Section PROPERTIES.
Variable initial_move: moves.
Inductive wf_move: reg -> reg -> Prop :=
| wf_move_same: forall s d,
In (s, d) initial_move -> wf_move s d
| wf_move_temp_left: forall s d,
wf_move s d -> wf_move (temp s) d
| wf_move_temp_right: forall s d,
wf_move s d -> wf_move s (temp s).
Definition wf_moves (m: moves) : Prop :=
forall s d, In (s, d) m -> wf_move s d.
Hint Rewrite wf_moves_cons wf_moves_append: pmov.
Inductive wf_state: state -> Prop :=
| wf_state_intro: forall mu sigma tau,
wf_moves mu -> wf_moves sigma -> wf_moves tau ->
wf_state (State mu sigma tau).
End PROPERTIES.

Lemma parmove_wf_moves:
forall mu, wf_moves mu (parmove mu).