∀ {R : Type u_1} {S : Type u_2} [inst : CommRing R] [inst_1 : CommRing S] [inst_2 : Algebra R S] (r : R)
  [inst_3 : IsLocalization.Away r S],
  Algebra.Generators.cMulXSubOneCotangent S r =
    Algebra.Extension.Cotangent.mk ⟨MvPolynomial.C r * MvPolynomial.X () - 1, ⋯⟩