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_remove l l' a : NoDup (l++a::l') -> NoDup (l++l') /\ ~In a (l++l').