End reduce_strictly_pos.
Section reduce_in_q_null.
Variable E : Set.
Variable f : E -> Z.
Hypothesis eq_E_dec : eq_dec E.

(* Specifications: *)
Lemma reduce_in_queue_null :
forall q : queue E,
(forall x : E, In_queue E x q -> f x = 0%Z) -> reduce E f q = 0%Z.