User blog comment:Naruyoko/My Utterly Obscure and Slowly Evolve-Growing Function-Notation-Whatever/@comment-35470197-20190228224550/@comment-35470197-20190301231640

For example, Rule 13 implies equalities like \begin{eqnarray*} & & \langle 2 \rangle_{2} = \langle 2,2 \rangle_{2} \\ & & \langle 3 \rangle_{1,1} = \langle 3,3,3 \rangle_{1,1} \end{eqnarray*} but they yield contradictions.