Library
▹
Essentials
▹
Relations
Definition 1.4.22.
Let
S
be a set,
≺
be a
relation
on
S
. We define:
≺
is an equivalence relation
:
⇔
≺
is a preorder
and
≺
is symmetric
References.
https://en.wikipedia.org/wiki/Equivalence_relation
https://mathworld.wolfram.com/EquivalenceRelation.html
https://proofwiki.org/wiki/Definition:Equivalence_Relation
https://ncatlab.org/nlab/show/equivalence+relation
https://coq.inria.fr/library/Coq.Sets.Relations_1.html#Equivalence
https://leanprover-community.github.io/mathlib_docs/init/logic.html#equivalence