Section Binary.
Context {A : Type}.
Definition relation_equivalence : relation (relation A) :=
@predicate_equivalence (_::_::Tnil).
Global Instance: RewriteRelation relation_equivalence.
Defined.
Definition relation_conjunction (R : relation A) (R' : relation A) : relation A :=
@predicate_intersection (A::A::Tnil) R R'.
Definition relation_disjunction (R : relation A) (R' : relation A) : relation A :=
@predicate_union (A::A::Tnil) R R'.
(** Relation equivalence is an equivalence, and subrelation defines a partial order. *)
Global Instance relation_equivalence_equivalence :
Equivalence relation_equivalence.

Lemma PartialOrder_inverse `(PartialOrder eqA R) : PartialOrder eqA (flip R).