Item 2 (00HN) — The Clowder Project

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Style	Class	Font	Theorem Environments
Style 1	`book`	Alegreya Sans	`tcbthm`
Style 2	`book`	Alegreya Sans	`amsthm`
Style 3	`book`	Arno*	`amsthm`
Style 4	`book`	Computer Modern	`amsthm`

*To be replaced with Linus Romer's Elemaints when it is released.

The poset of relations from $A$ to $B$ is the poset
\[ \mathbf{Rel}\webleft (A,B\webright )\mathrel {\smash {\overset {\mathclap {\scriptscriptstyle \text{def}}}=}}\webleft (\mathrm{Rel}\webleft (A,B\webright ),\subset \webright ) \]

consisting of:
- The Underlying Set. The set $\mathrm{Rel}\webleft (A,B\webright )$ of Item 1.
- The Partial Order. The partial order
  
  \[ \subset \colon \mathrm{Rel}\webleft (A,B\webright )\times \mathrm{Rel}\webleft (A,B\webright )\to \{ \mathsf{true},\mathsf{false}\} \]
  
  on $\mathrm{Rel}\webleft (A,B\webright )$ given by inclusion of relations.

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