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▹
Essentials
▹
Relations
Definition 1.4.11.
Let
S
be a set,
≺
be a
relation
on
S
. We define:
≺
is symmetric
:
⇔
∀
s
,
t
∈
S
s.t.
s
≺
t
:
t
≺
s
⇔
≺
=
≺
T
Equivalence.
No proof.
References.
https://en.wikipedia.org/wiki/Symmetric_relation
https://mathworld.wolfram.com/SymmetricRelation.html
https://proofwiki.org/wiki/Definition:Symmetric_Relation
https://ncatlab.org/nlab/show/symmetric+relation
https://coq.inria.fr/library/Coq.Sets.Relations_1.html#Symmetric
https://leanprover-community.github.io/mathlib_docs/init/logic.html#symmetric