∀ {P : CategoryTheory.MorphismProperty AlgebraicGeometry.Scheme} (S : AlgebraicGeometry.Scheme)
  [inst : P.IsStableUnderBaseChange] [inst_1 : AlgebraicGeometry.Scheme.IsJointlySurjectivePreserving P]
  {X W : AlgebraicGeometry.Scheme} (𝒰 : AlgebraicGeometry.Scheme.Cover (AlgebraicGeometry.Scheme.precoverage P) X)
  (f : W ⟶ X) [inst_2 : W.Over S] [inst_3 : X.Over S] [inst_4 : AlgebraicGeometry.Scheme.Cover.Over S 𝒰]
  [inst_5 : AlgebraicGeometry.Scheme.Hom.IsOver f S] (x : 𝒰.I₀),
  (AlgebraicGeometry.Scheme.Cover.pullbackCoverOver' S 𝒰 f).f x =
    (CategoryTheory.Limits.pullback.snd (AlgebraicGeometry.Scheme.Hom.asOver (𝒰.f x) S)
        (AlgebraicGeometry.Scheme.Hom.asOver f S)).left