unfold expRat_rel in *.
intuition.
destruct H.
exists (expRat x n).
intuition.
eapply expRat_eqRat_compat; eauto.
Qed.

Lemma expRat_rel_func : forall (r : Rat -> Prop) v1 v2 n,
expRat_rel r n v1 ->
expRat_rel r n v2 ->
(forall x1 x2, r x1 -> r x2 -> x1 == x2) ->
(exists r', r r') ->
v1 == v2.