  For a dilute system of non-relativistic bosons interacting through a positive
$L^1$ potential $v$ with scattering length $a$ we prove that the ground state
energy density satisfies the bound $e(\rho) \geq 4\pi a \rho^2 (1+
\frac{128}{15\sqrt{\pi}} \sqrt{\rho a^3} +o(\sqrt{\rho a^3}\,))$, thereby
proving the Lee-Huang-Yang formula for the energy density.
