Section FixM.
Variable M : SBTM.
Notation X := 1.
Notation "⦇" := 2.
Notation "⦈" := 3.
Notation tt := 4.
Notation ff := 5.
Notation "!! b" := (if b then tt else ff) (at level 1).
Definition enc_state (q : Fin.t (S (num_states M))) := ((S ff) + proj1_sig (Fin.to_nat q)).
Notation "! p" := (enc_state p) (at level 1).
Fixpoint all_fins (n : nat) : list (Fin.t n) :=
match n with
| 0 => nil
| S n => Fin.F1 :: map Fin.FS (all_fins n)
end.

Lemma in_all_fins n i :
In i (all_fins n).