Deduce that if $C$ is a non-empty closed convex set of $E$ and $u$ is a vector of $E$, then there exists a unique $v$ in $C$ such that
$$\forall w \in F, \quad \|u - v\| \leqslant \|u - w\|$$
We say that $v$ is the projection of $u$ onto $C$ and we denote $d(u, C) = \|u - v\|$.