(* MOVE THIS ONE ELSEWHERE! *)
Definition cjoins {A} {JA: Join A} (a b : A) : Type := {c : A | join a b c}.(* MOVE THIS ONE ELSEWHERE! *)
Definition cjoin_sub {A} {JA: Join A} (a c : A) : Type := {b : A | join a b c}.

Lemma pfull_pmaximal {A} {JA: Join A} {PA: Perm_alg A} {Pos_A: Pos_alg A} : full = maximal.