[texhax] Problem with spacing of {

[Michael Barr]

I actually have two problems.  First the file:
\documentclass{article}
\begin{document}
\def\bx#1{\hbox to 5em{$#1$\hss}}

$$
\begin{array}{rcl}
d^id^j&=&\cases{\bx{d^{j-1}d^i}&$i<   j$\cr
                \bx{d^jd^{i+1}}&$i\ge j$} \\[5pt]
s^js^i&=&\cases{\bx{s^is^{j-1}}&$i<   j$\cr
                \bx{s^{i+1}s^j}&$i\ge j$}\\[5pt]
d^is^j&=&\cases{\bx{s^{j-1}d^i}&$i<   j$\cr
                \bx{1}&$i=j,j-1$\cr
                \bx{s^jd^{i-1}}&$i> j-1$}\\[5pt]
s^jd^i&=&\cases{\bx{d^is^{j+1}}&$i\le j$\cr
                \bx{d^{i+1}s^j}&$i>   j$}
\end{array}
$$

\end{document}
 
I was attempting to make the cases line up so I put the first arguments in 
a box all of the same width.  This almost worked except that the three 
high brace is wider than the two high.  I think the three high one is 
fabricated, while the others are from the math extension font.  Is there 
any way of avoiding that?  The second problem has to do with the vertical 
space.  The [5pt] adds no vertical space.  If I use [8pt], I do with the 
first two, but not the third.  I have to add 10pt, 10pt, and 12pt to get 
the kind of space I want.  Any idea what is happening with these?  Or is 
there a better way to do what I am trying to do?

Michael Barr