∀ {C : Type u_4} [inst : CategoryTheory.Category.{u_5, u_4} C] {D : Type u_2}
  [inst_1 : CategoryTheory.Category.{u_3, u_2} D] {J : CategoryTheory.GrothendieckTopology C}
  {K : CategoryTheory.GrothendieckTopology D} {F : CategoryTheory.Functor C D} {S : CategoryTheory.Sheaf J RingCat}
  {R : CategoryTheory.Sheaf K RingCat} [inst_2 : F.IsContinuous J K]
  (φ : S ⟶ (F.sheafPushforwardContinuous RingCat J K).obj R)
  [inst_3 : J.HasSheafCompose (CategoryTheory.forget₂ RingCat AddCommGrpCat)]
  [inst_4 : K.HasSheafCompose (CategoryTheory.forget₂ RingCat AddCommGrpCat)]
  [inst_5 : (SheafOfModules.pushforward φ).IsRightAdjoint] [inst_6 : CategoryTheory.HasWeakSheafify J AddCommGrpCat]
  [inst_7 : CategoryTheory.HasWeakSheafify K AddCommGrpCat] [inst_8 : J.WEqualsLocallyBijective AddCommGrpCat]
  [inst_9 : K.WEqualsLocallyBijective AddCommGrpCat] [inst_10 : F.Final] {X Y : Type u_1} (f : X ⟶ Y),
  CategoryTheory.CategoryStruct.comp ((SheafOfModules.freeFunctor.comp (SheafOfModules.pullback φ)).map f)
      (SheafOfModules.pullbackObjFreeIso φ Y).hom =
    CategoryTheory.CategoryStruct.comp (SheafOfModules.pullbackObjFreeIso φ X).hom (SheafOfModules.freeFunctor.map f)