Section LOGIC.
Variable U : Set.

(* Specifications: *)
Lemma ex_not_not_all :
forall P : U -> Prop, (exists n : U, ~ P n) -> ~ (forall n : U, P n).
Lemma ex_not_not_all2 :
forall P : U -> Prop, (exists n : U, P n) -> ~ (forall n : U, ~ P n).
Lemma PNNP : forall p : Prop, p -> ~ ~ p.
End LOGIC.
Lemma sigma_f_null :
forall (E : Set) (f : E -> Z) (l : list E),
(forall x_ : E, f x_ = 0%Z) -> sigma E l f = 0%Z.
Lemma null_st :
forall (c0 : Config) (s0 : Site),
legal c0 -> s0 <> owner -> no_message c0 -> st c0 s0 = 0%Z.
Lemma not_empty_implies_last :
forall (E : Set) (q : queue E),
q <> empty E -> exists x : E, first E q = value E x.
Lemma different_queue1 :
forall (E : Set) (q : queue E) (m : E), input E m q <> first_out E q.
Lemma different_queue2 :
forall (E : Set) (q : queue E) (m : E),
first E q = value E m -> q <> first_out E q.