Definition FLIP mu :=
  match mu with
    Build_SM_Injection locBSrc locBTgt pSrc pTgt local extBSrc extBTgt fSrc fTgt extern =>
    Build_SM_Injection extBSrc extBTgt fSrc fTgt extern locBSrc locBTgt pSrc pTgt local
  end.

Lemma FLIPlocal: forall mu, local_of (FLIP mu) = extern_of mu.