Corollary 1

If $x$ and $y$ are permutable under the associative law $\top$ so are $\top^m x$ and $\top^n y$ for all integers $m > 0$ and $n > 0$; in particular $\top^m x$ and $\top^n x$ are permutable for all $x$ and all integers $m > 0$ and $n > 0$.