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Yixuan Chen
Iris
Commits
0dfda8e4
Commit
0dfda8e4
authored
4 years ago
by
Robbert Krebbers
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Fix indentation.
parent
d68378bf
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theories/bi/big_op.v
+21
-21
21 additions, 21 deletions
theories/bi/big_op.v
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21 deletions
theories/bi/big_op.v
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21
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0dfda8e4
...
...
@@ -1384,27 +1384,27 @@ Section map2.
persistently_pure
big_sepM_persistently
.
Qed
.
Lemma
big_sepM2_forall
`{
BiAffine
PROP
}
Φ
m1
m2
:
(
∀
k
x1
x2
,
Persistent
(
Φ
k
x1
x2
))
→
([
∗
map
]
k
↦
x1
;
x2
∈
m1
;
m2
,
Φ
k
x1
x2
)
⊣⊢
⌜∀
k
:
K
,
is_Some
(
m1
!!
k
)
↔
is_Some
(
m2
!!
k
)
⌝
∧
(
∀
k
x1
x2
,
⌜
m1
!!
k
=
Some
x1
⌝
→
⌜
m2
!!
k
=
Some
x2
⌝
→
Φ
k
x1
x2
)
.
Proof
.
rewrite
big_sepM2_eq
/
big_sepM2_def
=>
?
.
apply
and_proper
=>
//.
rewrite
big_sepM_forall
.
apply
forall_proper
=>
k
.
apply
(
anti_symm
_)
.
-
apply
forall_intro
=>
x1
.
apply
forall_intro
=>
x2
.
rewrite
(
forall_elim
(
x1
,
x2
))
.
rewrite
impl_curry
-
pure_and
.
apply
impl_mono
=>
//.
apply
pure_mono
.
rewrite
map_lookup_zip_with
.
by
intros
[
->
->
]
.
-
apply
forall_intro
=>
[[
x1
x2
]]
.
rewrite
(
forall_elim
x1
)
(
forall_elim
x2
)
.
rewrite
impl_curry
-
pure_and
.
apply
impl_mono
=>
//.
apply
pure_mono
.
rewrite
map_lookup_zip_with
.
by
destruct
(
m1
!!
k
),
(
m2
!!
k
)=>
/=
//
?;
simplify_eq
.
Qed
.
Lemma
big_sepM2_impl
Φ
Ψ
m1
m2
:
Lemma
big_sepM2_forall
`{
BiAffine
PROP
}
Φ
m1
m2
:
(
∀
k
x1
x2
,
Persistent
(
Φ
k
x1
x2
))
→
([
∗
map
]
k
↦
x1
;
x2
∈
m1
;
m2
,
Φ
k
x1
x2
)
⊣⊢
⌜∀
k
:
K
,
is_Some
(
m1
!!
k
)
↔
is_Some
(
m2
!!
k
)
⌝
∧
(
∀
k
x1
x2
,
⌜
m1
!!
k
=
Some
x1
⌝
→
⌜
m2
!!
k
=
Some
x2
⌝
→
Φ
k
x1
x2
)
.
Proof
.
rewrite
big_sepM2_eq
/
big_sepM2_def
=>
?
.
apply
and_proper
=>
//.
rewrite
big_sepM_forall
.
apply
forall_proper
=>
k
.
apply
(
anti_symm
_)
.
-
apply
forall_intro
=>
x1
.
apply
forall_intro
=>
x2
.
rewrite
(
forall_elim
(
x1
,
x2
))
.
rewrite
impl_curry
-
pure_and
.
apply
impl_mono
=>
//.
apply
pure_mono
.
rewrite
map_lookup_zip_with
.
by
intros
[
->
->
]
.
-
apply
forall_intro
=>
[[
x1
x2
]]
.
rewrite
(
forall_elim
x1
)
(
forall_elim
x2
)
.
rewrite
impl_curry
-
pure_and
.
apply
impl_mono
=>
//.
apply
pure_mono
.
rewrite
map_lookup_zip_with
.
by
destruct
(
m1
!!
k
),
(
m2
!!
k
)=>
/=
//
?;
simplify_eq
.
Qed
.
Lemma
big_sepM2_impl
Φ
Ψ
m1
m2
:
([
∗
map
]
k
↦
y1
;
y2
∈
m1
;
m2
,
Φ
k
y1
y2
)
-∗
□
(
∀
k
x1
x2
,
⌜
m1
!!
k
=
Some
x1
⌝
→
⌜
m2
!!
k
=
Some
x2
⌝
→
Φ
k
x1
x2
-∗
Ψ
k
x1
x2
)
-∗
...
...
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