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Rice Wine
Iris
Commits
3b226c83
Commit
3b226c83
authored
Oct 25, 2017
by
Robbert Krebbers
Browse files
Plain instances for the big ops.
parent
0b092348
Changes
1
Hide whitespace changes
Inline
Side-by-side
theories/base_logic/big_op.v
View file @
3b226c83
...
...
@@ -149,6 +149,14 @@ Section list.
by
rewrite
persistently_impl_wand
persistently_elim
wand_elim_l
.
Qed
.
Global
Instance
big_sepL_nil_plain
Φ
:
Plain
([
∗
list
]
k
↦
x
∈
[],
Φ
k
x
).
Proof
.
simpl
;
apply
_
.
Qed
.
Global
Instance
big_sepL_plain
Φ
l
:
(
∀
k
x
,
Plain
(
Φ
k
x
))
→
Plain
([
∗
list
]
k
↦
x
∈
l
,
Φ
k
x
).
Proof
.
revert
Φ
.
induction
l
as
[|
x
l
IH
]=>
Φ
?
/=
;
apply
_
.
Qed
.
Global
Instance
big_sepL_plain_id
Ps
:
TCForall
Plain
Ps
→
Plain
([
∗
]
Ps
).
Proof
.
induction
1
;
simpl
;
apply
_
.
Qed
.
Global
Instance
big_sepL_nil_persistent
Φ
:
Persistent
([
∗
list
]
k
↦
x
∈
[],
Φ
k
x
).
Proof
.
simpl
;
apply
_
.
Qed
.
...
...
@@ -342,12 +350,19 @@ Section gmap.
by
rewrite
persistently_impl_wand
persistently_elim
wand_elim_l
.
Qed
.
Global
Instance
big_sepM_empty_plain
Φ
:
Plain
([
∗
map
]
k
↦
x
∈
∅
,
Φ
k
x
).
Proof
.
rewrite
/
big_opM
map_to_list_empty
.
apply
_
.
Qed
.
Global
Instance
big_sepM_plain
Φ
m
:
(
∀
k
x
,
Plain
(
Φ
k
x
))
→
Plain
([
∗
map
]
k
↦
x
∈
m
,
Φ
k
x
).
Proof
.
intros
.
apply
big_sepL_plain
=>
_
[??]
;
apply
_
.
Qed
.
Global
Instance
big_sepM_empty_persistent
Φ
:
Persistent
([
∗
map
]
k
↦
x
∈
∅
,
Φ
k
x
).
Proof
.
rewrite
/
big_opM
map_to_list_empty
.
apply
_
.
Qed
.
Global
Instance
big_sepM_persistent
Φ
m
:
(
∀
k
x
,
Persistent
(
Φ
k
x
))
→
Persistent
([
∗
map
]
k
↦
x
∈
m
,
Φ
k
x
).
Proof
.
intros
.
apply
big_sepL_persistent
=>
_
[??]
;
apply
_
.
Qed
.
Global
Instance
big_sepM_nil_timeless
Φ
:
Timeless
([
∗
map
]
k
↦
x
∈
∅
,
Φ
k
x
).
Proof
.
rewrite
/
big_opM
map_to_list_empty
.
apply
_
.
Qed
.
...
...
@@ -490,11 +505,18 @@ Section gset.
by
rewrite
persistently_impl_wand
persistently_elim
wand_elim_l
.
Qed
.
Global
Instance
big_sepS_empty_plain
Φ
:
Plain
([
∗
set
]
x
∈
∅
,
Φ
x
).
Proof
.
rewrite
/
big_opS
elements_empty
.
apply
_
.
Qed
.
Global
Instance
big_sepS_plain
Φ
X
:
(
∀
x
,
Plain
(
Φ
x
))
→
Plain
([
∗
set
]
x
∈
X
,
Φ
x
).
Proof
.
rewrite
/
big_opS
.
apply
_
.
Qed
.
Global
Instance
big_sepS_empty_persistent
Φ
:
Persistent
([
∗
set
]
x
∈
∅
,
Φ
x
).
Proof
.
rewrite
/
big_opS
elements_empty
.
apply
_
.
Qed
.
Global
Instance
big_sepS_persistent
Φ
X
:
(
∀
x
,
Persistent
(
Φ
x
))
→
Persistent
([
∗
set
]
x
∈
X
,
Φ
x
).
Proof
.
rewrite
/
big_opS
.
apply
_
.
Qed
.
Global
Instance
big_sepS_nil_timeless
Φ
:
Timeless
([
∗
set
]
x
∈
∅
,
Φ
x
).
Proof
.
rewrite
/
big_opS
elements_empty
.
apply
_
.
Qed
.
Global
Instance
big_sepS_timeless
Φ
X
:
...
...
@@ -578,11 +600,18 @@ Section gmultiset.
□
?q
([
∗
mset
]
y
∈
X
,
Φ
y
)
⊣
⊢
([
∗
mset
]
y
∈
X
,
□
?q
Φ
y
).
Proof
.
apply
(
big_opMS_commute
_
).
Qed
.
Global
Instance
big_sepMS_empty_plain
Φ
:
Plain
([
∗
mset
]
x
∈
∅
,
Φ
x
).
Proof
.
rewrite
/
big_opMS
gmultiset_elements_empty
.
apply
_
.
Qed
.
Global
Instance
big_sepMS_plain
Φ
X
:
(
∀
x
,
Plain
(
Φ
x
))
→
Plain
([
∗
mset
]
x
∈
X
,
Φ
x
).
Proof
.
rewrite
/
big_opMS
.
apply
_
.
Qed
.
Global
Instance
big_sepMS_empty_persistent
Φ
:
Persistent
([
∗
mset
]
x
∈
∅
,
Φ
x
).
Proof
.
rewrite
/
big_opMS
gmultiset_elements_empty
.
apply
_
.
Qed
.
Global
Instance
big_sepMS_persistent
Φ
X
:
(
∀
x
,
Persistent
(
Φ
x
))
→
Persistent
([
∗
mset
]
x
∈
X
,
Φ
x
).
Proof
.
rewrite
/
big_opMS
.
apply
_
.
Qed
.
Global
Instance
big_sepMS_nil_timeless
Φ
:
Timeless
([
∗
mset
]
x
∈
∅
,
Φ
x
).
Proof
.
rewrite
/
big_opMS
gmultiset_elements_empty
.
apply
_
.
Qed
.
Global
Instance
big_sepMS_timeless
Φ
X
:
...
...
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