∀ {R : Type u_1} [inst : CommRing R] {X Y : CommAlgCat R} (f : X ⟶ Y),
  CategoryTheory.CategoryStruct.comp
      (CommAlgCat.ofHom (Algebra.TensorProduct.map (AlgHom.id R ↑(CommAlgCat.of R R)) (CommAlgCat.Hom.hom f)))
      (CommAlgCat.isoMk (Algebra.TensorProduct.lid R ↑Y)).hom =
    CategoryTheory.CategoryStruct.comp (CommAlgCat.isoMk (Algebra.TensorProduct.lid R ↑X)).hom f