  We establish the inequality for Henneaux-Teitelboim's total energy-momentum
for asymptotically anti-de Sitter initial data sets which are asymptotic to
arbitrary $t$-slice in anti-de Sitter spacetime. In particular, when $t=0$, it
generalizes Chru\'{s}ciel-Maerten-Tod's inequality in the center of AdS mass
coordinates. We also show that the determinant of energy-momentum endomorphism
${\bf Q}$ is the geometric invariant of asymptotically anti-de Sitter
spacetimes.
