Induction step. Let n 2 and suppose that the lemma holds for all insertion permutations of size strictly less than n. Let π = (π(1), . . . , π(n)) be a permutation drawn uniformly at random from Sn. The rst element π(1) will become the root of the tree Tπ. Since the distribution of π(1) is u.a.r. from [n], the root of the tree is chosen uniformly at random, as required by the construction of ~ ...
