∀ {M : Type u_1} [inst : CommMonoid M] {S : Submonoid M} {r : Localization S → Localization S → Sort u_2}
  [h : ∀ (a c : M) (b d : ↥S), Subsingleton (r (Localization.mk a b) (Localization.mk c d))] (t b : M × ↥S),
  Subsingleton (r ⟦t⟧ ⟦b⟧)