  We extend Brill's positive mass theorem to a large class of asymptotically
flat, maximal, $U(1)^2$-invariant initial data sets on simply connected four
dimensional manifolds $\Sigma$. Moreover, we extend the local mass angular
momenta inequality result Ref [1] for $U(1)^2$ invariant black holes to the
case with nonzero stress energy tensor with positive matter density and
energy-momentum current invariant under the above symmetries.
