∀ {R : Type u} {A : Type v} [inst : CommSemiring R] [inst_1 : NonUnitalNonAssocSemiring A] [inst_2 : Module R A]
  [inst_3 : IsScalarTower R A A] [inst_4 : SMulCommClass R A A] (S : Set (NonUnitalSubalgebra R A)),
  (sInf S).toNonUnitalSubsemiring = sInf (NonUnitalSubalgebra.toNonUnitalSubsemiring '' S)