Definition is_class_compatible (mu: moves) : Prop :=
  forall s d, In (s, d) mu -> regclass s = regclass d.

(* Specifications: *)
Lemma parmove_preserves_register_classes: forall mu, is_class_compatible mu -> is_class_compatible (parmove mu).
Lemma parmove_preserves_register_classes: forall mu, is_class_compatible mu -> is_class_compatible (parmove mu).