∀ {M : Type u_1} [inst : CommMonoid M] (S : Submonoid M) (p : M) (q : ↥S)
  (motive : (x : M × ↥S) → (Localization.r' S) (p, q) x → Prop) (x : M × ↥S) (x_1 : (Localization.r' S) (p, q) x),
  (∀ (x : M) (y : ↥S) (x_2 : (Localization.r' S) (p, q) (x, y)), motive (x, y) x_2) → motive x x_1