(** The elements of a multi-unit separation algebra can be partitioned
    into equivalance classes, where two elements are in the class iff
    they have the same unit.
  *)

  Definition comparable {A} `{Sep_alg A}  (a b:A)
    := core a = core b.

Lemma join_comparable2 {A} {J: Join A}{PA: Perm_alg A}{SA: Sep_alg A}: forall phi1 phi2 phi3, join phi1 phi2 phi3 -> comparable phi1 phi2.