Section NormedModule1.
Context {K : AbsRing} {V : NormedModule K}.
Definition norm : V -> R := NormedModule.norm K _ (NormedModule.class K V).
Definition norm_factor : R := NormedModule.norm_factor K _ (NormedModule.class K V).

Lemma norm_scal :
forall (l : K) (x : V),
norm (scal l x) <= abs l * norm x.