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_filter f l : NoDup l -> NoDup (filter f l).