Instance compond_relation_proper {A: Type}: Proper (same_relation A ==> same_relation A ==> same_relation A) compond_relation.

Lemma relation_conjunction_inclusion: forall {A} (R1 R2 R3 R4: relation A),
inclusion _ R1 R2 ->
inclusion _ R3 R4 ->
inclusion _ (relation_conjunction R1 R3) (relation_conjunction R2 R4).