Definition mkinitial_SM (mu: SM_Injection) frgnS frgnT :=
  match mu with
  Build_SM_Injection locBSrc locBTgt pSrc pTgt local extBSrc extBTgt fSrc fTgt extern =>
  Build_SM_Injection (fun b => false) (fun b => false) (fun b => false) (fun b => false) (fun b => None)
                     (DomSrc mu) (DomTgt mu) frgnS frgnT (as_inj mu)
  end.

Lemma local_of_vis mu: forall b1 b2 d (LOC: local_of mu b1 = Some (b2,d)) (WD: SM_wd mu), vis mu b1 = true.