∀ {R : Type u_1} {S : Type u_2} [inst : CommRing R] [inst_1 : CommRing S] [inst_2 : Algebra R S] [Module.Free R S]
  {A : Type u_6} [inst_4 : Ring A] [inst_5 : Algebra R A] [inst_6 : Algebra S A] [IsScalarTower R S A] [Module.Free S A]
  {a : A}, (Algebra.norm R) ((Algebra.norm S) a) = (Algebra.norm R) a