∀ {R : Type u} {A : Type v} [inst : CommSemiring R] [inst_1 : Semiring A] [inst_2 : Algebra R A] {ι : Sort u_1}
  (S : ι → Subalgebra R A), Subalgebra.toSubmodule (⨅ i, S i) = ⨅ i, Subalgebra.toSubmodule (S i)