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Let L be a regular language. Define L = { xay in Sigma | xy in L , a in Sigma } .

Let L be a regular language. Define L={xay in \Sigma | xy in L, a in \Sigma }. We
take the strings in L, and add exactly one symbol anywhere in the string for anywhere
it could be placed, even possibly at the beginning or end. Prove that if L is regular,
then so is L

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