∀ {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) (X : CategoryTheory.CosimplicialObject.Augmented C)
  (G : F ⟶ CategoryTheory.CosimplicialObject.Augmented.toArrow.obj X),
  (CategoryTheory.CosimplicialObject.equivalenceRightToLeft F X G).left = G.left