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

Lemma joinlist_swap {A} {JA : Join A} {PA : Perm_alg A} (a b x : A) l : joinlist (a :: b :: l) x = joinlist (b :: a :: l) x.