∀ {M : Type u_2} [inst : CommMonoid M] {S : Submonoid M} {p : Localization S → Sort u_1}
  (f : (a : M) → (b : ↥S) → p (Localization.mk a b)),
  (∀ {a c : M} {b d : ↥S} (h : (Localization.r S) (a, b) (c, d)), ⋯ ▸ f a b = f c d) →
    ∀ (y z : M × ↥S) (h : (OreLocalization.oreEqv S M) y z), ⋯ ▸ ⋯ ▸ f y.1 y.2 = ⋯ ▸ f z.1 z.2