(** Elememt [a] is a subelement of [c] .  This relation forms a partial order. *)

(* Specifications: *)
Lemma join_join_sub {A} `{Perm_alg A}: forall {a b c},
join a b c ->
join_sub a c.
Lemma join_join_sub' {A} `{Perm_alg A}: forall {a b c},
join a b c ->
join_sub b c.
Lemma join_sub_refl {A} {J: Join A}{PA: Perm_alg A}{SA: Sep_alg A}: forall a,
join_sub a a.