{R : Type u_1} →
  [inst : CommSemiring R] →
    (S : Type u_2) →
      [inst_1 : CommSemiring S] →
        [inst_2 : Algebra R S] →
          {P : Type u_3} →
            [inst_3 : CommSemiring P] →
              (Q : Type u_4) →
                [inst_4 : CommSemiring Q] →
                  [inst_5 : Algebra P Q] →
                    (f : R →+* P) → (r : R) → [IsLocalization.Away r S] → [IsLocalization.Away (f r) Q] → S →+* Q