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da3aa7e4
Commit
da3aa7e4
authored
Jan 23, 2017
by
Jacques-Henri Jourdan
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Prove slice_iff.
parent
e0a45a07
Pipeline
#3754
passed with stage
in 11 minutes and 47 seconds
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theories/base_logic/lib/boxes.v
theories/base_logic/lib/boxes.v
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theories/base_logic/lib/boxes.v
View file @
da3aa7e4
...
...
@@ -239,6 +239,24 @@ Proof.
-
iExists
Φ
;
iSplit
;
by
rewrite
big_sepM_fmap
.
Qed
.
Lemma
slice_iff
E
q
f
P
Q
Q'
γ
b
:
↑
N
⊆
E
→
f
!!
γ
=
Some
b
→
▷
□
(
Q
↔
Q'
)
-
∗
slice
N
γ
Q
-
∗
▷
?q
box
N
f
P
={
E
}=
∗
∃
γ
'
P'
,
⌜
delete
γ
f
!!
γ
'
=
None
⌝
∗
▷
?q
▷
□
(
P
↔
P'
)
∗
slice
N
γ
'
Q'
∗
▷
?q
box
N
(<[
γ
'
:
=
b
]>(
delete
γ
f
))
P'
.
Proof
.
iIntros
(??)
"#HQQ' #Hs Hb"
.
destruct
b
.
-
iMod
(
slice_delete_full
with
"Hs Hb"
)
as
(
P'
)
"(HQ & Heq & Hb)"
;
try
done
.
iDestruct
(
"HQQ'"
with
"HQ"
)
as
"HQ'"
.
iMod
(
slice_insert_full
with
"HQ' Hb"
)
as
(
γ
'
)
"(% & #Hs' & Hb)"
;
try
done
.
iExists
γ
'
,
_
.
iFrame
"∗#%"
.
iIntros
"!>"
.
do
2
iNext
.
iRewrite
"Heq"
.
iAlways
.
by
iSplit
;
iIntros
"[? $]"
;
iApply
"HQQ'"
.
-
iMod
(
slice_delete_empty
with
"Hs Hb"
)
as
(
P'
)
"(Heq & Hb)"
;
try
done
.
iMod
(
slice_insert_empty
with
"Hb"
)
as
(
γ
'
)
"(% & #Hs' & Hb)"
;
try
done
.
iExists
γ
'
,
_
.
iFrame
"∗#%"
.
iIntros
"!>"
.
do
2
iNext
.
iRewrite
"Heq"
.
iAlways
.
by
iSplit
;
iIntros
"[? $]"
;
iApply
"HQQ'"
.
Qed
.
Lemma
slice_split
E
q
f
P
Q1
Q2
γ
b
:
↑
N
⊆
E
→
f
!!
γ
=
Some
b
→
slice
N
γ
(
Q1
∗
Q2
)
-
∗
▷
?q
box
N
f
P
={
E
}=
∗
∃
γ
1
γ
2
,
...
...
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