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Fairis
Commits
63c020e4
Commit
63c020e4
authored
Feb 02, 2016
by
Robbert Krebbers
Browse files
More consistent naming for frame preserving updates.
parent
9d629ec8
Changes
2
Hide whitespace changes
Inline
Side-by-side
modures/cmra.v
View file @
63c020e4
...
...
@@ -318,17 +318,17 @@ Proof.
*
by
intros
Hx
z
?
;
exists
y
;
split
;
[
done
|
apply
(
Hx
z
)].
*
by
intros
Hx
z
n
?
;
destruct
(
Hx
z
n
)
as
(
?&<-&?
).
Qed
.
Lemma
ra_updateP_id
(
P
:
A
→
Prop
)
x
:
P
x
→
x
⇝
:
P
.
Lemma
cm
ra_updateP_id
(
P
:
A
→
Prop
)
x
:
P
x
→
x
⇝
:
P
.
Proof
.
by
intros
?
z
n
?
;
exists
x
.
Qed
.
Lemma
ra_updateP_compose
(
P
Q
:
A
→
Prop
)
x
:
Lemma
cm
ra_updateP_compose
(
P
Q
:
A
→
Prop
)
x
:
x
⇝
:
P
→
(
∀
y
,
P
y
→
y
⇝
:
Q
)
→
x
⇝
:
Q
.
Proof
.
intros
Hx
Hy
z
n
?
.
destruct
(
Hx
z
n
)
as
(
y
&?&?
);
auto
.
by
apply
(
Hy
y
).
Qed
.
Lemma
ra_updateP_weaken
(
P
Q
:
A
→
Prop
)
x
:
x
⇝
:
P
→
(
∀
y
,
P
y
→
Q
y
)
→
x
⇝
:
Q
.
Proof
.
eauto
using
ra_updateP_compose
,
ra_updateP_id
.
Qed
.
Lemma
cm
ra_updateP_weaken
(
P
Q
:
A
→
Prop
)
x
:
x
⇝
:
P
→
(
∀
y
,
P
y
→
Q
y
)
→
x
⇝
:
Q
.
Proof
.
eauto
using
cm
ra_updateP_compose
,
cm
ra_updateP_id
.
Qed
.
Lemma
ra_updateP_op
(
P1
P2
Q
:
A
→
Prop
)
x1
x2
:
Lemma
cm
ra_updateP_op
(
P1
P2
Q
:
A
→
Prop
)
x1
x2
:
x1
⇝
:
P1
→
x2
⇝
:
P2
→
(
∀
y1
y2
,
P1
y1
→
P2
y2
→
Q
(
y1
⋅
y2
))
→
x1
⋅
x2
⇝
:
Q
.
Proof
.
intros
Hx1
Hx2
Hy
z
n
?
.
...
...
@@ -337,9 +337,12 @@ Proof.
first
by
rewrite
associative
(
commutative
_
x2
)
-
associative
.
exists
(
y1
⋅
y2
);
split
;
last
rewrite
(
commutative
_
y1
)
-
associative
;
auto
.
Qed
.
Lemma
ra_update_op
x1
x2
y1
y2
:
x1
⇝
y1
→
x2
⇝
y2
→
x1
⋅
x2
⇝
y1
⋅
y2
.
Lemma
cmra_updateP_op
'
(
P1
P2
:
A
→
Prop
)
x1
x2
:
x1
⇝
:
P1
→
x2
⇝
:
P2
→
x1
⋅
x2
⇝
:
λ
y
,
∃
y1
y2
,
y
=
y1
⋅
y2
∧
P1
y1
∧
P2
y2
.
Proof
.
eauto
10
using
cmra_updateP_op
.
Qed
.
Lemma
cmra_update_op
x1
x2
y1
y2
:
x1
⇝
y1
→
x2
⇝
y2
→
x1
⋅
x2
⇝
y1
⋅
y2
.
Proof
.
rewrite
!
cmra_update_updateP
;
eauto
using
ra_updateP_op
with
congruence
.
rewrite
!
cmra_update_updateP
;
eauto
using
cm
ra_updateP_op
with
congruence
.
Qed
.
End
cmra
.
...
...
@@ -487,13 +490,16 @@ Section prod.
Qed
.
Lemma
prod_update
x
y
:
x
.1
⇝
y
.1
→
x
.2
⇝
y
.2
→
x
⇝
y
.
Proof
.
intros
??
z
n
[
??
];
split
;
simpl
in
*
;
auto
.
Qed
.
Lemma
prod_updateP
(
P
:
A
*
B
→
Prop
)
P1
P2
x
:
x
.1
⇝
:
P1
→
x
.2
⇝
:
P2
→
(
∀
a
b
,
P1
a
→
P2
b
→
P
(
a
,
b
))
→
x
⇝
:
P
.
Lemma
prod_updateP
P
1
P2
(
Q
:
A
*
B
→
Prop
)
x
:
x
.1
⇝
:
P1
→
x
.2
⇝
:
P2
→
(
∀
a
b
,
P1
a
→
P2
b
→
Q
(
a
,
b
))
→
x
⇝
:
Q
.
Proof
.
intros
Hx1
Hx2
HP
z
n
[
??
];
simpl
in
*
.
destruct
(
Hx1
(
z
.1
)
n
)
as
(
a
&?&?
),
(
Hx2
(
z
.2
)
n
)
as
(
b
&?&?
);
auto
.
exists
(
a
,
b
);
repeat
split
;
auto
.
Qed
.
Lemma
prod_updateP
'
P1
P2
x
:
x
.1
⇝
:
P1
→
x
.2
⇝
:
P2
→
x
⇝
:
λ
y
,
P1
(
y
.1
)
∧
P2
(
y
.2
).
Proof
.
eauto
using
prod_updateP
.
Qed
.
End
prod
.
Arguments
prodRA
:
clear
implicits
.
...
...
modures/option.v
View file @
63c020e4
...
...
@@ -147,10 +147,12 @@ Proof.
destruct
(
Hx
(
unit
x
)
n
)
as
(
y
'
&?&?
);
rewrite
?
cmra_unit_r
;
auto
.
by
exists
(
Some
y
'
);
split
;
[
auto
|
apply
cmra_validN_op_l
with
(
unit
x
)].
Qed
.
Lemma
option_updateP
'
(
P
:
A
→
Prop
)
x
:
x
⇝
:
P
→
Some
x
⇝
:
λ
y
,
default
False
y
P
.
Proof
.
eauto
using
option_updateP
.
Qed
.
Lemma
option_update
x
y
:
x
⇝
y
→
Some
x
⇝
Some
y
.
Proof
.
intros
;
apply
cmra_update_updateP
,
(
option_updateP
(
y
=
));
[
|
naive_solver
].
by
apply
cmra_update_updateP
.
rewrite
!
cmra_update_updateP
;
eauto
using
option_updateP
with
congruence
.
Qed
.
End
cmra
.
...
...
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