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

Lemma joinlist_join_sub {A} {JA : Join A} {PA : Perm_alg A} (x phi : A) l : joinlist l phi -> In x l -> join_sub x phi.