(** 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).

Lemma wf_f2b_order:
well_founded f2b_order.