(* * Copyright (c) 2009-2010, Andrew Appel, Robert Dockins and Aquinas Hobor. * *)
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.
Definition compareM {A} {JA: Join A}{PA: Perm_alg A}{SA: Sep_alg A}{AG: ageable A}{XA: Age_alg A} : modality
:= exist _ compareR valid_rel_compare.