To prove investment lemma
Two observations about ranks
- rank of a node >= rank of any of its descendents
- Rank Rule: if a node has 2 children of equal rank, then its rank is greater than that of each child
- Proof of Rank Rule: node x has two children, u and v
w(x) > w(u) + w(v) >= 2 r(u) + 1
floor(log (w(x)) >= r(u) + 1