# Regular Tree Languages are closed under quotient?

The Wikipedia page for Regular Tree Grammars notes that if $$L_1$$ and $$L_2$$ are regular tree languages, than $$L_1 \setminus L_2$$ is as well. However, it doesn't define this quotient operation for trees, and doesn't give a reference for this specific fact.

I'm wondering if someone can point me to a formal definition of the quotient operaiton on tree languages, and a proof that they are indeed closed under this operation.

• Are you sure that the symbol is not intended to denote set difference? – Jan Johannsen Apr 26 at 7:41
• @JanJohannsen... derp. Yep, that's probably exactly what it is. – jmite Apr 26 at 16:02