(*The join of all four components - useful for stating match_state conditions*)
Definition as_inj (mu: SM_Injection) : meminj :=
join (extern_of mu) (local_of mu).

Lemma priv_locBlocks: forall mu (WD:SM_wd mu)
b1 b2 z (L: priv_of mu b1 = Some(b2,z)),
pubBlocksSrc mu b1 = false /\
locBlocksSrc mu b1 = true /\ locBlocksTgt mu b2 = true /\
extBlocksSrc mu b1 = false /\ extBlocksTgt mu b2 = false /\
frgnBlocksSrc mu b1 = false /\ frgnBlocksTgt mu b2 = false /\
DomSrc mu b1 = true /\ DomTgt mu b2 = true.