Suppose that formula_10. Let formula_11 be the full formula_2-ary tree of depth formula_13 (thus, every node of formula_11 at level formula_15 has formula_2 children, while the nodes at level formula_13 are leaves). Every word of length formula_18 over an formula_2-ary alphabet corresponds to a node in this tree at depth formula_20. The formula_21th word in the prefix code corresponds to a node formula_22; let formula_23 be the set of all leaf nodes (i.e. of nodes at depth formula_13) in the subtree of formula_11 rooted at formula_22. That subtree being of height formula_27, we have