Inductive D_queue : queue Message -> Prop :=
  | D_empty : D_queue (empty Message)
  | D_dec : forall qm : queue Message, D_queue (input Message dec qm).Inductive D_queue : queue Message -> Prop :=
  | D_empty : D_queue (empty Message)
  | D_dec : forall qm : queue Message, D_queue (input Message dec qm).Inductive D_queue : queue Message -> Prop :=
  | D_empty : D_queue (empty Message)
  | D_dec : forall qm : queue Message, D_queue (input Message dec qm).Inductive alternate : queue Message -> Prop :=
  | alt_null : alternate (empty Message)
  | alt_single_inc :
      forall s0 : Site,
      alternate (input Message (inc_dec s0) (empty Message))
  | alt_any_alt :
      forall (qm : queue Message) (m : Message),
      (forall s : Site, m <> inc_dec s) ->
      alternate qm -> alternate (input Message m qm)
  | alt_inc_dec :
      forall (qm : queue Message) (s0 : Site),
      alternate qm ->
      alternate (input Message (inc_dec s0) (input Message dec qm)).Inductive alternate : queue Message -> Prop :=
  | alt_null : alternate (empty Message)
  | alt_single_inc :
      forall s0 : Site,
      alternate (input Message (inc_dec s0) (empty Message))
  | alt_any_alt :
      forall (qm : queue Message) (m : Message),
      (forall s : Site, m <> inc_dec s) ->
      alternate qm -> alternate (input Message m qm)
  | alt_inc_dec :
      forall (qm : queue Message) (s0 : Site),
      alternate qm ->
      alternate (input Message (inc_dec s0) (input Message dec qm)).Inductive alternate : queue Message -> Prop :=
  | alt_null : alternate (empty Message)
  | alt_single_inc :
      forall s0 : Site,
      alternate (input Message (inc_dec s0) (empty Message))
  | alt_any_alt :
      forall (qm : queue Message) (m : Message),
      (forall s : Site, m <> inc_dec s) ->
      alternate qm -> alternate (input Message m qm)
  | alt_inc_dec :
      forall (qm : queue Message) (s0 : Site),
      alternate qm ->
      alternate (input Message (inc_dec s0) (input Message dec qm)).Inductive alternate : queue Message -> Prop :=
  | alt_null : alternate (empty Message)
  | alt_single_inc :
      forall s0 : Site,
      alternate (input Message (inc_dec s0) (empty Message))
  | alt_any_alt :
      forall (qm : queue Message) (m : Message),
      (forall s : Site, m <> inc_dec s) ->
      alternate qm -> alternate (input Message m qm)
  | alt_inc_dec :
      forall (qm : queue Message) (s0 : Site),
      alternate qm ->
      alternate (input Message (inc_dec s0) (input Message dec qm)).Inductive alternate : queue Message -> Prop :=
  | alt_null : alternate (empty Message)
  | alt_single_inc :
      forall s0 : Site,
      alternate (input Message (inc_dec s0) (empty Message))
  | alt_any_alt :
      forall (qm : queue Message) (m : Message),
      (forall s : Site, m <> inc_dec s) ->
      alternate qm -> alternate (input Message m qm)
  | alt_inc_dec :
      forall (qm : queue Message) (s0 : Site),
      alternate qm ->
      alternate (input Message (inc_dec s0) (input Message dec qm)).

(* Specifications: *)
Lemma not_D_queue : forall (q0 : queue Message) (m : Message), m <> dec -> ~ D_queue (input Message m q0).
Lemma D_first_out : forall q0 : queue Message, D_queue q0 -> D_queue (first_out Message q0).
Lemma alt_first_out : forall q0 : queue Message, alternate q0 -> alternate (first_out Message q0).
Lemma D_collect : forall s1 s2 : Site, D_queue (b0 s0 owner) -> D_queue (Collect_message Message b0 s1 s2 s0 owner).
Lemma D_post_elsewhere : forall (s1 s2 : Site) (m : Message), s1 <> s0 \/ s2 <> owner -> D_queue (b0 s0 owner) -> D_queue (Post_message Message m b0 s1 s2 s0 owner).
Lemma D_post_dec : D_queue (Post_message Message dec b0 s0 owner s0 owner).
Lemma alt_collect : forall s1 s2 : Site, alternate (b0 s0 owner) -> alternate (Collect_message Message b0 s1 s2 s0 owner).
Lemma alt_post_elsewhere : forall (s1 s2 : Site) (m : Message), s1 <> s0 \/ s2 <> owner -> alternate (b0 s0 owner) -> alternate (Post_message Message m b0 s1 s2 s0 owner).
Lemma alt_post_any : forall m : Message, (forall s : Site, m <> inc_dec s) -> alternate (b0 s0 owner) -> alternate (Post_message Message m b0 s0 owner s0 owner).
Lemma alt_post_inc : forall s1 : Site, alternate (b0 s0 owner) -> b0 s0 owner = empty Message \/ last Message (b0 s0 owner) = value Message dec -> alternate (Post_message Message (inc_dec s1) b0 s0 owner s0 owner).
Lemma not_D_queue : forall (q0 : queue Message) (m : Message), m <> dec -> ~ D_queue (input Message m q0).
Lemma D_first_out : forall q0 : queue Message, D_queue q0 -> D_queue (first_out Message q0).
Lemma alt_first_out : forall q0 : queue Message, alternate q0 -> alternate (first_out Message q0).
Lemma D_collect : forall s1 s2 : Site, D_queue (b0 s0 owner) -> D_queue (Collect_message Message b0 s1 s2 s0 owner).
Lemma D_post_elsewhere : forall (s1 s2 : Site) (m : Message), s1 <> s0 \/ s2 <> owner -> D_queue (b0 s0 owner) -> D_queue (Post_message Message m b0 s1 s2 s0 owner).
Lemma D_post_dec : D_queue (Post_message Message dec b0 s0 owner s0 owner).
Lemma alt_collect : forall s1 s2 : Site, alternate (b0 s0 owner) -> alternate (Collect_message Message b0 s1 s2 s0 owner).
Lemma alt_post_elsewhere : forall (s1 s2 : Site) (m : Message), s1 <> s0 \/ s2 <> owner -> alternate (b0 s0 owner) -> alternate (Post_message Message m b0 s1 s2 s0 owner).
Lemma alt_post_any : forall m : Message, (forall s : Site, m <> inc_dec s) -> alternate (b0 s0 owner) -> alternate (Post_message Message m b0 s0 owner s0 owner).
Lemma alt_post_inc : forall s1 : Site, alternate (b0 s0 owner) -> b0 s0 owner = empty Message \/ last Message (b0 s0 owner) = value Message dec -> alternate (Post_message Message (inc_dec s1) b0 s0 owner s0 owner).