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George Pirlea
Iris
Commits
11eacd8b
Commit
11eacd8b
authored
May 23, 2018
by
Robbert Krebbers
Browse files
A stronger version of `cinv_open`.
This version allows one to either close or cancel the invariant after opening it.
parent
b043f3a3
Changes
1
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Inline
Side-by-side
theories/base_logic/lib/cancelable_invariants.v
View file @
11eacd8b
...
...
@@ -70,6 +70,21 @@ Section proofs.
iIntros
"!>"
.
iExists
P
.
iSplit
;
last
done
.
iIntros
"!# !>"
;
iSplit
;
auto
.
Qed
.
Lemma
cinv_open_strong
E
N
γ
p
P
:
↑
N
⊆
E
→
cinv
N
γ
P
-
∗
cinv_own
γ
p
={
E
,
E
∖↑
N
}=
∗
▷
P
∗
cinv_own
γ
p
∗
(
▷
P
∨
cinv_own
γ
1
={
E
∖↑
N
,
E
}=
∗
True
).
Proof
.
iIntros
(?)
"#Hinv Hγ"
.
iDestruct
"Hinv"
as
(
P'
)
"[#HP' Hinv]"
.
iInv
N
as
"[HP | >Hγ']"
"Hclose"
.
-
iIntros
"!> {$Hγ}"
.
iSplitL
"HP"
.
+
iNext
.
iApply
"HP'"
.
done
.
+
iIntros
"[HP|Hγ]"
.
*
iApply
"Hclose"
.
iLeft
.
iNext
.
by
iApply
"HP'"
.
*
iApply
"Hclose"
.
iRight
.
by
iNext
.
-
iDestruct
(
cinv_own_1_l
with
"Hγ' Hγ"
)
as
%[].
Qed
.
Lemma
cinv_alloc
E
N
P
:
▷
P
={
E
}=
∗
∃
γ
,
cinv
N
γ
P
∗
cinv_own
γ
1
.
Proof
.
iIntros
"HP"
.
iMod
(
cinv_alloc_strong
∅
E
N
)
as
(
γ
_
)
"[Hγ Halloc]"
.
...
...
@@ -78,23 +93,18 @@ Section proofs.
Lemma
cinv_cancel
E
N
γ
P
:
↑
N
⊆
E
→
cinv
N
γ
P
-
∗
cinv_own
γ
1
={
E
}=
∗
▷
P
.
Proof
.
iIntros
(?)
"#Hinv Hγ"
.
iDestruct
"Hinv"
as
(
P'
)
"[#HP' Hinv]"
.
iInv
N
as
"[HP|>Hγ']"
"Hclose"
.
-
iMod
(
"Hclose"
with
"[Hγ]"
)
as
"_"
;
first
by
eauto
.
iModIntro
.
iNext
.
iApply
"HP'"
.
done
.
-
iDestruct
(
cinv_own_1_l
with
"Hγ Hγ'"
)
as
%[].
iIntros
(?)
"#Hinv Hγ"
.
iMod
(
cinv_open_strong
with
"Hinv Hγ"
)
as
"($ & Hγ & H)"
;
first
done
.
iApply
"H"
.
by
iRight
.
Qed
.
Lemma
cinv_open
E
N
γ
p
P
:
↑
N
⊆
E
→
cinv
N
γ
P
-
∗
cinv_own
γ
p
={
E
,
E
∖↑
N
}=
∗
▷
P
∗
cinv_own
γ
p
∗
(
▷
P
={
E
∖↑
N
,
E
}=
∗
True
).
Proof
.
iIntros
(?)
"#Hinv Hγ"
.
iDestruct
"Hinv"
as
(
P'
)
"[#HP' Hinv]"
.
iInv
N
as
"[HP | >Hγ']"
"Hclose"
.
-
iIntros
"!> {$Hγ}"
.
iSplitL
"HP"
.
+
iNext
.
iApply
"HP'"
.
done
.
+
iIntros
"HP"
.
iApply
"Hclose"
.
iLeft
.
iNext
.
by
iApply
"HP'"
.
-
iDestruct
(
cinv_own_1_l
with
"Hγ' Hγ"
)
as
%[].
iIntros
(?)
"#Hinv Hγ"
.
iMod
(
cinv_open_strong
with
"Hinv Hγ"
)
as
"($ & $ & H)"
;
first
done
.
iIntros
"!> HP"
.
iApply
"H"
;
auto
.
Qed
.
End
proofs
.
...
...
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