Inductive compond_relation {A: Type} (R1 R2: relation A) : relation A :=
  | compond_intro: forall x y z, R1 x y -> R2 y z -> compond_relation R1 R2 x z.Inductive compond_relation {A: Type} (R1 R2: relation A) : relation A :=
  | compond_intro: forall x y z, R1 x y -> R2 y z -> compond_relation R1 R2 x z.

(* Specifications: *)
Lemma compond_relation_spec: forall {A} (R1 R2: relation A) x z, compond_relation R1 R2 x z -> exists y, R1 x y /\ R2 y z.
Lemma compond_relation_inclusion: forall {A} (R1 R2 R3 R4: relation A), inclusion _ R1 R2 -> inclusion _ R3 R4 -> inclusion _ (compond_relation R1 R3) (compond_relation R2 R4).