∀ {R : Type u_1} {S : Type u_2} [inst : CommSemiring R] [inst_1 : CommSemiring S] [inst_2 : Algebra R S]
  {s : Subalgebra R S} {M : Submonoid S} {H : M ≤ s.toSubmonoid} {x : S}, (x ∈ s.saturation M H) = ∃ m ∈ M, m • x ∈ s