  We show that for a simple graph $G$, $c'(G)\leq\Delta(G)+2$ where $c'(G)$ is
the choice index (or edge-list chromatic number) of $G$, and $\Delta(G)$ is the
maximum degree of $G$.
  As a simple corollary of this result, we show that the total chromatic number
$\chi_T(G)$ of a simple graph satisfies the inequality $\chi_T(G)\leq\
\Delta(G)+4$ and the total choice number $c_T(G)$ also satisfies this
inequality.
  We also relate these bounds to the Hall index and the Hall condition index of
a simple graph, and to the total Hall number and the total Hall condition
number of a simple graph.
