∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C]
  [inst_1 :
    ∀ (n : ℕ) (f : CategoryTheory.Arrow C),
      CategoryTheory.Limits.HasWidePushout f.left (fun x => f.right) fun x => f.hom]
  (f : CategoryTheory.Arrow C), CategoryTheory.CosimplicialObject.augmentedCechConerve.obj f = f.augmentedCechConerve