intuition.
eapply fold_add_body_eq; intuition.
Qed.

Lemma fold_add_factor_constant_r : forall (A : Set)(ls : list A)(f : A -> Rat) init c,
fold_left (fun r a => r + (f a) * c) ls (init * c) ==
(fold_left (fun r a => r + (f a)) ls init) * c.