Inductive match_freelists (j:meminj): list (block * Z * Z) -> list (block * Z * Z) -> Prop :=
match_freelists_nil: match_freelists j nil nil
| match_freelists_cons: forall b1 lo1 hi1 t1 b2 lo2 hi2 t2 delta,
j b1 = Some (b2,delta) ->
lo2 = lo1+delta -> hi2 = hi1+delta ->
match_freelists j t1 t2 ->
match_freelists j ((b1,lo1,hi1)::t1) ((b2,lo2,hi2)::t2).

Lemma replace_externs_meminj_preserves_globals_as_inj:
forall {F V} (ge: Genv.t F V) nu (WDnu: SM_wd nu)
(PG: meminj_preserves_globals ge (as_inj nu) /\
(forall b, isGlobalBlock ge b = true -> frgnBlocksSrc nu b = true))
mu  fSrc fTgt (Hyp: mu = replace_externs nu fSrc fTgt)
(WDmu: SM_wd mu)
(FRG: forall b, frgnBlocksSrc nu b = true -> fSrc b = true),
meminj_preserves_globals ge (as_inj mu) /\
(forall b, isGlobalBlock ge b = true -> frgnBlocksSrc mu b = true).