Library
▹
Essentials
▹
Relations
Definition 1.4.14.
Let
S
be a set,
⪯
be a
relation
on
S
. We define:
⪯
is a preorder
:
⇔
⪯
is reflexive
and
⪯
is transitive
References.
https://en.wikipedia.org/wiki/Preorder
https://mathworld.wolfram.com/Preorder.html
https://proofwiki.org/wiki/Definition:Preordering
https://ncatlab.org/nlab/show/preorder
https://coq.inria.fr/library/Coq.Sets.Relations_1.html#Preorder
https://leanprover-community.github.io/mathlib_docs/init/algebra/order.html#preorder