∀ {R : Type u_1} [inst : NonUnitalNonAssocRing R] (s t : NonUnitalSubring R) {a b : R},
  a ∈ (s.toSubsemigroup ⊓ t.toSubsemigroup).carrier →
    b ∈ (s.toSubsemigroup ⊓ t.toSubsemigroup).carrier → a * b ∈ (s.toSubsemigroup ⊓ t.toSubsemigroup).carrier