In a paper I see the following lemma about unlabeled binary trees:
If $s_1$ and $s_2$ are both m-node binary trees, then the number of n-node binary trees containing $s_1$ as a subtree is the same as the number of n-node binary trees containing $s_2$.
It goes on to use this to show that if you want to compute the number of n-node binary trees that have m-node as a subtree, it doesn't matter what m-node tree you use.
I feel like I'm either misinterpreting this or missing something obvious. But isn't the following setup a contradiction to this lemma:
Nodes 2a and 6a produce the same tree, so tree 1 is only the subtree of 5 4-node trees while tree 2 is a subtree of 6 4-node trees.