Set Implicit Arguments.
Section contents.
Variable T: Set.
Inductive SkipList: list T -> list T -> Prop :=
| SkipList_head (x: T) l l': SkipList l l' -> SkipList (x :: l) (x :: l')
| SkipList_tail (x: T) l l': SkipList l l' -> SkipList l (x :: l')
| SkipList_nil l: SkipList nil l.
Hint Constructors SkipList.

(* Specifications: *)
Lemma SkipList_refl (l: list T): SkipList l l.
Lemma NoDup_SkipList (l: list T): NoDup l -> forall l', SkipList l' l -> NoDup l'.
Proof with auto.