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2b96b14d
Commit
2b96b14d
authored
Mar 21, 2016
by
Robbert Krebbers
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Make use of COFE on lists in big ops.
parent
0781afe2
Pipeline
#376
passed with stage
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2
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1
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2 changed files
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+6
7
algebra/cmra_big_op.v
algebra/cmra_big_op.v
+3
2
algebra/upred_big_op.v
algebra/upred_big_op.v
+3
5
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algebra/cmra_big_op.v
View file @
2b96b14d
From
iris
.
algebra
Require
Export
cmra
.
From
iris
.
algebra
Require
Export
cmra
list
.
From
iris
.
prelude
Require
Import
gmap
.
Fixpoint
big_op
{
A
:
cmraT
}
`
{
Empty
A
}
(
xs
:
list
A
)
:
A
:
=
...
...
@@ 25,8 +25,9 @@ Proof.

by
rewrite
!
assoc
(
comm
_
x
).

by
trans
(
big_op
xs2
).
Qed
.
Global
Instance
big_op_
proper
:
Proper
((
≡
)
==>
(
≡
)
)
big_op
.
Global
Instance
big_op_
ne
n
:
Proper
(
dist
n
==>
dist
n
)
big_op
.
Proof
.
by
induction
1
;
simpl
;
repeat
apply
(
_
:
Proper
(
_
==>
_
==>
_
)
op
).
Qed
.
Global
Instance
big_op_proper
:
Proper
((
≡
)
==>
(
≡
))
big_op
:
=
ne_proper
_
.
Lemma
big_op_app
xs
ys
:
big_op
(
xs
++
ys
)
≡
big_op
xs
⋅
big_op
ys
.
Proof
.
induction
xs
as
[
x
xs
IH
]
;
simpl
;
first
by
rewrite
?left_id
.
...
...
algebra/upred_big_op.v
View file @
2b96b14d
From
iris
.
algebra
Require
Export
upred
.
From
iris
.
algebra
Require
Export
upred
list
.
From
iris
.
prelude
Require
Import
gmap
fin_collections
.
Import
uPred
.
...
...
@@ 44,11 +44,9 @@ Proof. by induction 1 as [P Q Ps Qs HPQ ? IH]; rewrite /= ?HPQ ?IH. Qed.
Global
Instance
big_sep_proper
:
Proper
((
≡
)
==>
(
⊣
⊢
))
(@
uPred_big_sep
M
).
Proof
.
by
induction
1
as
[
P
Q
Ps
Qs
HPQ
?
IH
]
;
rewrite
/=
?HPQ
?IH
.
Qed
.
Global
Instance
big_and_ne
n
:
Proper
(
Forall2
(
dist
n
)
==>
dist
n
)
(@
uPred_big_and
M
).
Global
Instance
big_and_ne
n
:
Proper
(
dist
n
==>
dist
n
)
(@
uPred_big_and
M
).
Proof
.
by
induction
1
as
[
P
Q
Ps
Qs
HPQ
?
IH
]
;
rewrite
/=
?HPQ
?IH
.
Qed
.
Global
Instance
big_sep_ne
n
:
Proper
(
Forall2
(
dist
n
)
==>
dist
n
)
(@
uPred_big_sep
M
).
Global
Instance
big_sep_ne
n
:
Proper
(
dist
n
==>
dist
n
)
(@
uPred_big_sep
M
).
Proof
.
by
induction
1
as
[
P
Q
Ps
Qs
HPQ
?
IH
]
;
rewrite
/=
?HPQ
?IH
.
Qed
.
Global
Instance
big_and_mono'
:
Proper
(
Forall2
(
⊢
)
==>
(
⊢
))
(@
uPred_big_and
M
).
...
...
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