Definition:Proper Subtower in Set
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Definition
Let $X$ be a set.
Let $\struct {T, \preccurlyeq}$ be a tower in $X$.
Then $\struct {T, \preccurlyeq}$ is a proper subtower in $X$ if and only if:
- $T$ is a proper subset of some set $T' \subseteq X$
and:
- $\struct {T', \preccurlyeq}$ is a tower in $X$.
Historical Note
The name proper subtower in set has been specifically coined for $\mathsf{Pr} \infty \mathsf{fWiki}$, and may or may not appear in the literature.