induction ls1; intuition; simpl in *; intuition.
Qed.

Lemma fold_add_init_nat_h :
forall (A : Set)(f : A -> nat)(ls : list A)(init1 init2 : nat),
(fold_left (fun acc a => acc + (f a))%nat ls (init1 + init2) =
init1 + fold_left (fun acc a => acc + (f a))%nat ls init2)%nat.