∀ {R : Type u_1} {S : Type u_2} {ι : Type u_3} {σ : Type u_4} [inst : CommRing R] [inst_1 : CommRing S]
  [inst_2 : Algebra R S] [inst_3 : Finite σ] {P : Algebra.SubmersivePresentation R S ι σ} {R₀ : Type u_5}
  [inst_4 : CommRing R₀] [inst_5 : Algebra R₀ R] [inst_6 : Algebra R₀ S] [inst_7 : IsScalarTower R₀ R S],
  P.coeffs ⊆ ↑(algebraMap R₀ R).range → P.HasCoeffs R₀