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 FreeEffect_PropagateLeft: forall
m sp lo hi m'
(FREE : Mem.free m sp lo hi = Some m')
mu m2 (SMV : sm_valid mu m m2)
(WD: SM_wd mu) spb'
(AI: as_inj mu sp = Some (spb', 0))
(VIS : vis mu sp = true) b2 ofs
(EFF : FreeEffect m2 lo hi spb' b2 ofs = true)
(LB: locBlocksTgt mu b2 = false),
exists b1 delta,
foreign_of mu b1 = Some (b2, delta) /\
FreeEffect m lo hi sp b1 (ofs - delta) = true /\
Mem.perm m b1 (ofs - delta) Max Nonempty.