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.