(*The join of all four components - useful for stating
  match_state conditions*)
Definition as_inj (mu: SM_Injection) : meminj :=
  join (extern_of mu) (local_of mu).

Lemma as_inj_DomRng: forall mu b1 b2 d, as_inj mu b1 = Some(b2, d) -> SM_wd mu -> DomSrc mu b1 = true /\ DomTgt mu b2 = true.