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

Lemma compond_assoc: forall {A: Type} (R1 R2 R3: relation A), same_relation _ (compond_relation (compond_relation R1 R2) R3) (compond_relation R1 (compond_relation R2 R3)).