-- Lean 4 proof step from Mathlib.AlgebraicGeometry.StructureSheaf (hypothesis)
Goal:
R M : Type u
inst : CommRing R
inst_1 : AddCommGroup M
inst_2 : Module R M
f : R
⊢ IsUnit (M :=
    Module.End 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 M))
        (op (basicOpen f))))
    ((algebraMap R
            (Module.End 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 M))
                (op (basicOpen f)))) :
          (a : R) → Module.End R ((structureSheafInType R M).obj.obj (op (basicOpen f))))
        f :
      Module.End 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 M))
          (op (basicOpen f))))
have this : IsUnit (M :=
  Module.End
    (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 (basicOpen f)))
    (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 M))
      (op (basicOpen f))))
  ((algebraMap
          (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 (basicOpen f)))
          (Module.End
            (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 (basicOpen f)))
            (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 M))
              (op (basicOpen f)))) :
        (a : (structureSheafInType R R).obj.obj (op (basicOpen f))) →
          Module.End ((structureSheafInType R R).obj.obj (op (basicOpen f)))
            ((structureSheafInType R M).obj.obj (op (basicOpen f))))
      ((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 (basicOpen f))) :
          (a : R) → (structureSheafInType R R).obj.obj (op (basicOpen f)))
        f) :
    Module.End
      (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 (basicOpen f)))
      (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 M))
        (op (basicOpen f))))
Tactic: have := (isUnit_basicOpen f).map
    (algebraMap _ (Module.End Γ(R, basicOpen f) Γ(M, basicOpen f)))