intuition.
eapply eqRat_trans.
eapply sumList_body_eq; intuition.
apply ratMult_comm.
eapply eqRat_trans.
eapply sumList_factor_constant_r.
apply ratMult_comm.
Qed.

Lemma fold_add_body_const : forall (A : Set)(ls : list A) c init,
fold_left (fun r a => r + c) ls init == c * (length ls / 1) + init.