End Add.
(********************************)
(** ** Lists without redundancy *)
(********************************)
Section ReDun.
Variable A : Type.
Inductive NoDup : list A -> Prop :=
| NoDup_nil : NoDup []
| NoDup_cons : forall x l, ~ In x l -> NoDup l -> NoDup (x::l).

Lemma NoDup_Add a l l' : Add a l l' -> (NoDup l' <-> NoDup l /\ ~In a l).