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:<math>f(L)=\bigcup_{s\in L} f(s)</math>
[[Regular language]]s are closed under string substitution. That is, if each letter in the alphabet of a regular language is substituted by another regular language, the result is still a regular language.<ref>Hopcroft, Ullman (1979), Sect.3.2, Theorem 3.4, p.60</ref>
Similarly, [[context-free language]]s are closed under string substitution.<ref>Hopcroft, Ullman (1979), Sect.6.2, Theorem 6.2, p.131</ref><ref group="note">Although every regular language is also context-free, the previous theorem is not implied by the current one, since the former yields a shaper result for regular languages.</ref>
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