∀ {J : Type w} {C : Type u} [inst : CategoryTheory.Category.{v, u} C] {X Y : C} {f : J → (X ⟶ Y)}
  [inst_1 : CategoryTheory.Limits.HasWideCoequalizer f] [inst_2 : Nonempty J] {W : C} (k : Y ⟶ W)
  (h : ∀ (j₁ j₂ : J), CategoryTheory.CategoryStruct.comp (f j₁) k = CategoryTheory.CategoryStruct.comp (f j₂) k) {Z : C}
  (h_1 : W ⟶ Z),
  CategoryTheory.CategoryStruct.comp (CategoryTheory.Limits.wideCoequalizer.π f)
      (CategoryTheory.CategoryStruct.comp (CategoryTheory.Limits.wideCoequalizer.desc k h) h_1) =
    CategoryTheory.CategoryStruct.comp k h_1