More on idea of proof
I will save the money you give me in “bank accounts” at each node in the tree, each of which will be required to maintain a certain minimum balance.
Minimum balance in a bank account at node will be related to its number of descendents (money invariant below)
payment I make to you for each operation:
- some will come out of bank accounts at nodes
- some will come from new investment (what you paid me)