induction n; intuition; simpl in *.
unfold sumList.
simpl.
eapply eqRat_impl_leRat.
rewrite <- ratIdentityIndiscernables.
intuition.
eapply leRat_trans.
2:{
eapply eqRat_impl_leRat.
symmetry.
eapply sumList_cons.
}
simpl.
eapply leRat_trans.
eapply ratDistance_le_trans.
eapply IHn.
eapply leRat_refl.
rewrite ratAdd_comm.
intuition.
Qed.

Theorem Single_impl_ListHybrid_sum :
ListHybrid_Advantage
<=
sumList (forNats maxA) (fun i => DistSingle_Adv c1 c2 (B1 i) B2).