Inductive NoDup : list A -> Prop :=
    | NoDup_nil : NoDup []
    | NoDup_cons : forall x l, ~ In x l -> NoDup l -> NoDup (x::l).Inductive NoDup : list A -> Prop :=
    | NoDup_nil : NoDup []
    | NoDup_cons : forall x l, ~ In x l -> NoDup l -> NoDup (x::l).Inductive NoDup : list A -> Prop :=
    | NoDup_nil : NoDup []
    | NoDup_cons : forall x l, ~ In x l -> NoDup l -> NoDup (x::l).

Lemma NoDup_app (l1 l2 : list A): NoDup l1 -> NoDup l2 -> (forall a, In a l1 -> ~ In a l2) -> NoDup (l1 ++ l2).