∀ {R : Type u_4} {S : Type u_3} {A : Type u_2} {B : Type u_1} [inst : CommSemiring R] [inst_1 : CommSemiring S]
  [inst_2 : Semiring A] [inst_3 : Semiring B] [inst_4 : Algebra R S] [inst_5 : Algebra S A] [inst_6 : Algebra S B]
  [inst_7 : Algebra R A] [inst_8 : Algebra R B] [inst_9 : IsScalarTower R S A] [inst_10 : IsScalarTower R S B]
  (h : Function.Surjective ⇑(algebraMap R S)) (f : A ≃ₐ[R] B) (r : S),
  (↑↑(AlgHom.extendScalarsOfSurjective h ↑f).toRingHom).toFun ((algebraMap S A) r) = (algebraMap S B) r