(** 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_unit1 {A} `{Perm_alg A}: forall x y z, unit_for x z -> y = z -> join x y z.