Definition two_lists_rect x y: P x y := two_lists_rect_pre (x, y).Instance Reflexive_Permutation T: Reflexive Permutation := @Permutation_refl T.Instance Reflexive_Symmetric T: Symmetric Permutation := @Permutation_sym T.Instance Reflexive_Transitive T: Transitive Permutation := @perm_trans T.

Lemma Permutation_concatMap T U (f g: T -> list U) l: (forall x, In x l -> Permutation (f x) (g x)) -> Permutation (concat (map f l)) (concat (map g l)).