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Gaëtan Gilbert
Iris
Commits
79086c8a
Commit
79086c8a
authored
5 years ago
by
Robbert Krebbers
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Remove some useless newlines.
parent
b7eb65ed
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2 changed files
theories/algebra/list.v
+6
-12
6 additions, 12 deletions
theories/algebra/list.v
theories/bi/big_op.v
+4
-8
4 additions, 8 deletions
theories/bi/big_op.v
with
10 additions
and
20 deletions
theories/algebra/list.v
+
6
−
12
View file @
79086c8a
...
...
@@ -21,30 +21,24 @@ Global Instance take_ne : NonExpansive (@take A n) := _.
Global
Instance
drop_ne
:
NonExpansive
(
@
drop
A
n
)
:=
_
.
Global
Instance
head_ne
:
NonExpansive
(
head
(
A
:=
A
))
.
Proof
.
destruct
1
;
by
constructor
.
Qed
.
Global
Instance
list_lookup_ne
i
:
NonExpansive
(
lookup
(
M
:=
list
A
)
i
)
.
Global
Instance
list_lookup_ne
i
:
NonExpansive
(
lookup
(
M
:=
list
A
)
i
)
.
Proof
.
intros
????
.
by
apply
dist_option_Forall2
,
Forall2_lookup
.
Qed
.
Global
Instance
list_alter_ne
n
f
i
:
Proper
(
dist
n
==>
dist
n
)
f
→
Proper
(
dist
n
==>
dist
n
)
(
alter
(
M
:=
list
A
)
f
i
)
:=
_
.
Global
Instance
list_insert_ne
i
:
NonExpansive2
(
insert
(
M
:=
list
A
)
i
)
:=
_
.
Global
Instance
list_inserts_ne
i
:
NonExpansive2
(
@
list_inserts
A
i
)
:=
_
.
Global
Instance
list_delete_ne
i
:
NonExpansive
(
delete
(
M
:=
list
A
)
i
)
:=
_
.
Global
Instance
list_insert_ne
i
:
NonExpansive2
(
insert
(
M
:=
list
A
)
i
)
:=
_
.
Global
Instance
list_inserts_ne
i
:
NonExpansive2
(
@
list_inserts
A
i
)
:=
_
.
Global
Instance
list_delete_ne
i
:
NonExpansive
(
delete
(
M
:=
list
A
)
i
)
:=
_
.
Global
Instance
option_list_ne
:
NonExpansive
(
@
option_list
A
)
.
Proof
.
intros
????;
by
apply
Forall2_option_list
,
dist_option_Forall2
.
Qed
.
Global
Instance
list_filter_ne
n
P
`{
∀
x
,
Decision
(
P
x
)}
:
Proper
(
dist
n
==>
iff
)
P
→
Proper
(
dist
n
==>
dist
n
)
(
filter
(
B
:=
list
A
)
P
)
:=
_
.
Global
Instance
replicate_ne
:
NonExpansive
(
@
replicate
A
n
)
:=
_
.
Global
Instance
replicate_ne
:
NonExpansive
(
@
replicate
A
n
)
:=
_
.
Global
Instance
reverse_ne
:
NonExpansive
(
@
reverse
A
)
:=
_
.
Global
Instance
last_ne
:
NonExpansive
(
@
last
A
)
.
Proof
.
intros
????;
by
apply
dist_option_Forall2
,
Forall2_last
.
Qed
.
Global
Instance
resize_ne
n
:
NonExpansive2
(
@
resize
A
n
)
:=
_
.
Global
Instance
resize_ne
n
:
NonExpansive2
(
@
resize
A
n
)
:=
_
.
Lemma
list_dist_cons_inv_l
n
x
l
k
:
x
::
l
≡
{
n
}
≡
k
→
∃
y
k'
,
x
≡
{
n
}
≡
y
∧
l
≡
{
n
}
≡
k'
∧
k
=
y
::
k'
.
...
...
This diff is collapsed.
Click to expand it.
theories/bi/big_op.v
+
4
−
8
View file @
79086c8a
...
...
@@ -906,13 +906,11 @@ Section map2.
Qed
.
Global
Instance
big_sepM2_mono'
:
Proper
(
pointwise_relation
_
(
pointwise_relation
_
(
pointwise_relation
_
(
⊢
)))
==>
(
=
)
==>
(
=
)
==>
(
⊢
))
(
big_sepM2
(
PROP
:=
PROP
)
(
K
:=
K
)
(
A
:=
A
)
(
B
:=
B
))
.
==>
(
=
)
==>
(
=
)
==>
(
⊢
))
(
big_sepM2
(
PROP
:=
PROP
)
(
K
:=
K
)
(
A
:=
A
)
(
B
:=
B
))
.
Proof
.
intros
f
g
Hf
m1
?
<-
m2
?
<-.
apply
big_sepM2_mono
;
intros
;
apply
Hf
.
Qed
.
Global
Instance
big_sepM2_proper'
:
Proper
(
pointwise_relation
_
(
pointwise_relation
_
(
pointwise_relation
_
(
⊣⊢
)))
==>
(
=
)
==>
(
=
)
==>
(
⊣⊢
))
(
big_sepM2
(
PROP
:=
PROP
)
(
K
:=
K
)
(
A
:=
A
)
(
B
:=
B
))
.
==>
(
=
)
==>
(
=
)
==>
(
⊣⊢
))
(
big_sepM2
(
PROP
:=
PROP
)
(
K
:=
K
)
(
A
:=
A
)
(
B
:=
B
))
.
Proof
.
intros
f
g
Hf
m1
?
<-
m2
?
<-.
apply
big_sepM2_proper
;
intros
;
apply
Hf
.
Qed
.
Lemma
big_sepM2_empty
Φ
:
([
∗
map
]
k
↦
y1
;
y2
∈
∅
;
∅
,
Φ
k
y1
y2
)
⊣⊢
emp
.
...
...
@@ -923,15 +921,13 @@ Section map2.
Lemma
big_sepM2_empty'
`{
BiAffine
PROP
}
P
Φ
:
P
⊢
[
∗
map
]
k
↦
y1
;
y2
∈
∅
;
∅
,
Φ
k
y1
y2
.
Proof
.
rewrite
big_sepM2_empty
.
apply
(
affine
_)
.
Qed
.
Lemma
big_sepM2_empty_l
m1
Φ
:
([
∗
map
]
k
↦
y1
;
y2
∈
m1
;
∅
,
Φ
k
y1
y2
)
⊢
⌜
m1
=
∅⌝.
Lemma
big_sepM2_empty_l
m1
Φ
:
([
∗
map
]
k
↦
y1
;
y2
∈
m1
;
∅
,
Φ
k
y1
y2
)
⊢
⌜
m1
=
∅⌝.
Proof
.
rewrite
big_sepM2_dom
dom_empty_L
.
apply
pure_mono
,
dom_empty_inv_L
.
Qed
.
Lemma
big_sepM2_empty_r
m2
Φ
:
([
∗
map
]
k
↦
y1
;
y2
∈
∅
;
m2
,
Φ
k
y1
y2
)
⊢
⌜
m2
=
∅⌝.
Lemma
big_sepM2_empty_r
m2
Φ
:
([
∗
map
]
k
↦
y1
;
y2
∈
∅
;
m2
,
Φ
k
y1
y2
)
⊢
⌜
m2
=
∅⌝.
Proof
.
rewrite
big_sepM2_dom
dom_empty_L
.
apply
pure_mono
=>?
.
eapply
(
dom_empty_inv_L
(
D
:=
gset
K
))
.
eauto
.
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