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Rodolphe Lepigre
Iris
Commits
457cf079
Commit
457cf079
authored
Dec 21, 2015
by
Robbert Krebbers
Browse files
Missing stuff on finite maps.
parent
6c4592ef
Changes
1
Hide whitespace changes
Inline
Side-by-side
modures/fin_maps.v
View file @
457cf079
...
...
@@ -39,6 +39,9 @@ Proof.
intros
x
y
?
m
m'
?
j
;
destruct
(
decide
(
i
=
j
))
;
simplify_map_equality
;
[
by
constructor
|
by
apply
lookup_ne
].
Qed
.
Global
Instance
singleton_ne
`
{
Cofe
A
}
(
i
:
K
)
n
:
Proper
(
dist
n
==>
dist
n
)
(
singletonM
i
:
A
→
gmap
K
A
).
Proof
.
by
intros
???
;
apply
insert_ne
.
Qed
.
Global
Instance
delete_ne
`
{
Dist
A
}
(
i
:
K
)
n
:
Proper
(
dist
n
==>
dist
n
)
(
delete
(
M
:
=
gmap
K
A
)
i
).
Proof
.
...
...
@@ -66,7 +69,7 @@ Proof.
Qed
.
Global
Instance
map_ra_singleton_timeless
`
{
Cofe
A
}
(
i
:
K
)
(
x
:
A
)
:
Timeless
x
→
Timeless
({[
i
↦
x
]}
:
gmap
K
A
)
:
=
_
.
Instance
map_fmap_ne
`
{
Dist
A
,
Dist
B
}
(
f
:
A
→
B
)
n
:
Global
Instance
map_fmap_ne
`
{
Dist
A
,
Dist
B
}
(
f
:
A
→
B
)
n
:
Proper
(
dist
n
==>
dist
n
)
f
→
Proper
(
dist
n
==>
dist
n
)
(
fmap
(
M
:
=
gmap
K
)
f
).
Proof
.
by
intros
?
m
m'
Hm
k
;
rewrite
!
lookup_fmap
;
apply
option_fmap_ne
.
Qed
.
...
...
@@ -183,6 +186,10 @@ Proof. by intros ?? j; destruct (decide (i = j)); simplify_map_equality. Qed.
Lemma
map_insert_op
`
{
Op
A
}
(
m1
m2
:
gmap
K
A
)
i
x
:
m2
!!
i
=
None
→
<[
i
:
=
x
]>(
m1
⋅
m2
)
=
<[
i
:
=
x
]>
m1
⋅
m2
.
Proof
.
by
intros
Hi
;
apply
(
insert_merge_l
_
)
;
rewrite
Hi
.
Qed
.
Lemma
map_singleton_op
`
{
Op
A
}
(
i
:
K
)
(
x
y
:
A
)
:
({[
i
↦
x
⋅
y
]}
:
gmap
K
A
)
=
{[
i
↦
x
]}
⋅
{[
i
↦
y
]}.
Proof
.
by
apply
symmetry
,
merge_singleton
.
Qed
.
Canonical
Structure
mapRA
(
A
:
cmraT
)
:
cmraT
:
=
CMRAT
(
gmap
K
A
).
Global
Instance
map_fmap_cmra_monotone
`
{
CMRA
A
,
CMRA
B
}
(
f
:
A
→
B
)
`
{!
CMRAMonotone
f
}
:
CMRAMonotone
(
fmap
f
:
gmap
K
A
→
gmap
K
B
).
...
...
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