{R : Type u_5} →
  [inst : CommRing R] →
    (S : Submonoid R) →
      (P : Type u_6) →
        [inst_1 : CommRing P] →
          [inst_2 : Algebra R P] →
            (P' : Type u_7) →
              [inst_3 : CommRing P'] →
                [inst_4 : Algebra R P'] →
                  [IsLocalization S P] → [IsLocalization S P'] → FractionalIdeal S P ≃+* FractionalIdeal S P'