∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] {J : CategoryTheory.GrothendieckTopology C} {A : Type u'}
  [inst_1 : CategoryTheory.Category.{v', u'} A] {H : J.OneHypercoverFamily} {P : CategoryTheory.Functor Cᵒᵖ A}
  (hP : ∀ ⦃X : C⦄ (E : J.OneHypercover X), H E → Nonempty (CategoryTheory.Limits.IsLimit (E.multifork P))) {X : C}
  {S : CategoryTheory.Sieve X} {E : J.OneHypercover X} (hE : H E) (le : E.sieve₀ ≤ S)
  (F : CategoryTheory.Limits.Multifork (CategoryTheory.GrothendieckTopology.Cover.index ⟨S, ⋯⟩ P)) (i : E.I₀),
  CategoryTheory.CategoryStruct.comp
      (CategoryTheory.GrothendieckTopology.OneHypercoverFamily.IsSheafIff.lift hP hE le F) (P.map (E.f i).op) =
    F.ι { Y := E.X i, f := E.f i, hf := ⋯ }