∀ {X Y : AlgebraicGeometry.Scheme} (f : X ⟶ Y) {V : X.Opens} {U : Y.Opens} (hU : AlgebraicGeometry.IsAffineOpen U)
  (hV : AlgebraicGeometry.IsAffineOpen V) (i : V ≤ (TopologicalSpace.Opens.map f.base).obj U)
  {Z : AlgebraicGeometry.Scheme} (h : Y ⟶ Z),
  CategoryTheory.CategoryStruct.comp (AlgebraicGeometry.Spec.map (AlgebraicGeometry.Scheme.Hom.appLE f U V i))
      (CategoryTheory.CategoryStruct.comp hU.fromSpec h) =
    CategoryTheory.CategoryStruct.comp hV.fromSpec (CategoryTheory.CategoryStruct.comp f h)