∀ (R S : Type u) [inst : CommRing R] [inst_1 : CommRing S] {Z : AlgebraicGeometry.Scheme}
  (h : AlgebraicGeometry.Spec { carrier := R × S, commRing := Prod.instCommRing } ⟶ Z),
  CategoryTheory.CategoryStruct.comp CategoryTheory.Limits.coprod.inr
      (CategoryTheory.CategoryStruct.comp (AlgebraicGeometry.coprodSpec R S) h) =
    CategoryTheory.CategoryStruct.comp (AlgebraicGeometry.Spec.map (CommRingCat.ofHom (RingHom.snd R S))) h