(** We define the ``adherence'' of the problem [mu] as the set of
  registers that partially overlap with one of the registers
  possibly assigned by the parallel move: destinations and temporaries.
  Again, we define the complement of the ``adherence'' set, which is
  more convenient for Coq reasoning. *)

Definition no_adherence (r: reg) : Prop :=
  forall x, In x (dests mu) \/ is_temp x -> no_overlap x r.

Lemma no_overlap_pairwise: forall r1 r2 m, pairwise_disjoint m -> In r1 m -> In r2 m -> no_overlap r1 r2.