{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)) →
          [CategoryTheory.Presheaf.IsLocallySurjective AlgebraicGeometry.Scheme.zariskiTopology
                (CategoryTheory.Limits.Sigma.desc f)] →
            AlgebraicGeometry.Scheme.zariskiTopology.yoneda.obj
                (AlgebraicGeometry.Scheme.LocalRepresentability.glueData hf).glued ≅
              F