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 $$\forall w \in F, \quad \|u - v\| \leqslant \|u - w\|$$
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
$$\forall w \in F, \quad \|u - v\| \leqslant \|u - w\|$$