Instance Permutation_length' A {JA : Join A} {PA : Perm_alg A} :
  Proper (@Permutation A ==> @eq A ==> Logic.iff) joinlist | 10.

Lemma app_joinlist {A} {JA : Join A} {SA : Sep_alg A} {PA : Perm_alg A} l1 l2 x : joinlist (l1 ++ l2) x -> exists x1 x2, joinlist l1 x1 /\ joinlist l2 x2 /\ join x1 x2 x.