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 vals_def_inject_getBlock j b2: forall vals1 vals2 (INJ: Val.inject_list j vals1 vals2) (DEF : vals_def vals1 = true) (GB: getBlocks vals2 b2 = true), exists b1 d, j b1 = Some(b2,d) /\ getBlocks vals1 b1 = true.