induction 1; intuition; simpl in *.
inversion H0; clear H0; subst.
econstructor; eauto.
inversion H; clear H; subst.
inversion H2; clear H2; subst.
econstructor; eauto.
econstructor; eauto.
eapply eqRat_refl.
rewrite H5.
rewrite H7.
repeat rewrite <- ratAdd_assoc.
eapply ratAdd_eqRat_compat; intuition.
eapply ratAdd_comm.
Qed.

Lemma sumList_rel_all_0 : forall (A : Type)(rel : A -> Rat -> Prop)(ls : list A),
(forall a, In a ls -> rel a 0) ->
sumList_rel rel ls 0.