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2ac324bd
Commit
2ac324bd
authored
Jan 14, 2016
by
Robbert Krebbers
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Plain Diff
Remove useless notion ValidTimeless.
parent
b853c0af
Changes
6
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6 changed files
with
7 additions
and
51 deletions
+7
-51
modures/auth.v
modures/auth.v
+0
-8
modures/cmra.v
modures/cmra.v
+0
-12
modures/excl.v
modures/excl.v
+0
-2
modures/fin_maps.v
modures/fin_maps.v
+0
-19
modures/logic.v
modures/logic.v
+7
-4
modures/option.v
modures/option.v
+0
-6
No files found.
modures/auth.v
View file @
2ac324bd
...
...
@@ -134,14 +134,6 @@ Proof.
split
;
simpl
;
[
apply
ra_empty_valid
|].
by
intros
x
;
constructor
;
simpl
;
rewrite
(
left_id
_
_
).
Qed
.
Global
Instance
auth_frag_valid_timeless
(
x
:
A
)
:
ValidTimeless
x
→
ValidTimeless
(
◯
x
).
Proof
.
by
intros
??
;
apply
(
valid_timeless
x
).
Qed
.
Global
Instance
auth_valid_timeless
`
{
Empty
A
,
!
RAIdentity
A
}
(
x
:
A
)
:
ValidTimeless
x
→
ValidTimeless
(
●
x
).
Proof
.
by
intros
?
[??]
;
split
;
[
apply
ra_empty_least
|
apply
(
valid_timeless
x
)].
Qed
.
Lemma
auth_frag_op
(
a
b
:
A
)
:
◯
(
a
⋅
b
)
≡
◯
a
⋅
◯
b
.
Proof
.
done
.
Qed
.
Lemma
auth_includedN'
n
(
x
y
:
authC
A
)
:
...
...
modures/cmra.v
View file @
2ac324bd
...
...
@@ -116,13 +116,6 @@ Definition cmra_update {A : cmraT} (x y : A) := ∀ z n,
Infix
"⇝"
:
=
cmra_update
(
at
level
70
).
Instance
:
Params
(@
cmra_update
)
3
.
(** Timeless validity *)
(* Not sure whether this is useful, see the rule [uPred_valid_elim_timeless]
in logic.v *)
Class
ValidTimeless
{
A
:
cmraT
}
(
x
:
A
)
:
=
valid_timeless
:
validN
1
x
→
valid
x
.
Arguments
valid_timeless
{
_
}
_
{
_
}
_
.
(** Properties **)
Section
cmra
.
Context
{
A
:
cmraT
}.
...
...
@@ -275,8 +268,6 @@ Section discrete.
Qed
.
Definition
discreteRA
:
cmraT
:
=
CMRAT
discrete_cofe_mixin
discrete_cmra_mixin
discrete_extend_mixin
.
Global
Instance
discrete_timeless
(
x
:
A
)
:
ValidTimeless
(
x
:
discreteRA
).
Proof
.
by
intros
?.
Qed
.
Lemma
discrete_updateP
(
x
:
A
)
(
P
:
A
→
Prop
)
`
{!
Inhabited
(
sig
P
)}
:
(
∀
z
,
✓
(
x
⋅
z
)
→
∃
y
,
P
y
∧
✓
(
y
⋅
z
))
→
(
x
:
discreteRA
)
⇝
:
P
.
Proof
.
...
...
@@ -344,9 +335,6 @@ Section prod.
Qed
.
Canonical
Structure
prodRA
:
cmraT
:
=
CMRAT
prod_cofe_mixin
prod_cmra_mixin
prod_cmra_extend_mixin
.
Instance
pair_timeless
(
x
:
A
)
(
y
:
B
)
:
ValidTimeless
x
→
ValidTimeless
y
→
ValidTimeless
(
x
,
y
).
Proof
.
by
intros
??
[??]
;
split
;
apply
(
valid_timeless
_
).
Qed
.
End
prod
.
Arguments
prodRA
:
clear
implicits
.
...
...
modures/excl.v
View file @
2ac324bd
...
...
@@ -127,8 +127,6 @@ Proof.
Qed
.
Canonical
Structure
exclRA
:
cmraT
:
=
CMRAT
excl_cofe_mixin
excl_cmra_mixin
excl_cmra_extend_mixin
.
Global
Instance
excl_valid_timeless
(
x
:
excl
A
)
:
ValidTimeless
x
.
Proof
.
by
destruct
x
;
intros
?.
Qed
.
(* Updates *)
Lemma
excl_update
(
x
:
A
)
y
:
✓
y
→
Excl
x
⇝
y
.
...
...
modures/fin_maps.v
View file @
2ac324bd
...
...
@@ -151,25 +151,6 @@ Proof.
Qed
.
Canonical
Structure
mapRA
:
cmraT
:
=
CMRAT
map_cofe_mixin
map_cmra_mixin
map_cmra_extend_mixin
.
Global
Instance
map_empty_valid_timeless
:
ValidTimeless
(
∅
:
gmap
K
A
).
Proof
.
by
intros
??
;
rewrite
lookup_empty
.
Qed
.
Global
Instance
map_ra_insert_valid_timeless
(
m
:
gmap
K
A
)
i
x
:
ValidTimeless
x
→
ValidTimeless
m
→
m
!!
i
=
None
→
ValidTimeless
(<[
i
:
=
x
]>
m
).
Proof
.
intros
??
Hi
Hm
j
;
destruct
(
decide
(
i
=
j
))
;
simplify_map_equality
.
{
specialize
(
Hm
j
)
;
simplify_map_equality
.
by
apply
(
valid_timeless
_
).
}
generalize
j
;
clear
dependent
j
;
rapply
(
valid_timeless
m
).
intros
j
;
destruct
(
decide
(
i
=
j
))
;
simplify_map_equality
;
[
by
rewrite
Hi
|].
by
specialize
(
Hm
j
)
;
simplify_map_equality
.
Qed
.
Global
Instance
map_ra_singleton_valid_timeless
(
i
:
K
)
x
:
ValidTimeless
x
→
ValidTimeless
{[
i
↦
x
]}.
Proof
.
intros
?
;
apply
(
map_ra_insert_valid_timeless
_
_
_
_
_
).
by
rewrite
lookup_empty
.
Qed
.
End
cmra
.
Arguments
mapRA
_
{
_
_
}
_
.
...
...
modures/logic.v
View file @
2ac324bd
...
...
@@ -706,12 +706,15 @@ Lemma own_valid (a : M) : uPred_own a ⊆ (✓ a)%I.
Proof
.
move
=>
x
n
Hv
[
a'
?]
;
cofe_subst
;
eauto
using
cmra_valid_op_l
.
Qed
.
Lemma
valid_intro
{
A
:
cmraT
}
(
a
:
A
)
:
✓
a
→
True
%
I
⊆
(
✓
a
:
uPred
M
)%
I
.
Proof
.
by
intros
?
x
n
?
_;
simpl
;
apply
cmra_valid_validN
.
Qed
.
Lemma
valid_elim_timeless
{
A
:
cmraT
}
(
a
:
A
)
:
ValidTimeless
a
→
¬
✓
a
→
(
✓
a
:
uPred
M
)%
I
⊆
False
%
I
.
Lemma
valid_elim
{
A
:
cmraT
}
(
a
:
A
)
:
¬
✓
{
1
}
a
→
(
✓
a
:
uPred
M
)%
I
⊆
False
%
I
.
Proof
.
intros
?
Hvalid
x
[|
n
]
??
;
[
done
|
apply
Hvalid
].
apply
(
valid_timeless
_
),
cmra_valid_le
with
(
S
n
)
;
auto
with
lia
.
intros
Ha
x
[|
n
]
??
;
[|
apply
Ha
,
cmra_valid_le
with
(
S
n
)]
;
auto
with
lia
.
Qed
.
Lemma
valid_mono
{
A
B
:
cmraT
}
(
a
:
A
)
(
b
:
B
)
:
(
∀
n
,
✓
{
n
}
a
→
✓
{
n
}
b
)
→
(
✓
a
)%
I
⊆
(
✓
b
:
uPred
M
)%
I
.
Proof
.
by
intros
?
x
n
?
;
simpl
;
auto
.
Qed
.
Lemma
own_invalid
(
a
:
M
)
:
¬
✓
{
1
}
a
→
uPred_own
a
⊆
False
%
I
.
Proof
.
by
intros
;
rewrite
->
own_valid
,
->
valid_elim
.
Qed
.
(* Big ops *)
Global
Instance
uPred_big_and_proper
:
Proper
((
≡
)
==>
(
≡
))
(@
uPred_big_and
M
).
...
...
modures/option.v
View file @
2ac324bd
...
...
@@ -142,12 +142,6 @@ Lemma option_op_positive_dist_l n x y : x ⋅ y ={n}= None → x ={n}= None.
Proof
.
by
destruct
x
,
y
;
inversion_clear
1
.
Qed
.
Lemma
option_op_positive_dist_r
n
x
y
:
x
⋅
y
={
n
}=
None
→
y
={
n
}=
None
.
Proof
.
by
destruct
x
,
y
;
inversion_clear
1
.
Qed
.
Global
Instance
None_valid_timeless
:
ValidTimeless
(@
None
A
).
Proof
.
done
.
Qed
.
Global
Instance
Some_valid_timeless
x
:
ValidTimeless
x
→
ValidTimeless
(
Some
x
).
Proof
.
by
intros
?
y
;
apply
(
valid_timeless
x
).
Qed
.
End
cmra
.
Arguments
optionRA
:
clear
implicits
.
...
...
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