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

(* Specifications: *)
Lemma compond_eq_right: forall {A: Type} (R: relation A), same_relation _(compond_relation R eq) R.
Lemma compond_eq_left: forall {A: Type} (R: relation A), same_relation _(compond_relation eq R) R.
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).