inequality in Sobolev spaces

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Let $I\subset \Bbb R$ be a bounded interval and $u∈ W^{1,p} (I)$. Let $(u_n)_n\subset C^{\infty}(I)$ such that $u_n\to u\in W^{1,p} (I)$.

I see in some proof that $||u_n'-u'||_{L^p} \le ||u_n-u||_{W^{1,p} (I)}$.

Where this inequality come from?

Many thanks for any help in the right direction.