∀ (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)
  (i : Algebra.Smooth.DescentAux.vars✝ D),
  ↑(Algebra.Smooth.DescentAux.q✝ D i).coeffs ⊆
    Set.range ⇑(MvPolynomial.map (algebraMap (↥(Algebra.Smooth.DescentAux.subalgebra✝ R D)) A))