Definition replace_externs (mu:SM_Injection) fSrc' fTgt': SM_Injection :=
  match mu with
    Build_SM_Injection locBSrc locBTgt pSrc pTgt local extBSrc extBTgt fSrc fTgt extern =>
    Build_SM_Injection locBSrc locBTgt pSrc pTgt local extBSrc extBTgt fSrc' fTgt' extern
  end.

Lemma replace_externs_local: forall mu frgSrc' frgTgt', local_of (replace_externs mu frgSrc' frgTgt') = local_of mu.