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Gaëtan Gilbert
Iris
Commits
88c7fc6d
Commit
88c7fc6d
authored
5 years ago
by
Ralf Jung
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fix metatheory
parent
d903a458
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theories/heap_lang/metatheory.v
+8
-8
8 additions, 8 deletions
theories/heap_lang/metatheory.v
with
8 additions
and
8 deletions
theories/heap_lang/metatheory.v
+
8
−
8
View file @
88c7fc6d
...
...
@@ -99,23 +99,23 @@ Lemma heap_closed_alloc σ l n w :
map_Forall
(
λ
_
v
,
is_closed_val
v
)
(
heap
σ
)
→
(
∀
i
:
Z
,
0
≤
i
→
i
<
n
→
heap
σ
!!
(
l
+
ₗ
i
)
=
None
)
→
map_Forall
(
λ
_
v
,
is_closed_val
v
)
(
heap
σ
∪
heap
_array
l
(
replicate
(
Z
.
to_nat
n
)
w
))
.
(
heap_array
l
(
replicate
(
Z
.
to_nat
n
)
w
)
∪
heap
σ
)
.
Proof
.
intros
Hn
Hw
Hσ
Hl
.
eapply
(
map_Forall_ind
(
λ
k
v
,
((
heap
σ
∪
heap
_array
l
(
replicate
(
Z
.
to_nat
n
)
w
))
(
λ
k
v
,
((
heap_array
l
(
replicate
(
Z
.
to_nat
n
)
w
)
∪
heap
σ
)
!!
k
=
Some
v
)))
.
-
apply
map_Forall_empty
.
-
intros
m
i
x
Hi
Hix
Hkwm
Hm
.
apply
map_Forall_insert_2
;
auto
.
apply
lookup_union_Some
in
Hix
;
last
first
.
{
symmetry
;
eapply
heap_array_map_disjoint
;
{
eapply
heap_array_map_disjoint
;
rewrite
replicate_length
Z2Nat
.
id
;
auto
with
lia
.
}
destruct
Hix
as
[
[
j
Hj
]
%
elem_of_map_to_list
%
elem_of_list
_lookup
_1
|
(?
&
?
&
?
&
[
->
Hlt
%
inj_lt
]
%
lookup_replicate_1
)
%
heap_array
_lookup
]
.
{
apply
map_Forall_to_list
in
Hσ
.
by
e
apply
Forall_
lookup
in
Hσ
;
eauto
;
simpl
in
*.
}
rewrite
!
Z2Nat
.
id
in
H
lt
;
eauto
with
lia
.
destruct
Hix
as
[
(?
&
?
&
?
&
[
->
Hlt
%
inj_lt
]
%
lookup_replicate_1
)
%
heap_array
_lookup
|
[
j
Hj
]
%
elem_of_map_to_list
%
elem_of_list
_lookup
_1
]
.
+
rewrite
!
Z2Nat
.
id
in
Hlt
;
eauto
with
lia
.
+
apply
map_
Forall_
to_list
in
Hσ
.
by
eapply
Forall_lookup
in
H
σ
;
eauto
;
simpl
in
*
.
-
apply
map_Forall_to_list
,
Forall_forall
.
intros
[?
?];
apply
elem_of_map_to_list
.
Qed
.
...
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