(** 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 PermAlg_ext: forall (T: Type) (J: @Join T) (sa1 sa2: @Perm_alg T J), sa1=sa2.