proposition: 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').
proof: Proof. intros; apply Permutation_app; auto. Qed.
imports: List Setoid Compare_dec Morphisms FinFun PeanoNat