Instance inclusion_proper {A}: Proper (same_relation A ==> same_relation A ==> iff) (inclusion A).

(* Specifications: *)
Lemma app_same_relation: forall {A: Type} (R1 R2: relation A) (a1 a2: A),
same_relation A R1 R2 ->
(R1 a1 a2 <-> R2 a1 a2).