∀ {R : Type u_1} {A : Type w} [inst : CommRing R] [inst_1 : CommRing A] [inst_2 : Algebra R A]
  [inst_3 : FaithfulSMul R A] [inst_4 : IsDomain A] {s : Set A},
  (AlgebraicIndependent.matroid R A).Spanning s ↔ Algebra.IsAlgebraic (↥(Algebra.adjoin R s)) A