intuition.
eapply fold_add_permutation; intuition.
Qed.

Lemma sumList_rel_body_eq_strong : forall (A : Type)(rel1 rel2 : A -> Rat -> Prop)(ls1 : list A) r1,
sumList_rel rel1 ls1 r1 ->
forall ls2 r2,
(forall a r', In a ls1 -> rel1 a r' -> rel2 a r') ->
r1 == r2 ->
ls1 = ls2 ->
sumList_rel rel2 ls2 r2.