Class LabeledMultiParams (P : BaseParams) :=
  {
    lb_name : Type ;
    lb_msg : Type ;
    lb_msg_eq_dec : forall x y : lb_msg, {x = y} + {x <> y} ;
    lb_name_eq_dec : forall x y : lb_name, {x = y} + {x <> y} ;
    lb_nodes : list lb_name ;
    lb_all_names_nodes : forall n, In n lb_nodes ;
    lb_no_dup_nodes : NoDup lb_nodes ;
    label : Type ;
    label_silent : label ;
    lb_init_handlers : lb_name -> data ;
    lb_net_handlers : lb_name -> lb_name -> lb_msg -> data -> label * (list output) * data * list (lb_name * lb_msg) ;
    lb_input_handlers : lb_name -> input -> data -> label * (list output) * data * list (lb_name * lb_msg)
  }.Class LabeledMultiParams (P : BaseParams) :=
  {
    lb_name : Type ;
    lb_msg : Type ;
    lb_msg_eq_dec : forall x y : lb_msg, {x = y} + {x <> y} ;
    lb_name_eq_dec : forall x y : lb_name, {x = y} + {x <> y} ;
    lb_nodes : list lb_name ;
    lb_all_names_nodes : forall n, In n lb_nodes ;
    lb_no_dup_nodes : NoDup lb_nodes ;
    label : Type ;
    label_silent : label ;
    lb_init_handlers : lb_name -> data ;
    lb_net_handlers : lb_name -> lb_name -> lb_msg -> data -> label * (list output) * data * list (lb_name * lb_msg) ;
    lb_input_handlers : lb_name -> input -> data -> label * (list output) * data * list (lb_name * lb_msg)
  }.Class LabeledMultiParams (P : BaseParams) :=
  {
    lb_name : Type ;
    lb_msg : Type ;
    lb_msg_eq_dec : forall x y : lb_msg, {x = y} + {x <> y} ;
    lb_name_eq_dec : forall x y : lb_name, {x = y} + {x <> y} ;
    lb_nodes : list lb_name ;
    lb_all_names_nodes : forall n, In n lb_nodes ;
    lb_no_dup_nodes : NoDup lb_nodes ;
    label : Type ;
    label_silent : label ;
    lb_init_handlers : lb_name -> data ;
    lb_net_handlers : lb_name -> lb_name -> lb_msg -> data -> label * (list output) * data * list (lb_name * lb_msg) ;
    lb_input_handlers : lb_name -> input -> data -> label * (list output) * data * list (lb_name * lb_msg)
  }.Class LabeledMultiParams (P : BaseParams) :=
  {
    lb_name : Type ;
    lb_msg : Type ;
    lb_msg_eq_dec : forall x y : lb_msg, {x = y} + {x <> y} ;
    lb_name_eq_dec : forall x y : lb_name, {x = y} + {x <> y} ;
    lb_nodes : list lb_name ;
    lb_all_names_nodes : forall n, In n lb_nodes ;
    lb_no_dup_nodes : NoDup lb_nodes ;
    label : Type ;
    label_silent : label ;
    lb_init_handlers : lb_name -> data ;
    lb_net_handlers : lb_name -> lb_name -> lb_msg -> data -> label * (list output) * data * list (lb_name * lb_msg) ;
    lb_input_handlers : lb_name -> input -> data -> label * (list output) * data * list (lb_name * lb_msg)
  }.Class LabeledMultiParams (P : BaseParams) :=
  {
    lb_name : Type ;
    lb_msg : Type ;
    lb_msg_eq_dec : forall x y : lb_msg, {x = y} + {x <> y} ;
    lb_name_eq_dec : forall x y : lb_name, {x = y} + {x <> y} ;
    lb_nodes : list lb_name ;
    lb_all_names_nodes : forall n, In n lb_nodes ;
    lb_no_dup_nodes : NoDup lb_nodes ;
    label : Type ;
    label_silent : label ;
    lb_init_handlers : lb_name -> data ;
    lb_net_handlers : lb_name -> lb_name -> lb_msg -> data -> label * (list output) * data * list (lb_name * lb_msg) ;
    lb_input_handlers : lb_name -> input -> data -> label * (list output) * data * list (lb_name * lb_msg)
  }.Class LabeledMultiParams (P : BaseParams) :=
  {
    lb_name : Type ;
    lb_msg : Type ;
    lb_msg_eq_dec : forall x y : lb_msg, {x = y} + {x <> y} ;
    lb_name_eq_dec : forall x y : lb_name, {x = y} + {x <> y} ;
    lb_nodes : list lb_name ;
    lb_all_names_nodes : forall n, In n lb_nodes ;
    lb_no_dup_nodes : NoDup lb_nodes ;
    label : Type ;
    label_silent : label ;
    lb_init_handlers : lb_name -> data ;
    lb_net_handlers : lb_name -> lb_name -> lb_msg -> data -> label * (list output) * data * list (lb_name * lb_msg) ;
    lb_input_handlers : lb_name -> input -> data -> label * (list output) * data * list (lb_name * lb_msg)
  }.Class LabeledMultiParams (P : BaseParams) :=
  {
    lb_name : Type ;
    lb_msg : Type ;
    lb_msg_eq_dec : forall x y : lb_msg, {x = y} + {x <> y} ;
    lb_name_eq_dec : forall x y : lb_name, {x = y} + {x <> y} ;
    lb_nodes : list lb_name ;
    lb_all_names_nodes : forall n, In n lb_nodes ;
    lb_no_dup_nodes : NoDup lb_nodes ;
    label : Type ;
    label_silent : label ;
    lb_init_handlers : lb_name -> data ;
    lb_net_handlers : lb_name -> lb_name -> lb_msg -> data -> label * (list output) * data * list (lb_name * lb_msg) ;
    lb_input_handlers : lb_name -> input -> data -> label * (list output) * data * list (lb_name * lb_msg)
  }.Class LabeledMultiParams (P : BaseParams) :=
  {
    lb_name : Type ;
    lb_msg : Type ;
    lb_msg_eq_dec : forall x y : lb_msg, {x = y} + {x <> y} ;
    lb_name_eq_dec : forall x y : lb_name, {x = y} + {x <> y} ;
    lb_nodes : list lb_name ;
    lb_all_names_nodes : forall n, In n lb_nodes ;
    lb_no_dup_nodes : NoDup lb_nodes ;
    label : Type ;
    label_silent : label ;
    lb_init_handlers : lb_name -> data ;
    lb_net_handlers : lb_name -> lb_name -> lb_msg -> data -> label * (list output) * data * list (lb_name * lb_msg) ;
    lb_input_handlers : lb_name -> input -> data -> label * (list output) * data * list (lb_name * lb_msg)
  }.Class LabeledMultiParams (P : BaseParams) :=
  {
    lb_name : Type ;
    lb_msg : Type ;
    lb_msg_eq_dec : forall x y : lb_msg, {x = y} + {x <> y} ;
    lb_name_eq_dec : forall x y : lb_name, {x = y} + {x <> y} ;
    lb_nodes : list lb_name ;
    lb_all_names_nodes : forall n, In n lb_nodes ;
    lb_no_dup_nodes : NoDup lb_nodes ;
    label : Type ;
    label_silent : label ;
    lb_init_handlers : lb_name -> data ;
    lb_net_handlers : lb_name -> lb_name -> lb_msg -> data -> label * (list output) * data * list (lb_name * lb_msg) ;
    lb_input_handlers : lb_name -> input -> data -> label * (list output) * data * list (lb_name * lb_msg)
  }.Class LabeledMultiParams (P : BaseParams) :=
  {
    lb_name : Type ;
    lb_msg : Type ;
    lb_msg_eq_dec : forall x y : lb_msg, {x = y} + {x <> y} ;
    lb_name_eq_dec : forall x y : lb_name, {x = y} + {x <> y} ;
    lb_nodes : list lb_name ;
    lb_all_names_nodes : forall n, In n lb_nodes ;
    lb_no_dup_nodes : NoDup lb_nodes ;
    label : Type ;
    label_silent : label ;
    lb_init_handlers : lb_name -> data ;
    lb_net_handlers : lb_name -> lb_name -> lb_msg -> data -> label * (list output) * data * list (lb_name * lb_msg) ;
    lb_input_handlers : lb_name -> input -> data -> label * (list output) * data * list (lb_name * lb_msg)
  }.Class LabeledMultiParams (P : BaseParams) :=
  {
    lb_name : Type ;
    lb_msg : Type ;
    lb_msg_eq_dec : forall x y : lb_msg, {x = y} + {x <> y} ;
    lb_name_eq_dec : forall x y : lb_name, {x = y} + {x <> y} ;
    lb_nodes : list lb_name ;
    lb_all_names_nodes : forall n, In n lb_nodes ;
    lb_no_dup_nodes : NoDup lb_nodes ;
    label : Type ;
    label_silent : label ;
    lb_init_handlers : lb_name -> data ;
    lb_net_handlers : lb_name -> lb_name -> lb_msg -> data -> label * (list output) * data * list (lb_name * lb_msg) ;
    lb_input_handlers : lb_name -> input -> data -> label * (list output) * data * list (lb_name * lb_msg)
  }.Class LabeledMultiParams (P : BaseParams) :=
  {
    lb_name : Type ;
    lb_msg : Type ;
    lb_msg_eq_dec : forall x y : lb_msg, {x = y} + {x <> y} ;
    lb_name_eq_dec : forall x y : lb_name, {x = y} + {x <> y} ;
    lb_nodes : list lb_name ;
    lb_all_names_nodes : forall n, In n lb_nodes ;
    lb_no_dup_nodes : NoDup lb_nodes ;
    label : Type ;
    label_silent : label ;
    lb_init_handlers : lb_name -> data ;
    lb_net_handlers : lb_name -> lb_name -> lb_msg -> data -> label * (list output) * data * list (lb_name * lb_msg) ;
    lb_input_handlers : lb_name -> input -> data -> label * (list output) * data * list (lb_name * lb_msg)
  }.Class LabeledMultiParams (P : BaseParams) :=
  {
    lb_name : Type ;
    lb_msg : Type ;
    lb_msg_eq_dec : forall x y : lb_msg, {x = y} + {x <> y} ;
    lb_name_eq_dec : forall x y : lb_name, {x = y} + {x <> y} ;
    lb_nodes : list lb_name ;
    lb_all_names_nodes : forall n, In n lb_nodes ;
    lb_no_dup_nodes : NoDup lb_nodes ;
    label : Type ;
    label_silent : label ;
    lb_init_handlers : lb_name -> data ;
    lb_net_handlers : lb_name -> lb_name -> lb_msg -> data -> label * (list output) * data * list (lb_name * lb_msg) ;
    lb_input_handlers : lb_name -> input -> data -> label * (list output) * data * list (lb_name * lb_msg)
  }.Definition unlabeled_net_handlers me src m st :=
let '(lb, out, st', ps) := lb_net_handlers me src m st in (out, st', ps).Definition unlabeled_input_handlers me inp st :=
let '(lb, out, st', ps) := lb_input_handlers me inp st in (out, st', ps).Global Instance unlabeled_multi_params : MultiParams base_params :=
  {
    name := lb_name ;
    msg := lb_msg ;
    msg_eq_dec := lb_msg_eq_dec ;
    name_eq_dec := lb_name_eq_dec ;
    nodes := lb_nodes ;
    all_names_nodes := lb_all_names_nodes ;
    no_dup_nodes := lb_no_dup_nodes ;
    init_handlers := lb_init_handlers;
    net_handlers := unlabeled_net_handlers ;
    input_handlers := unlabeled_input_handlers
  }.Definition lb_step_relation := A -> L -> A -> list trace -> Prop.Definition lb_step_ex (step : lb_step_relation) (l : L) (a : A) : Prop :=
  exists a' tr, step a l a' tr.Record event := { evt_a : A ; evt_l : L ; evt_trace : list trace }.Record event := { evt_a : A ; evt_l : L ; evt_trace : list trace }.Record event := { evt_a : A ; evt_l : L ; evt_trace : list trace }.Record event := { evt_a : A ; evt_l : L ; evt_trace : list trace }.Definition enabled (step : lb_step_relation) (l : L) (e : event) : Prop :=
    lb_step_ex step l (evt_a e).Definition occurred (l : L) (e : event) : Prop := l = evt_l e.Definition inf_enabled (step : lb_step_relation) (l : L) (s : infseq event) : Prop :=
    inf_often (now (enabled step l)) s.Definition cont_enabled (step : lb_step_relation) (l : L) (s : infseq event) : Prop :=
    continuously (now (enabled step l)) s.Definition inf_occurred (l : L) (s : infseq event) : Prop :=
    inf_often (now (occurred l)) s.Definition strong_fairness (step : lb_step_relation) (silent : L) (s : infseq event) : Prop :=
    forall l : L, l <> silent -> inf_enabled step l s -> inf_occurred l s.Definition weak_fairness (step : lb_step_relation) (silent : L) (s : infseq event) : Prop :=
    forall l : L, l <> silent -> cont_enabled step l s -> inf_occurred l s.

Lemma strong_fairness_weak : forall step silent s, strong_fairness step silent s -> weak_fairness step silent s.