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

Lemma Permutation_add_inside : forall a (l l' tl tl' : list A), Permutation l l' -> Permutation tl tl' -> Permutation (l ++ a :: tl) (l' ++ a :: tl').