Induction step
assume for i, prove for i+1.
consider two numbers: X, Y. Say Xi is ith digit of X (from the right)
Xi+1 < Yi+1 then i+1th BinSort will put them in order
Xi+1 > Yi+1 , same thing
Xi+1 = Yi+1 , order depends on
last i digits. Induction hypothesis says already sorted
for these digits. (Careful about
ensuring that your BinSort preserves order aka stable
)