  We prove that, after centering and diffusively rescaling space and time, the
collection of rightmost infinite open paths in a supercritical oriented
percolation configuration on the space-time lattice Z^2_{even}:={(x,i) in Z^2:
x+i is even} converges in distribution to the Brownian web. This proves a
conjecture of Wu and Zhang. Our key observation is that each rightmost infinite
open path can be approximated by a percolation exploration cluster, and
different exploration clusters evolve independently before they intersect.
