∀ {R : Type u_4} [inst : CommSemiring R] {M : Submonoid R} (S : Type u_1) [inst_1 : CommSemiring S]
  [inst_2 : Algebra R S] {P : Type u_3} [inst_3 : CommSemiring P] [inst_4 : IsLocalization M S] {T : Submonoid P}
  (Q : Type u_2) [inst_5 : CommSemiring Q] [inst_6 : Algebra P Q] [inst_7 : IsLocalization T Q] (h : R ≃+* P)
  (H : Submonoid.map h.toMonoidHom M = T) (H' : Submonoid.map h.symm.toMonoidHom T = M) (x : S),
  (IsLocalization.map S ↑h.symm ⋯) ((IsLocalization.map Q ↑h ⋯) x) = x