∀ {σ : Type u_1} {R : Type u_2} (A : Type u_3) [inst : CommSemiring R] [inst_1 : CommSemiring A] [inst_2 : Algebra R A]
  (f : MvPowerSeries σ R),
  (algebraMap (MvPowerSeries σ R) (MvPowerSeries σ A)) f = (MvPowerSeries.map (algebraMap R A)) f