u}) ↦ (↑R : Type u) →+* (↑S : Type u)) (CC :=
              CommRingCat.carrier) RingCat (FD := fun (R S : RingCat.{u}) ↦ (↑R : Type u) →+* (↑S : Type u)) (CD :=
              RingCat.carrier) ⋙
            forget₂ RingCat (FC := fun (R S : RingCat.{u}) ↦ (↑R : Type u) →+* (↑S : Type u)) (CC := RingCat.carrier)
              AddCommGrpCat (FD := fun (x1 x2 : AddCommGrpCat.{u}) ↦ (↑x1 : Type u) →+ (↑x2 : Type u)) (CD :=
              AddCommGrpCat.carrier))
          (Limits.colimit.cocone ((OpenNhds.inclusion x).op ⋙ structurePresheafInCommRingCat R)),
      isColimit :=
        Limits.isColimitOfPreserves
          (forget₂ CommRingCat (FC := fun (R S : CommRingCat.{u}) ↦ (↑R : Type u) →+* (↑S : Type u)) (CC :=
              CommRingCat.carrier) RingCat (FD := fun (R S : RingCat.{u}) ↦ (↑R : Type u) →+* (↑S : Type u)) (CD :=
              RingCat.carrier) ⋙
            forget₂ RingCat (FC := fun (R S : RingCat.{u}) ↦ (↑R : Type u) →+* (↑S : Type u)) (CC := RingCat.carrier)
              AddCommGrpCat (FD := fun (x1 x2 : AddCommGrpCat.{u}) ↦ (↑x1 : Type u) →+ (↑x2 : Type u)) (CD :=
              AddCommGrpCat.carrier))
          (Limits.colimit.isColimit ((OpenNhds.inclusion x).op ⋙ structurePresheafInCommRingCat R)) }
U : Opens (↑(PrimeSpectrum.Top R) : Type u)
hxU : x ∈ U
s :
  ToType (FC := fun (x1 x2 : AddCommGrpCat.{u}) ↦ (↑x1 : Type u) →+ (↑x2 : Type u)) (CC := AddCommGrpCat.carrier)
    (Functor.obj (PresheafOfModules.presheaf (moduleStructurePresheaf R R)) (op U))
this :
  germ (PresheafOfModules.presheaf (moduleStructurePresheaf R R)) U x hxU ≫ α.hom =
    CategoryTheory.Functor.map
      (forget₂ CommRingCat (FC := fun (R S : CommRingCat.{u}) ↦ (↑R : Type u) →+* (↑S : Type u)) (CC :=
          CommRingCat.carrier) RingCat (FD := fun (R S : RingCat.{u}) ↦ (↑R : Type u) →+* (↑S : Type u)) (CD :=
          RingCat.carrier) ⋙
        forget₂ RingCat (FC := fun (R S : RingCat.{u}) ↦ (↑R : Type u) →+* (↑S : Type u)) (CC := RingCat.carrier)
          AddCommGrpCat (FD := fun (x1 x2 : AddCommGrpCat.{u}) ↦ (↑x1 : Type u) →+ (↑x2 : Type u)) (CD :=
          AddCommGrpCat.carrier))
      (germ (structurePresheafInCommRingCat R) U x hxU)
⊢ Eq (α := (↑(stalk (structurePresheafInCommRingCat R) x) : Type u))
    (((CommRingCat.Hom.hom (germ (structurePresheafInCommRingCat R) U x hxU) :
            (↑(Functor.obj (structurePresheafInCommRingCat R) (op U)) : Type u) →+*
              (↑(stalk (structurePresheafInCommRingCat R) x) : Type u)) :
          (a : (structureSheafInType R R).obj.obj (op U)) → (↑((structurePresheafInCommRingCat R).stalk x) : Type u))
        ((algebraMap R
                (Functor.obj
                  (ObjectProperty.FullSubcategory.obj (P :=
                    CategoryTheory.Presheaf.IsSheaf (Opens.grothendieckTopology (↑(PrimeSpectrum.Top R) : Type u)))
                    (structureSheafInType R R))
                  (op U)) :
              (a : R) → (structureSheafInType R R).obj.obj (op U))
            r :
          Functor.obj
            (ObjectProperty.FullSubcategory.obj (P :=
              CategoryTheory.Presheaf.IsSheaf (Opens.grothendieckTopology (↑(PrimeSpectrum.Top R) : Type u)))
              (structureSheafInType R R))
            (op U)) :
      (↑(stalk (structurePresheafInCommRingCat R) x) : Type u))
    (((CommRingCat.Hom.hom (germ (structurePresheafInCommRingCat R) ⊤ x _root_.trivial) :
            (↑(CommRingCat.of
                    (Functor.obj (C := (Opens (↑(PrimeSpectrum.Top R) : Type u))ᵒᵖ)
                      (ObjectProperty.FullSubcategory.obj (P :=
                        CategoryTheory.Presheaf.IsSheaf (Opens.grothendieckTopology (↑(PrimeSpectrum.Top R) : Type u)))
                        (structureSheafInType R R))
                      (op ⊤))) :
                Type u) →+*
              (↑(stalk (structurePresheafInCommRingCat R) x) : Type u)) :
          (a : (structureSheafInType R R).obj.obj (op ⊤)) → (↑((structurePresheafInCommRingCat R).stalk x) : Type u))
        ((algebraMap R
                (Functor.obj (C := (Opens (↑(PrimeSpectrum.Top R) : Type u))ᵒᵖ)
                  (ObjectProperty.FullSubcategory.obj (P :=
                    CategoryTheory.Presheaf.IsSheaf (Opens.grothendieckTopology (↑(PrimeSpectrum.Top R) : Type u)))
                    (structureSheafInType R R))
                  (op ⊤)) :
              (a : R) → (structureSheafInType R R).obj.obj (op ⊤))
            r :
          Functor.obj (C := (Opens (↑(PrimeSpectrum.Top R) : Type u))ᵒᵖ)
            (ObjectProperty.FullSubcategory.obj (P :=
              CategoryTheory.Presheaf.IsSheaf (Opens.grothendieckTopology (↑(PrimeSpectrum.Top R) : Type u)))
              (structureSheafInType R R))
            (op ⊤)) :
      (↑(stalk (structurePresheafInCommRingCat R) x) : Type u))
have e_a : Eq (α := (↑(stalk (structurePresheafInCommRingCat R) x) : Type u))
  (((CommRingCat.Hom.hom (germ (structurePresheafInCommRingCat R) U x hxU) :
          (↑(Functor.obj (structurePresheafInCommRingCat R) (op U)) : Type u) →+*
            (↑(stalk (structurePresheafInCommRingCat R) x) : Type u)) :
        (a : (structureSheafInType R R).obj.obj (op U)) → (↑((structurePresheafInCommRingCat R).stalk x) : Type u))
      ((algebraMap R
              (Functor.obj
                (ObjectProperty.FullSubcategory.obj (P :=
                  CategoryTheory.Presheaf.IsSheaf (Opens.grothendieckTopology (↑(PrimeSpectrum.Top R) : Type u)))
                  (structureSheafInType R R))
                (op U)) :
            (a : R) → (structureSheafInType R R).obj.obj (op U))
          r :
        Functor.obj
          (ObjectProperty.FullSubcategory.obj (P :=
            CategoryTheory.Presheaf.IsSheaf (Opens.grothendieckTopology (↑(PrimeSpectrum.Top R) : Type u)))
            (structureSheafInType R R))
          (op U)) :
    (↑(stalk (structurePresheafInCommRingCat R) x) : Type u))
  ((ConcreteCategory.hom (FC := fun (R S : CommRingCat.{u}) ↦ (↑R : Type u) →+* (↑S : Type u)) (CC :=
          CommRingCat.carrier) (X := Functor.obj (structurePresheafInCommRingCat R) (op U)) (Y :=
          stalk (structurePresheafInCommRingCat R) x) (germ (structurePresheafInCommRingCat R) U x hxU) :
        (a : (↑((structurePresheafInCommRingCat R).obj (op U)) : Type u)) →
          (↑((structurePresheafInCommRingCat R).stalk x) : Type u))
      ((ConcreteCategory.hom (FC := fun (R S : CommRingCat.{u}) ↦ (↑R : Type u) →+* (↑S : Type u)) (CC :=
              CommRingCat.carrier) (X :=
              Functor.obj (C := (Opens (↑(PrimeSpectrum.Top R) : Type u))ᵒᵖ) (structurePresheafInCommRingCat R) (op ⊤))
              (Y := Functor.obj (structurePresheafInCommRingCat R) (op U))
              (CategoryTheory.Functor.map (structurePresheafInCommRingCat R) (Quiver.Hom.op (homOfLE sorry))) :
            (a : (↑((structurePresheafInCommRingCat R).obj (op ⊤)) : Type u)) →
              (↑((structurePresheafInCommRingCat R).obj (op U)) : Type u))
          ((algebraMap R
                (Functor.obj (C := (Opens (↑(PrimeSpectrum.Top R) : Type u))ᵒᵖ)
                  (ObjectProperty.FullSubcategory.obj (P :=
                    CategoryTheory.Presheaf.IsSheaf (Opens.grothendieckTopology (↑(PrimeSpectrum.Top R) : Type u)))
                    (structureSheafInType R R))
                  (op ⊤)) :
              (a : R) → (structureSheafInType R R).obj.obj (op ⊤))
            r) :
        (↑(Functor.obj (structurePresheafInCommRingCat R) (op U)) : Type u)) :
    (↑(stalk (structurePresheafInCommRingCat R) x) : Type u))
Tactic: erw [← (structurePresheafInCommRingCat R).germ_res_apply (homOfLE (le_top : U ≤ ⊤)) _ hxU]