Let $V$ be a Hilbert space, $a:V\times V\to \mathbb{R}$ (or $\mathbb{C}$) bilinear, continuous, and coercive: $a(v,v)\ge c\|v\|_V^2$ for some $c>0$. For each continuous linear functional $F\in V^*$, there exists a unique $u\in V$ such that $a(u,v)=F(v)$ for all $v\in V$.