intuition.
destruct l...
discriminate.
subst...
Qed.

(* Specifications: *)
Lemma length_ne_0_ne_nil A (l: list A): length l <> 0%nat -> l <> nil.
Lemma elemsR_le_S a b: elemsR le a b -> elemsR le (map S a) (map S b).
Lemma elemsR_impl A (R R' : relation A): (forall x y: A, R x y -> R' x y) -> forall l l', elemsR R l l' -> elemsR R' l l'.
End Permuted.