Section FixM.
Variable M : SBTM.
Notation END := 0.
Notation X := 1.
Notation "⦇" := 2.
Notation "⦈" := 3.
Notation tt := 4.
Notation ff := 5.
Notation "!! b" := (if b then tt else ff) (at level 1).
Notation "! p" := (@enc_state M p) (at level 1).

Lemma help_exists1 (P : state M -> tape -> option bool -> move -> Prop) :
(exists c q w m ls rs, P q (ls, c, rs) w m) ->  (exists q t w m, P q t w m).