**Lemma 21.1**

,
where *F*_{k} is a
Fibonacci number.

**Lemma 21.3**

For a node x in a Fibonacci heap, where k = degree(x),

size(x)
, where

size(x) = #nodes in subtree rooted at x

**Corollary 21.4**

D(n) = O(lgn)

By Lemma 21.3, n size(x) , where n = nodes in Fibonacci Heap and k = degree of any node x.

Then , and k = = O(lg n).