The quark model predicts that certain combinations of total cross sections should be equal at infinite energy. One such predictions is that σ̄π(∞)=23σ̄N(∞), where σ̄π(ν)=12[σπ+p(ν)+σπ-p(ν)] and σ̄N(ν)=14[σpp(ν)+σpn(ν)+σpn(ν)+σp̄n(ν)] are the average pion-nucleon and nucleon-nucleon cross sections, respectively, and ν is the laboratory beam energy. We have tested this prediction by using the implied superconvergence of the forward scattering amplitude T̄π(ν)-23T̄N(ν), where T̄π(ν) and T̄N(ν) are defined in an analogous way. We find that the sum rule is badly violated in the laboratory frame with pions as the beam but satisfied in the "antilaboratory frame" with protons as the beam. We conclude that the quark-model prediction is correct so long as it is interpreted in the antilaboratory frame.