(** Orders *)

Inductive f2b_index : Type :=
  | F2BI_before (n: nat)
  | F2BI_after (n: nat).(** Orders *)

Inductive f2b_index : Type :=
  | F2BI_before (n: nat)
  | F2BI_after (n: nat).(** Orders *)

Inductive f2b_index : Type :=
  | F2BI_before (n: nat)
  | F2BI_after (n: nat).Inductive f2b_order: f2b_index -> f2b_index -> Prop :=
  | f2b_order_before: forall n n',
      (n' < n)%nat ->
      f2b_order (F2BI_before n') (F2BI_before n)
  | f2b_order_after: forall n n',
      (n' < n)%nat ->
      f2b_order (F2BI_after n') (F2BI_after n)
  | f2b_order_switch: forall n n',
      f2b_order (F2BI_before n') (F2BI_after n).Inductive f2b_order: f2b_index -> f2b_index -> Prop :=
  | f2b_order_before: forall n n',
      (n' < n)%nat ->
      f2b_order (F2BI_before n') (F2BI_before n)
  | f2b_order_after: forall n n',
      (n' < n)%nat ->
      f2b_order (F2BI_after n') (F2BI_after n)
  | f2b_order_switch: forall n n',
      f2b_order (F2BI_before n') (F2BI_after n).Inductive f2b_order: f2b_index -> f2b_index -> Prop :=
  | f2b_order_before: forall n n',
      (n' < n)%nat ->
      f2b_order (F2BI_before n') (F2BI_before n)
  | f2b_order_after: forall n n',
      (n' < n)%nat ->
      f2b_order (F2BI_after n') (F2BI_after n)
  | f2b_order_switch: forall n n',
      f2b_order (F2BI_before n') (F2BI_after n).Inductive f2b_order: f2b_index -> f2b_index -> Prop :=
  | f2b_order_before: forall n n',
      (n' < n)%nat ->
      f2b_order (F2BI_before n') (F2BI_before n)
  | f2b_order_after: forall n n',
      (n' < n)%nat ->
      f2b_order (F2BI_after n') (F2BI_after n)
  | f2b_order_switch: forall n n',
      f2b_order (F2BI_before n') (F2BI_after n).

Lemma wf_f2b_order: well_founded f2b_order.