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Iris
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b00233e4
Commit
b00233e4
authored
Feb 17, 2016
by
Ralf Jung
Browse files
sts_ownS_op: fix stupid typo
parent
fa9570a8
Changes
2
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Inline
Side-by-side
algebra/sts.v
View file @
b00233e4
...
...
@@ -333,7 +333,7 @@ Lemma sts_op_auth_frag_up s T :
Proof
.
intros
;
apply
sts_op_auth_frag
;
auto
using
elem_of_up
,
closed_up
.
Qed
.
Lemma
sts_op_frag
S1
S2
T1
T2
:
T1
∪
T2
⊆
∅
→
sts
.
closed
S1
T1
→
sts
.
closed
S2
T2
→
T1
∩
T2
⊆
∅
→
sts
.
closed
S1
T1
→
sts
.
closed
S2
T2
→
sts_frag
(
S1
∩
S2
)
(
T1
∪
T2
)
≡
sts_frag
S1
T1
⋅
sts_frag
S2
T2
.
Proof
.
intros
HT
HS1
HS2
.
rewrite
/
sts_frag
.
...
...
program_logic/sts.v
View file @
b00233e4
...
...
@@ -53,18 +53,19 @@ Section sts.
(* The same rule as implication does *not* hold, as could be shown using
sts_frag_included. *)
Lemma
sts_ownS_weaken
E
γ
S1
S2
T
:
S1
⊆
S2
→
sts
.
closed
S2
T
→
sts_ownS
γ
S1
T
⊑
pvs
E
E
(
sts_ownS
γ
S2
T
).
Proof
.
intros
.
by
apply
own_update
,
sts_update_frag
.
Qed
.
Lemma
sts_ownS_weaken
E
γ
S1
S2
T
1
T2
:
T1
≡
T2
→
S1
⊆
S2
→
sts
.
closed
S2
T
2
→
sts_ownS
γ
S1
T
1
⊑
pvs
E
E
(
sts_ownS
γ
S2
T
2
).
Proof
.
intros
->
?
?
.
by
apply
own_update
,
sts_update_frag
.
Qed
.
Lemma
sts_own_weaken
E
γ
s
S
T
:
s
∈
S
→
sts
.
closed
S
T
→
sts_own
γ
s
T
⊑
pvs
E
E
(
sts_ownS
γ
S
T
).
Proof
.
intros
.
by
apply
own_update
,
sts_update_frag_up
.
Qed
.
Lemma
sts_own_weaken
E
γ
s
S
T1
T2
:
T1
≡
T2
→
s
∈
S
→
sts
.
closed
S
T2
→
sts_own
γ
s
T1
⊑
pvs
E
E
(
sts_ownS
γ
S
T2
).
(* FIXME for some reason, using "->" instead of "<-" does not work? *)
Proof
.
intros
<-
?
?.
by
apply
own_update
,
sts_update_frag_up
.
Qed
.
Lemma
sts_ownS_op
γ
S1
S2
T1
T2
:
T1
∪
T2
⊆
∅
→
sts
.
closed
S1
T1
→
sts
.
closed
S2
T2
→
T1
∩
T2
⊆
∅
→
sts
.
closed
S1
T1
→
sts
.
closed
S2
T2
→
sts_ownS
γ
(
S1
∩
S2
)
(
T1
∪
T2
)
≡
(
sts_ownS
γ
S1
T1
★
sts_ownS
γ
S2
T2
)%
I
.
Proof
.
intros
.
by
rewrite
/
sts_ownS
-
own_op
sts_op_frag
.
Qed
.
...
...
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