  We consider the Cauchy-Dirichlet problem $\partial_t u - F(t,x,u,Du,D^2 u) =
0 on (0,T)\times \R^n$ in viscosity sense. Comparison is established for
bounded semi-continuous (sub-/super-)solutions under structural assumption
(3.14) of the User's Guide plus a mild condition on $F$ such as to cope with
the unbounded domain. Comparison on $(0,T]$, space-time regularity and
existence are also discussed. Our analysis passes through an extension of the
parabolic theorem of sums which appears to be useful in its own right.
