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

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).