A hard-core point process is produced from a Poisson process of rate by deleting any point within distance v0 of another point, regardless of

A hard-core point process is produced from a Poisson process of rate λ

by deleting any point within distance v0 of another point, regardless of whether that point has itself already been deleted. Prove that the rate of the hard-core process is λ exp(−λπv2 0).