Global Instance PermutationA_app :
  Proper (PermutationA ==> PermutationA ==> PermutationA) (@app A).

Lemma NoDupA_equivlistA_decompose l1 l2 : NoDupA eqA l1 -> NoDupA eqA l2 -> equivlistA eqA l1 l2 -> exists l, Permutation l1 l /\ eqlistA eqA l l2.