Inductive D_queue : queue Message -> Prop :=
  | D_empty : D_queue (empty Message)
  | D_dec :
      forall qm : queue Message,
      alternate qm -> In_queue_before Message dec is_inc_dec qm -> D_queue qm.Inductive D_queue : queue Message -> Prop :=
  | D_empty : D_queue (empty Message)
  | D_dec :
      forall qm : queue Message,
      alternate qm -> In_queue_before Message dec is_inc_dec qm -> D_queue qm.Inductive D_queue : queue Message -> Prop :=
  | D_empty : D_queue (empty Message)
  | D_dec :
      forall qm : queue Message,
      alternate qm -> In_queue_before Message dec is_inc_dec qm -> D_queue qm.

Lemma alt_collect : forall s1 s2 : Site, alternate (b0 s0 owner) -> alternate (Collect_message Message b0 s1 s2 s0 owner).