(** 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 comparable_common_unit {A} `{Sep_alg A}: forall a b, comparable a b -> exists e, join e a a /\ join e b b.