simp only [normSq_coe] at this
a b c : ℤα
this :
  ↑normSq (OneHom.toFun (↑↑inclusion) (a * b)) =
    ↑normSq (OneHom.toFun (↑↑inclusion) a) * ↑normSq (OneHom.toFun (↑↑inclusion) b)
⊢ norm (a * b) = norm a * norm b
a b c : ℤα
this : ↑(norm (a * b)) = ↑(norm a) * ↑(norm b)
⊢ norm (a * b) = norm a * norm b