∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] {J : CategoryTheory.Precoverage C}
  [inst_1 : J.IsStableUnderBaseChange] {X : C} (E : J.ZeroHypercover X) {Y Z : C} (f : X ⟶ Z) (g : Y ⟶ Z)
  [inst_2 : CategoryTheory.Limits.HasPullback f g]
  [inst_3 : ∀ (i : E.I₀), CategoryTheory.Limits.HasPullback (E.f i) (CategoryTheory.Limits.pullback.fst f g)],
  (E.pullbackCoverOfLeft f g).toPreZeroHypercover = E.pullbackCoverOfLeft f g