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Dmitry Khalanskiy
Iris
Commits
c0b7f46f
Commit
c0b7f46f
authored
Dec 12, 2018
by
Robbert Krebbers
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`big_sepM_insert_2` that does not require the element not to be in the map.
parent
b16e3e3c
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theories/bi/big_op.v
theories/bi/big_op.v
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theories/bi/big_op.v
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c0b7f46f
...
...
@@ -568,6 +568,19 @@ Section gmap.
([
∗
map
]
k
↦
y
∈
m
,
Φ
k
y
)
⊣
⊢
Φ
i
x
∗
[
∗
map
]
k
↦
y
∈
delete
i
m
,
Φ
k
y
.
Proof
.
apply
big_opM_delete
.
Qed
.
Lemma
big_sepM_insert_2
Φ
m
i
x
:
TCOr
(
∀
x
,
Affine
(
Φ
i
x
))
(
Absorbing
(
Φ
i
x
))
→
Φ
i
x
-
∗
([
∗
map
]
k
↦
y
∈
m
,
Φ
k
y
)
-
∗
[
∗
map
]
k
↦
y
∈
<[
i
:
=
x
]>
m
,
Φ
k
y
.
Proof
.
intros
Ha
.
apply
wand_intro_r
.
destruct
(
m
!!
i
)
as
[
y
|]
eqn
:
Hi
;
last
first
.
{
by
rewrite
-
big_sepM_insert
.
}
assert
(
TCOr
(
Affine
(
Φ
i
y
))
(
Absorbing
(
Φ
i
x
))).
{
destruct
Ha
;
try
apply
_
.
}
rewrite
big_sepM_delete
//
assoc
.
rewrite
(
sep_elim_l
(
Φ
i
x
))
-
big_sepM_insert
?lookup_delete
//.
by
rewrite
insert_delete
.
Qed
.
Lemma
big_sepM_lookup_acc
Φ
m
i
x
:
m
!!
i
=
Some
x
→
([
∗
map
]
k
↦
y
∈
m
,
Φ
k
y
)
⊢
Φ
i
x
∗
(
Φ
i
x
-
∗
([
∗
map
]
k
↦
y
∈
m
,
Φ
k
y
)).
...
...
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