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_filter f l : NoDup l -> NoDup (filter f l).
Hypothesis decA: forall x y : A, {x = y} + {x <> y}.