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).
(** Effective computation of a list without duplicates *)
Hypothesis decA: forall x y : A, {x = y} + {x <> y}.
Fixpoint nodup (l : list A) : list A :=
match l with
| [] => []
| x::xs => if in_dec decA x xs then nodup xs else x::(nodup xs)
end.

Lemma nodup_inv k l a : nodup k = a :: l -> ~ In a l.