Given a complete binary tree with $n$ nodes. I'm trying to prove that a complete binary tree has exactly $\lceil n/2 \rceil$ leaves. I think I can do this by induction.
For $h(t)=0$, the tree is empty. So there are no leaves and the claim holds for an empty tree.
For $h(t)=1$, the tree has 1 node, that also is a leaf, so the claim holds. Here I'm stuck, I don't know what to choose as induction hypothesis and how to do the induction step.