∀ (P : CategoryTheory.MorphismProperty AlgebraicGeometry.Scheme) {S : AlgebraicGeometry.Scheme} {ι : Type u_1}
  {X : ι → AlgebraicGeometry.Scheme} {f : (i : ι) → X i ⟶ S},
  CategoryTheory.Presieve.ofArrows X f ∈ (AlgebraicGeometry.Scheme.precoverage P).coverings S ↔
    (∀ (x : ↥S), ∃ i, x ∈ Set.range ⇑(f i)) ∧ ∀ (i : ι), P (f i)