Section prod_NormedModule.
Context {K : AbsRing} {U V : NormedModule K}.
Definition prod_norm (x : U * V) :=
sqrt (norm (fst x) ^ 2 + norm (snd x) ^ 2).

Lemma prod_norm_triangle :
forall x y : U * V,
prod_norm (plus x y) <= prod_norm x + prod_norm y.