∀ {J : Type u_3} {C : Type u_2} [inst : CategoryTheory.Category.{u_1, u_2} C] {X Y : C} (f : J → (X ⟶ Y))
  [inst_1 : CategoryTheory.Limits.HasWideEqualizer f] [inst_2 : Nonempty J],
  CategoryTheory.CategoryStruct.comp
      (CategoryTheory.Iso.refl (CategoryTheory.Limits.limit.cone (CategoryTheory.Limits.parallelFamily f)).pt).hom
      (CategoryTheory.Limits.Trident.ofι (CategoryTheory.Limits.wideEqualizer.ι f) ⋯).ι =
    CategoryTheory.Limits.Trident.ι (CategoryTheory.Limits.limit.cone (CategoryTheory.Limits.parallelFamily f))