It is shown that the minimum electron streaming speed required in Bohm-Block criterion for the existence of one-dimensional double-layer solutions can be relaxed by the presence of a sufficient population of trapped electrons with energies in the parallel motion ranging up to the double-layer potential energy. The resulting auroral double-layer criterion is found to be relatively independent of the forms of the particle distribution functions. The trapped electrons can be identified with the energy-degraded primary electrons and the secondary electrons on auroral field lines. The magnetic mirror due to the converging geomagnetic field and the electron-neutral collisions in the upper atmosphere are necessary elements in building up the trapped electron population.