Inductive uniq: list A -> Prop :=
  uniq_nil: uniq nil
| uniq_cons: forall a l, ~ In a l -> uniq l -> uniq (a::l).Inductive uniq: list A -> Prop :=
  uniq_nil: uniq nil
| uniq_cons: forall a l, ~ In a l -> uniq l -> uniq (a::l).Inductive uniq: list A -> Prop :=
  uniq_nil: uniq nil
| uniq_cons: forall a l, ~ In a l -> uniq l -> uniq (a::l).

Lemma uniq_app_inv_r l1 l2: uniq (l1 ++ l2) -> uniq l2.