Chomsky Schützenberger enumeration theorem
There is a proof in the book of Kuich &amp; Salomaa, Semirings, Automata, Languages and another one in the paper of Panholzer, "Gröbner Bases and the Defining Polynomial of a Context-free Grammar Generating Function", J. of Automata, Languages and Combinatorics 10 (2005), 79–97.   I wish there were a simple and clear proof of the result.