Sandwich Principle/Linguistic Note

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Linguistic Note on Sandwich Principle

The name Sandwich Principle for this lemma appears to have been coined by Raymond M. Smullyan and Melvin Fitting in their Set Theory and the Continuum Problem, revised ed..

As they explain, when $x \subset y \subset z$, we may consider $y$ to be sandwiched between $x$ and $z$.

Thus the Sandwich Principle tells us that, given the conditions constraining $x$, $y$ and $\map g x$, there can be no such $y$ sandwiched between $x$ and $\map g x$.