∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] {J : CategoryTheory.Precoverage C} {S : C}
  (E : J.ZeroHypercover S) [inst_1 : E.Small],
  E.restrictIndexOfSmall.toPreZeroHypercover =
    E.restrictIndex (CategoryTheory.Precoverage.ZeroHypercover.Small.restrictFun E)