Technical Correspondence: A Note On A Study Of Cases

is the constant of the pumping lemma, the pumped substring cannot be longer than k, and therefore the only other place we might be able to pump would be in the middle as and the middle cs, But this would result in violating the condit ion that l may not be greater than i. Thus, z cannot be pumped without violating the pumping lemma, and hence (7) is not context free. Since context f ree languages are closed under intersect ion with regular sets, it follows that (6) is not contex t f ree either. Since context f ree languages are also closed under substitution, this means that (5) is also not contextf ree . Finally, since (5) is the intersection of English, with the regular set (4), it follows that Englishj is not contextfree. Q.E.D.