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 X) Y = restrict_sm mu Y.