P-Sequence Space with P-Norm forms Normed Vector Space

Theorem
A $p$-Sequence Space with a $p$-norm forms a normed vector space.

Proof
We have that:
 * a $p$-sequence space is a vector space


 * the $p$-norm on the $p$-sequence space is a norm

By definition, $\struct {\ell^p, \norm {\, \cdot \,}_p}$ is a normed vector space.