(R : Type u_1) →
  [inst : CommRing R] →
    {A : Type u} →
      {B : Type u_2} →
        [inst_1 : CommRing A] →
          [inst_2 : Algebra R A] →
            [inst_3 : CommRing B] →
              [inst_4 : Algebra A B] →
                (D : Algebra.Smooth.DescentAux✝ A B) → Algebra (↥(Algebra.Smooth.DescentAux.subalgebra✝ R D)) A