Structural induction is not only possible, but fun and
easy (well, possibly for grad-student values thereof). What
you want to do is remember that induction consists of a base
and a recursive case -- for mathematical induction, this
comes from the fact that every natural number but zero is
the successor of another nat.
For a binary tree, you'd prove theorems inductively by
proving them on leaf nodes, then proving that if both of an
interior node's children satisfy the theorem, the interior
node must as well. (It's a bit more difficult with lazy
languages, but that's not your problem here.)
Nice job on the root node, btw.
--
F
o
x
t
r
o
t
U
n
i
f
o
r
m
Found a typo in this node? /msg me
% man 3 strfry