The lemma ensures that (for a large enough "k"), it is possible to do the construction while leaving enough strings for the relativized ENP answers. Also, we can ensure that for the relativized ENP, linear time suffices, even for function problems (if given a function oracle and linear output size) and with exponentially small (with linear exponent) error probability. Also, this construction is effective in that given an arbitrary oracle A we can arrange the oracle B to have PA≤PB and EXPNPA=EXPNPB=BPPB. Also, for a ZPP=EXP oracle (and hence ZPP=BPP=EXP<NEXP), one would fix the answers in the relativized E computation to a special nonanswer, thus ensuring that no fake answers are given.