(** * [permutation]: definition and basic properties *)
Definition permutation (l m:list A) := meq (list_contents l) (list_contents m).

Lemma permut_add_cons_inside_eq :
forall a a' l l1 l2, eqA a a' ->
permutation l (l1 ++ l2) ->
permutation (a :: l) (l1 ++ a' :: l2).