Smullyan's Drinking Principle/Informal Proof
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Theorem
Suppose that there is at least one person in the pub.
Then there is a person $x$ in the pub such that if $x$ is drinking, then everyone in the pub is drinking.
Informal Proof
There are two cases:
- $(1): \quad$ Everyone in the pub is drinking.
- $(2): \quad$ Someone in the pub is not drinking.
Suppose first that everyone in the pub is drinking.
Then $x$ can be chosen to be any person in the pub.
Suppose instead that someone in the pub is not drinking.
Then $x$ can be chosen to be any person in the pub who is not drinking.
$\blacksquare$
Source of Name
This entry was named for Raymond Merrill Smullyan.