induction l...
intros.
destruct IHl...
destruct (X a)...
Qed.

Lemma elemsRuniq A B (R: A -> B -> Prop) (l: list A):
(forall x, In x l -> forall y, R x y -> forall y', R x y' -> y = y') -> forall r, elemsR R l r -> forall r', elemsR R l r' -> r = r'.