In the answer to the following comment, it is shown why $\rho(x,x') = 0$ implies $x = x'$: http://math.stackexchange.com/questions/163678/a-proof-that-skorohod-metric-is-a-metrichttps://math.stackexchange.com/questions/163678/a-proof-that-skorohod-metric-is-a-metric