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efd340e5
Commit
efd340e5
authored
Feb 20, 2016
by
Ralf Jung
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provide tactics to more easily apply wands
parent
75aed833
Changes
3
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3 changed files
with
21 additions
and
6 deletions
+21
-6
algebra/upred.v
algebra/upred.v
+15
-0
program_logic/auth.v
program_logic/auth.v
+3
-3
program_logic/sts.v
program_logic/sts.v
+3
-3
No files found.
algebra/upred.v
View file @
efd340e5
...
...
@@ -623,6 +623,21 @@ Lemma wand_elim_l' P Q R : P ⊑ (Q -★ R) → (P ★ Q) ⊑ R.
Proof
.
intros
->
;
apply
wand_elim_l
.
Qed
.
Lemma
wand_elim_r'
P
Q
R
:
Q
⊑
(
P
-
★
R
)
→
(
P
★
Q
)
⊑
R
.
Proof
.
intros
->
;
apply
wand_elim_r
.
Qed
.
Lemma
wand_apply_l
P
Q
Q'
R
R'
:
P
⊑
(
Q'
-
★
R'
)
→
R'
⊑
R
→
Q
⊑
Q'
→
(
P
★
Q
)
⊑
R
.
Proof
.
intros
->
->
<-
;
apply
wand_elim_l
.
Qed
.
Lemma
wand_apply_r
P
Q
Q'
R
R'
:
P
⊑
(
Q'
-
★
R'
)
→
R'
⊑
R
→
Q
⊑
Q'
→
(
Q
★
P
)
⊑
R
.
Proof
.
intros
->
->
<-
;
apply
wand_elim_r
.
Qed
.
Lemma
wand_apply_l'
P
Q
Q'
R
:
P
⊑
(
Q'
-
★
R
)
→
Q
⊑
Q'
→
(
P
★
Q
)
⊑
R
.
Proof
.
intros
->
<-
;
apply
wand_elim_l
.
Qed
.
Lemma
wand_apply_r'
P
Q
Q'
R
:
P
⊑
(
Q'
-
★
R
)
→
Q
⊑
Q'
→
(
Q
★
P
)
⊑
R
.
Proof
.
intros
->
<-
;
apply
wand_elim_r
.
Qed
.
Lemma
wand_frame_l
P
Q
R
:
(
Q
-
★
R
)
⊑
(
P
★
Q
-
★
P
★
R
).
Proof
.
apply
wand_intro_l
.
rewrite
-
assoc
.
apply
sep_mono_r
,
wand_elim_r
.
Qed
.
Lemma
wand_frame_r
P
Q
R
:
(
Q
-
★
R
)
⊑
(
Q
★
P
-
★
R
★
P
).
Proof
.
apply
wand_intro_l
.
rewrite
![(
_
★
P
)%
I
]
comm
-
assoc
.
apply
sep_mono_r
,
wand_elim_r
.
Qed
.
Lemma
sep_and
P
Q
:
(
P
★
Q
)
⊑
(
P
∧
Q
).
Proof
.
auto
.
Qed
.
Lemma
impl_wand
P
Q
:
(
P
→
Q
)
⊑
(
P
-
★
Q
).
...
...
program_logic/auth.v
View file @
efd340e5
...
...
@@ -116,9 +116,9 @@ Section auth.
rewrite
(
auth_opened
(
E
∖
N
))
!
pvs_frame_r
!
sep_exist_r
.
apply
(
fsa_strip_pvs
fsa
).
apply
exist_elim
=>
a'
.
rewrite
(
forall_elim
a'
).
rewrite
[(
▷
_
★
_
)%
I
]
comm
.
(* Getting this wand eliminated is really annoying. *)
rewrite
[(
■
_
★
_
)%
I
]
comm
-!
assoc
[(
▷φ
_
★
_
★
_
)%
I
]
assoc
[(
▷φ
_
★
_
)%
I
]
comm
.
rewrite
wand_elim_r
fsa_frame_l
.
eapply
wand_apply_r
;
first
(
by
eapply
(
wand_frame_l
(
own
γ
_
)))
;
last
first
.
{
rewrite
assoc
[(
_
★
own
_
_
)%
I
]
comm
-
assoc
.
done
.
}
rewrite
fsa_frame_l
.
apply
(
fsa_mono_pvs
fsa
)=>
x
.
rewrite
sep_exist_l
;
apply
exist_elim
=>
L
.
rewrite
sep_exist_l
;
apply
exist_elim
=>
Lv
.
...
...
program_logic/sts.v
View file @
efd340e5
...
...
@@ -133,9 +133,9 @@ Section sts.
rewrite
(
sts_opened
(
E
∖
N
))
!
pvs_frame_r
!
sep_exist_r
.
apply
(
fsa_strip_pvs
fsa
).
apply
exist_elim
=>
s
.
rewrite
(
forall_elim
s
).
rewrite
[(
▷
_
★
_
)%
I
]
comm
.
(* Getting this wand eliminated is really annoying. *)
rewrite
[(
■
_
★
_
)%
I
]
comm
-!
assoc
[(
▷φ
_
★
_
★
_
)%
I
]
assoc
[(
▷φ
_
★
_
)%
I
]
comm
.
rewrite
wand_elim_r
fsa_frame_l
.
eapply
wand_apply_r
;
first
(
by
eapply
(
wand_frame_l
(
own
γ
_
)))
;
last
first
.
{
rewrite
assoc
[(
_
★
own
_
_
)%
I
]
comm
-
assoc
.
done
.
}
rewrite
fsa_frame_l
.
apply
(
fsa_mono_pvs
fsa
)=>
x
.
rewrite
sep_exist_l
;
apply
exist_elim
=>
s'
.
rewrite
sep_exist_l
;
apply
exist_elim
=>
T'
.
...
...
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