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

Lemma PermutationA_cons_app l l₁ l₂ x : PermutationA l (l₁ ++ l₂) -> PermutationA (x :: l) (l₁ ++ x :: l₂).