I have the following question:
I have seen the statement that for the Shift operation, defined as:
Shift($L$) = { $yx$ | $xy \in L$}

Where the following is mentioned: "For any regular language $L$, Shift($L$) is regular as well."

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Shift defined as: Shift($L$) = { $yx$ | $xy \in L$}

I tried approaching this by forming a proof from the fact that a Shifted language is pulling from the same set of words / symbols as it's non shifted counterpart, but couldn't reach anything conclusive.

How would one prove that the shift operation preserves regularity?