#[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').