Question: In Example, what principle allows us to conclude that two nodes must represent the same person?
Example: (of an unexpected use for binary trees). You-yes, you! We're talking to you. You, personally, have an ancestor who has an ancestor who is the ancestor of both their genetic parents-within the last 1,000 years. That is, some ancestor A of yours, with parents P1, P2, has some earlier ancestor B from whom both P1 and P2 descended. All within the last millennium. No kidding! We're about to prove it (by contradiction), in case you don't believe this wild claim.