Proof By Induction

public class WeightedQuickUnionPathCompressionUF {
private int[] id; // id[i] = parent of i
private int[] sz; // sz[i] = number of objects in subtree rooted at i
private int count; // number of components

[code]....

Show that, in each tree produced by the method of weighted quick unionwith or without path compression, the degree of the root (i.e., the number of its dependants) is not less than the height of the tree. I know that the height of a tree with 2^n nodes is n, however i dont know how to quantify the number of dependents in a way to use induction to prove that dependents>=height.