proposition: Lemma inc_dec_not_in_collect : forall (b : Bag_of_message) (m : Message) (s0 s1 s2 s3 : Site), first Message (b s1 s2) = value Message m -> ~ inc_dec_in_queue s3 (b s0 owner) -> m <> inc_dec s3 -> ~ inc_dec_in_queue s3 (Collect_message Message b s1 s2 s0 owner).
proof: Proof. intros. case (eq_queue_dec s1 s0 s2 owner). intros. decompose [and] a. rewrite H2; rewrite H3. rewrite collect_here. apply inc_dec_not_in_first_out with (m := m). rewrite <- H2; rewrite <- H3; auto. auto. auto. intro. rewrite collect_elsewhere. auto. auto. Qed.
imports: DistributedReferenceCounting.machine2.invariant0 DistributedReferenceCounting.machine2.invariant1 DistributedReferenceCounting.machine2.invariant2 DistributedReferenceCounting.machine2.invariant3 DistributedReferenceCounting.machine2.invariant4