∀ {F : CategoryTheory.Sheaf AlgebraicGeometry.Scheme.zariskiTopology (Type u)} {ι : Type u}
  {X : ι → AlgebraicGeometry.Scheme} {f : (i : ι) → CategoryTheory.yoneda.obj (X i) ⟶ F.val}
  (hf : ∀ (i : ι), AlgebraicGeometry.IsOpenImmersion.presheaf (f i)) {i : ι},
  (AlgebraicGeometry.Scheme.LocalRepresentability.yonedaGluedToSheaf hf).val.app (Opposite.op (X i))
      (AlgebraicGeometry.Scheme.LocalRepresentability.toGlued hf i) =
    CategoryTheory.yonedaEquiv (f i)