#[export] Instance Permutation_app' :
 Proper (@Permutation A ==> @Permutation A ==> @Permutation A) (@app A).

Lemma Permutation_app_middle : forall l l1 l2 l3 l4, Permutation (l1 ++ l2) (l3 ++ l4) -> Permutation (l1 ++ l ++ l2) (l3 ++ l ++ l4).