∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] {X Y : C} (f g : X ⟶ Y) {D : Type u₂}
  [inst_1 : CategoryTheory.Category.{v₂, u₂} D] (G : CategoryTheory.Functor C D)
  [inst_2 : CategoryTheory.Limits.HasEqualizer f g] [inst_3 : CategoryTheory.Limits.HasEqualizer (G.map f) (G.map g)]
  {Z : D} (h : G.obj X ⟶ Z),
  CategoryTheory.CategoryStruct.comp (CategoryTheory.Limits.equalizerComparison f g G)
      (CategoryTheory.CategoryStruct.comp (CategoryTheory.Limits.equalizer.ι (G.map f) (G.map g)) h) =
    CategoryTheory.CategoryStruct.comp (G.map (CategoryTheory.Limits.equalizer.ι f g)) h