Inductive structured_match_callstack mu (m: mem) (tm: mem):
callstack -> Values.block -> Values.block -> Prop :=
| st_mcs_nil:
forall hi bound tbound,
match_globalenvs prog (restrict (as_inj mu) (vis mu)) hi ->
Ple hi bound -> Ple hi tbound ->
structured_match_callstack mu m tm nil bound tbound
| st_mcs_cons:
forall cenv tf e le te sp lo hi cs bound tbound
(BOUND: Ple hi bound)
(TBOUND: Plt sp tbound)
(MTMP: match_temps (restrict (as_inj mu) (vis mu)) le te)
(MENV: match_env (restrict (as_inj mu) (vis mu)) cenv e sp lo hi)
(BOUND: match_bounds e m)
(PERM: padding_freeable (restrict (as_inj mu) (vis mu)) e tm sp tf.(fn_stackspace))
(SPlocal: locBlocksTgt mu sp = true) (*NEW*)
(*LENB: Here is the condition me_incr from match_env above, but we assert it on the entire as_inj mu*)
(ME_INCR: forall b tb delta,
(as_inj mu) b = Some(tb, delta) -> Plt b lo -> Plt tb sp)
(MCS: structured_match_callstack mu m tm cs lo sp),
structured_match_callstack mu m tm (Frame cenv tf e le te sp lo hi :: cs) bound tbound.

Lemma replace_locals_extern_incr_vis: forall mu nu pubS pubT
(Hnu: nu = replace_locals mu pubS pubT)
nu' (INC : extern_incr nu nu') (WDnu' : SM_wd nu') l m1'
b (VIS: vis mu b = true),
locBlocksSrc nu' b || DomSrc nu' b &&
(negb (locBlocksSrc nu' b) && REACH m1' (exportedSrc nu' l) b) = true.