Definition compareR {A} {JA: Join A}{SA: Sep_alg A}{AG: ageable A} : relation A
   := comparable.Definition extendR  {A} {JA: Join A}{PA: Perm_alg A}{AG: ageable A} : relation A := join_sub.

Lemma valid_rel_extend {A} {JA: Join A}{PA: Perm_alg A}{AG: ageable A}{XA: Age_alg A} : valid_rel extendR.