∀ {C : Type u_4} {D : Type u_6} {H : Type u_2} [inst : CategoryTheory.Category.{u_3, u_4} C]
  [inst_1 : CategoryTheory.Category.{u_5, u_6} D] [inst_2 : CategoryTheory.Category.{u_1, u_2} H]
  {F : CategoryTheory.Functor C H} {L : CategoryTheory.Functor C D} (W : CategoryTheory.MorphismProperty C)
  {G : CategoryTheory.Functor D H} (e : F ≅ L.comp G) [L.IsLocalization W] (Y : C)
  (s : CategoryTheory.Limits.Cocone ((CategoryTheory.CostructuredArrow.proj L (L.obj Y)).comp F))
  (j : CategoryTheory.CostructuredArrow L (L.obj Y)),
  CategoryTheory.CategoryStruct.comp (((CategoryTheory.Functor.LeftExtension.mk G e.hom).coconeAt (L.obj Y)).ι.app j)
      (CategoryTheory.CategoryStruct.comp (e.inv.app Y)
        (s.ι.app (CategoryTheory.CostructuredArrow.mk (CategoryTheory.CategoryStruct.id (L.obj Y))))) =
    s.ι.app j