Section ReDun.
Variable A : Type.
Inductive NoDup : list A -> Prop :=
| NoDup_nil : NoDup nil
| 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').