induction 1; intuition; subst.
econstructor.
rewrite <- H1.
trivial.
econstructor.
eapply IHsumList_rel.
intuition.
eapply eqRat_refl.
trivial.
eauto.
rewrite <- H3.
trivial.
Qed.

(* Specifications: *)
Lemma sumList_rel_plus_inv : forall (A : Type)(ls : list A) r (rel1 rel2 rel : A -> Rat -> Prop),
sumList_rel rel ls r ->
(forall a r, In a ls -> rel a r -> forall r1 r2, rel1 a r1 -> rel2 a r2 -> r == r1 + r2) ->
forall r1 r2, sumList_rel rel1 ls r1 -> sumList_rel rel2 ls r2 -> r == r1 + r2.