∀ {C : Type u_2} [inst : CategoryTheory.Category.{u_1, u_2} C] {S : C} {J : CategoryTheory.Precoverage C}
  (𝒰 : J.ZeroHypercover S) (i : 𝒰.I₀),
  CategoryTheory.CategoryStruct.comp (𝒰.f i) (CategoryTheory.CategoryStruct.id S) =
    CategoryTheory.CategoryStruct.comp (CategoryTheory.CategoryStruct.id (𝒰.X i)) (𝒰.f i)