intuition.
eapply eqRat_trans.
eapply fold_add_body_eq; intuition.
rewrite ratAdd_0_r.
apply eqRat_refl.
apply eqRat_refl.
apply fold_add_init.
Qed.

Lemma fold_add_eq_init : forall (A : Set)(ls : list A) init,
fold_left (fun r a => r + 0) ls init == init.