∀ {R : Type u_1} [inst : CommSemiring R] (M : Submonoid R) {S : Type u_2} [inst_1 : CommSemiring S]
  [inst_2 : Algebra R S] [inst_3 : IsLocalization M S] (z : S)
  (motive :
    (∃ a,
        (fun x =>
              match x with
              | (r, m) => IsLocalization.mk' S r m)
            a =
          z) →
      Prop)
  (x :
    ∃ a,
      (fun x =>
            match x with
            | (r, m) => IsLocalization.mk' S r m)
          a =
        z),
  (∀ (r : R) (m : ↥M)
      (hz :
        (fun x =>
              match x with
              | (r, m) => IsLocalization.mk' S r m)
            (r, m) =
          z),
      motive ⋯) →
    motive x