I came across a proof that the an AVL tree has O(log n) height and there’s one step which I do not understand.

Let $ N_h$ represent minimum number of nodes that can form an AVL tree of height h. Since we’re looking for **minimum** number of nodes, let its children’s minimum number of nodes be $ N_{h-1}$ and $ N_{h-2}$ .

Proof:

$ $ N_h = N_{h-1} + N_{h-2} + 1 \tag{1}$ $ $ $ N_{h-1} = N_{h-2} + N_{h-3} + 1 \tag{2}$ $ $ $ N_h = (N_{h-2} + N_{h-3} + 1 + ) + N_{h-2} + 1 \tag{3}$ $ $ $ N_h > 2N_{h-2} \tag{4}$ $ $ $ N_h > 2^{h/2} \tag{5} $ $

I do not understand how we went from (4) to (5). If anyone could explain, that’d be great. Thanks!