  In a one-generation fermion condensate scheme of electroweak symmetry
breaking, it is proven based on Schwinger-Dyson equation in the real-time
thermal field theory in the fermion bubble diagram approximation that, at
finite temperature $T$ below the symmetry restoration temperature $T_c$, a
massive Higgs boson and three massless Nambu-Goldstone bosons could emerge from
the spontaneous breaking of electroweak group $SU_L(2)\times U_Y(1) \to U_Q(1)$
if the two fermion flavors in the one generation are mass-degenerate, thus
Goldstone Theorem is rigorously valid in this case. However, if the two fermion
flavors have unequal masses, owing to "thermal flactuation", the Goldstone
Theorem will be true only approximately for a very large momentum cut-off
$\Lambda$ in zero temperature fermion loop or for low energy scales. All
possible pinch singularities are proven to cancel each other, as is expected in
a real-time thermal field theory.
