= Solution
The <context-free languages> $L_1=\{a^n b^n c^m:n,m\geq0\}$ and $L_2=\{a^m b^n c^n:n,m\geq0\}$ have <context-free grammars> $S\to TC$, $T\to aTb\mid\varepsilon$, $C\to cC\mid\varepsilon$, and $S\to AT$, $A\to aA\mid\varepsilon$, $T\to bTc\mid\varepsilon$, respectively.
Their <intersection> is $L=\{a^n b^n c^n:n\geq0\}$. Suppose $L$ satisfied the <pumping lemma for context-free languages> with length $p$. In a decomposition $a^p b^p c^p=uvwxy$ with $|vwx|\leq p$ and $|vx|>0$, the window $vwx$ cannot meet both the $a$ and $c$ blocks. Pumping down changes at least one count and leaves at least one count unchanged. Thus the three counts are unequal, or the word order is invalid, contrary to the <pumping lemma for context-free languages>. Hence \b[CFLs are not closed under <intersection>].
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