  For a non-equilibrium physical system defined along a closed time path (CTP),
a key constraint is the so-called largest time equation, which is a consequence
of unitarity and implies causality. In this paper, we present a simple proof
that if the propagators of a non-equilibrium effective action have the proper
pole structure, the largest time equation is obeyed to all loop orders. Ghost
fields and BRST symmetry are not needed. In particular, the arguments for the
proof can also be used to show that if ghost fields are introduced, their
contributions vanish.
