End Removal.
Hint Resolve rem_not_in rem_incl rem_mono rem_cons rem_cons' rem_app rem_in rem_neq.
(* * Duplicate-free lists *)
Inductive dupfree (X : Type) : list X -> Prop :=
| dupfreeN : dupfree nil
| dupfreeC x A : ~ x el A -> dupfree A -> dupfree (x::A).
Section Dupfree.
Variable X : Type.
Implicit Types A B : list X.

Lemma dupfree_inv x A :
dupfree (x::A) <-> ~ x el A /\ dupfree A.