∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] [inst_1 : CategoryTheory.Limits.HasFiniteProducts C]
  (U : CategoryTheory.Limits.FormalCoproduct C) {T : C} (hT : CategoryTheory.Limits.IsTerminal T)
  (n : SimplexCategoryᵒᵖ) (i : CategoryTheory.ToType (Opposite.unop n)) {Z : CategoryTheory.Limits.FormalCoproduct C}
  (h : U ⟶ Z),
  CategoryTheory.CategoryStruct.comp (U.cechIsoCechNerveApp hT n).hom
      (CategoryTheory.CategoryStruct.comp
        (CategoryTheory.Limits.WidePullback.π
          (fun x => (CategoryTheory.Limits.FormalCoproduct.isTerminalIncl T hT).from U) i)
        h) =
    CategoryTheory.CategoryStruct.comp (U.powerπ i) h