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Rice Wine
Iris
Commits
1edf71ef
Commit
1edf71ef
authored
Apr 11, 2017
by
Ralf Jung
Browse files
close cancellable invariants under logical biimplication
parent
35551d40
Changes
1
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Inline
Side-by-side
theories/base_logic/lib/cancelable_invariants.v
View file @
1edf71ef
...
...
@@ -16,11 +16,10 @@ Section defs.
Definition
cinv_own
(
γ
:
gname
)
(
p
:
frac
)
:
iProp
Σ
:
=
own
γ
p
.
Definition
cinv
(
N
:
namespace
)
(
γ
:
gname
)
(
P
:
iProp
Σ
)
:
iProp
Σ
:
=
inv
N
(
P
∨
cinv_own
γ
1
%
Qp
)%
I
.
(
∃
P'
,
□
▷
(
P
↔
P'
)
∗
inv
N
(
P
'
∨
cinv_own
γ
1
%
Qp
)
)
%
I
.
End
defs
.
Instance
:
Params
(@
cinv
)
5
.
Typeclasses
Opaque
cinv_own
cinv
.
Section
proofs
.
Context
`
{
invG
Σ
,
cinvG
Σ
}.
...
...
@@ -53,27 +52,43 @@ Section proofs.
iDestruct
(
cinv_own_valid
with
"H1 H2"
)
as
%[]%(
exclusive_l
1
%
Qp
).
Qed
.
Lemma
cinv_iff
N
γ
P
P'
:
▷
□
(
P
↔
P'
)
-
∗
cinv
N
γ
P
-
∗
cinv
N
γ
P'
.
Proof
.
iIntros
"#HP' Hinv"
.
iDestruct
"Hinv"
as
(
P''
)
"[#HP'' Hinv]"
.
iExists
_
.
iFrame
"Hinv"
.
iNext
.
iAlways
.
iSplit
.
-
iIntros
"?"
.
iApply
"HP''"
.
iApply
"HP'"
.
done
.
-
iIntros
"?"
.
iApply
"HP'"
.
iApply
"HP''"
.
done
.
Qed
.
Lemma
cinv_alloc
E
N
P
:
▷
P
={
E
}=
∗
∃
γ
,
cinv
N
γ
P
∗
cinv_own
γ
1
.
Proof
.
rewrite
/
cinv
/
cinv_own
.
iIntros
"HP"
.
iIntros
"HP"
.
iMod
(
own_alloc
1
%
Qp
)
as
(
γ
)
"H1"
;
first
done
.
iMod
(
inv_alloc
N
_
(
P
∨
own
γ
1
%
Qp
)%
I
with
"[HP]"
)
;
eauto
.
iMod
(
inv_alloc
N
_
(
P
∨
own
γ
1
%
Qp
)%
I
with
"[HP]"
)
;
first
by
eauto
.
iExists
_
.
iFrame
.
iExists
_
.
iFrame
.
iIntros
"!> !# !>"
.
iSplit
;
by
iIntros
"?"
.
Qed
.
Lemma
cinv_cancel
E
N
γ
P
:
↑
N
⊆
E
→
cinv
N
γ
P
-
∗
cinv_own
γ
1
={
E
}=
∗
▷
P
.
Proof
.
rewrite
/
cinv
.
iIntros
(?)
"#Hinv Hγ"
.
iInv
N
as
"[$|>Hγ']"
"Hclose"
;
first
iApply
"Hclose"
;
eauto
.
iDestruct
(
cinv_own_1_l
with
"Hγ Hγ'"
)
as
%[].
iIntros
(?)
"#Hinv Hγ"
.
iDestruct
"Hinv"
as
(
P'
)
"[#HP' Hinv]"
.
iInv
N
as
"[HP|>Hγ']"
"Hclose"
.
-
iMod
(
"Hclose"
with
"[Hγ]"
)
as
"_"
;
first
by
eauto
.
iModIntro
.
iNext
.
iApply
"HP'"
.
done
.
-
iDestruct
(
cinv_own_1_l
with
"Hγ Hγ'"
)
as
%[].
Qed
.
Lemma
cinv_open
E
N
γ
p
P
:
↑
N
⊆
E
→
cinv
N
γ
P
-
∗
cinv_own
γ
p
={
E
,
E
∖↑
N
}=
∗
▷
P
∗
cinv_own
γ
p
∗
(
▷
P
={
E
∖↑
N
,
E
}=
∗
True
).
Proof
.
rewrite
/
cinv
.
iIntros
(?)
"#Hinv Hγ"
.
iInv
N
as
"[$ | >Hγ']"
"Hclose"
.
-
iIntros
"!> {$Hγ} HP"
.
iApply
"Hclose"
;
eauto
.
iIntros
(?)
"#Hinv Hγ"
.
iDestruct
"Hinv"
as
(
P'
)
"[#HP' Hinv]"
.
iInv
N
as
"[HP | >Hγ']"
"Hclose"
.
-
iIntros
"!> {$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
%[].
Qed
.
End
proofs
.
Typeclasses
Opaque
cinv_own
cinv
.
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