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.

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

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