Hypothesis eq_E_dec : eq_dec E.

(* Specifications: *)
Lemma lt_sigma_sigma :
forall (l : list E) (f g : E -> Z),
(forall x : E, (f x <= g x)%Z) ->
(exists y : E, (f y < g y)%Z /\ In y l) -> (sigma l f < sigma l g)%Z.