Definition restrict_sm mu (X:block -> bool) :=
match mu with
  Build_SM_Injection locBSrc locBTgt pSrc pTgt local extBSrc extBTgt fSrc fTgt extern =>
  Build_SM_Injection locBSrc locBTgt pSrc pTgt (restrict local X)
                     extBSrc extBTgt fSrc fTgt (restrict extern X)
end.

Lemma restrict_sm_nest': forall mu X Y (HXY: forall b, Y b = true -> X b = true), restrict_sm (restrict_sm mu Y) X = restrict_sm mu Y.