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8cabea52
Commit
8cabea52
authored
May 31, 2016
by
Robbert Krebbers
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Make iDestruct and iCombine work with (sep)conjunctions under big_ops.
parent
63075f7c
Pipeline
#1200
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+54
-0
algebra/upred_big_op.v
algebra/upred_big_op.v
+23
-0
proofmode/coq_tactics.v
proofmode/coq_tactics.v
+31
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algebra/upred_big_op.v
View file @
8cabea52
...
...
@@ -214,6 +214,18 @@ Section gmap.
induction
(
map_to_list
m
)
as
[|[
i
x
]
l
IH
]
;
csimpl
;
rewrite
?later_True
//.
by
rewrite
later_sep
IH
.
Qed
.
Lemma
big_sepM_always
Φ
m
:
(
□
[
★
map
]
k
↦
x
∈
m
,
Φ
k
x
)
⊣
⊢
([
★
map
]
k
↦
x
∈
m
,
□
Φ
k
x
).
Proof
.
rewrite
/
uPred_big_sepM
.
induction
(
map_to_list
m
)
as
[|[
i
x
]
l
IH
]
;
csimpl
;
rewrite
?always_const
//.
by
rewrite
always_sep
IH
.
Qed
.
Lemma
big_sepM_always_if
p
Φ
m
:
(
□
?p
[
★
map
]
k
↦
x
∈
m
,
Φ
k
x
)
⊣
⊢
([
★
map
]
k
↦
x
∈
m
,
□
?p
Φ
k
x
).
Proof
.
destruct
p
;
simpl
;
auto
using
big_sepM_always
.
Qed
.
End
gmap
.
(** ** Big ops over finite sets *)
...
...
@@ -295,6 +307,17 @@ Section gset.
induction
(
elements
X
)
as
[|
x
l
IH
]
;
csimpl
;
first
by
rewrite
?later_True
.
by
rewrite
later_sep
IH
.
Qed
.
Lemma
big_sepS_always
Φ
X
:
(
□
[
★
set
]
y
∈
X
,
Φ
y
)
⊣
⊢
([
★
set
]
y
∈
X
,
□
Φ
y
).
Proof
.
rewrite
/
uPred_big_sepS
.
induction
(
elements
X
)
as
[|
x
l
IH
]
;
csimpl
;
first
by
rewrite
?always_const
.
by
rewrite
always_sep
IH
.
Qed
.
Lemma
big_sepS_always_if
q
Φ
X
:
(
□
?q
[
★
set
]
y
∈
X
,
Φ
y
)
⊣
⊢
([
★
set
]
y
∈
X
,
□
?q
Φ
y
).
Proof
.
destruct
q
;
simpl
;
auto
using
big_sepS_always
.
Qed
.
End
gset
.
(** ** Persistence *)
...
...
proofmode/coq_tactics.v
View file @
8cabea52
...
...
@@ -681,6 +681,20 @@ Proof. done. Qed.
Global
Instance
sep_split_ownM
(
a
b
:
M
)
:
SepSplit
(
uPred_ownM
(
a
⋅
b
))
(
uPred_ownM
a
)
(
uPred_ownM
b
)
|
99
.
Proof
.
by
rewrite
/
SepSplit
ownM_op
.
Qed
.
Global
Instance
sep_split_big_sepM
`
{
Countable
K
}
{
A
}
(
Φ
Ψ
1
Ψ
2
:
K
→
A
→
uPred
M
)
m
:
(
∀
k
x
,
SepSplit
(
Φ
k
x
)
(
Ψ
1
k
x
)
(
Ψ
2
k
x
))
→
SepSplit
([
★
map
]
k
↦
x
∈
m
,
Φ
k
x
)
([
★
map
]
k
↦
x
∈
m
,
Ψ
1
k
x
)
([
★
map
]
k
↦
x
∈
m
,
Ψ
2
k
x
).
Proof
.
rewrite
/
SepSplit
=>
?.
rewrite
-
big_sepM_sepM
.
by
apply
big_sepM_mono
.
Qed
.
Global
Instance
sep_split_big_sepS
`
{
Countable
A
}
(
Φ
Ψ
1
Ψ
2
:
A
→
uPred
M
)
X
:
(
∀
x
,
SepSplit
(
Φ
x
)
(
Ψ
1
x
)
(
Ψ
2
x
))
→
SepSplit
([
★
set
]
x
∈
X
,
Φ
x
)
([
★
set
]
x
∈
X
,
Ψ
1
x
)
([
★
set
]
x
∈
X
,
Ψ
2
x
).
Proof
.
rewrite
/
SepSplit
=>
?.
rewrite
-
big_sepS_sepS
.
by
apply
big_sepS_mono
.
Qed
.
Lemma
tac_sep_split
Δ
Δ
1
Δ
2
lr
js
P
Q1
Q2
:
SepSplit
P
Q1
Q2
→
...
...
@@ -759,6 +773,23 @@ Global Instance sep_destruct_later p P Q1 Q2 :
SepDestruct
p
P
Q1
Q2
→
SepDestruct
p
(
▷
P
)
(
▷
Q1
)
(
▷
Q2
).
Proof
.
by
rewrite
/
SepDestruct
-
later_sep
!
always_if_later
=>
->.
Qed
.
Global
Instance
sep_destruct_big_sepM
`
{
Countable
K
}
{
A
}
(
Φ
Ψ
1
Ψ
2
:
K
→
A
→
uPred
M
)
p
m
:
(
∀
k
x
,
SepDestruct
p
(
Φ
k
x
)
(
Ψ
1
k
x
)
(
Ψ
2
k
x
))
→
SepDestruct
p
([
★
map
]
k
↦
x
∈
m
,
Φ
k
x
)
([
★
map
]
k
↦
x
∈
m
,
Ψ
1
k
x
)
([
★
map
]
k
↦
x
∈
m
,
Ψ
2
k
x
).
Proof
.
rewrite
/
SepDestruct
=>
?.
rewrite
-
big_sepM_sepM
!
big_sepM_always_if
.
by
apply
big_sepM_mono
.
Qed
.
Global
Instance
sep_destruct_big_sepS
`
{
Countable
A
}
(
Φ
Ψ
1
Ψ
2
:
A
→
uPred
M
)
p
X
:
(
∀
x
,
SepDestruct
p
(
Φ
x
)
(
Ψ
1
x
)
(
Ψ
2
x
))
→
SepDestruct
p
([
★
set
]
x
∈
X
,
Φ
x
)
([
★
set
]
x
∈
X
,
Ψ
1
x
)
([
★
set
]
x
∈
X
,
Ψ
2
x
).
Proof
.
rewrite
/
SepDestruct
=>
?.
rewrite
-
big_sepS_sepS
!
big_sepS_always_if
.
by
apply
big_sepS_mono
.
Qed
.
Lemma
tac_sep_destruct
Δ
Δ
'
i
p
j1
j2
P
P1
P2
Q
:
envs_lookup
i
Δ
=
Some
(
p
,
P
)
→
SepDestruct
p
P
P1
P2
→
envs_simple_replace
i
p
(
Esnoc
(
Esnoc
Enil
j1
P1
)
j2
P2
)
Δ
=
Some
Δ
'
→
...
...
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