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Iris
Fairis
Commits
13680b70
Commit
13680b70
authored
Jan 15, 2016
by
Robbert Krebbers
Browse files
Properties about maps and is_Some.
parent
8ee34859
Changes
1
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Inline
Side-by-side
prelude/fin_maps.v
View file @
13680b70
...
...
@@ -337,6 +337,9 @@ Proof.
rewrite
?
lookup_delete
,
?
lookup_delete_ne
;
intuition
congruence
.
*
intros
[
??
].
by
rewrite
lookup_delete_ne
.
Qed
.
Lemma
lookup_delete_is_Some
{
A
}
(
m
:
M
A
)
i
j
:
is_Some
(
delete
i
m
!!
j
)
↔
i
≠
j
∧
is_Some
(
m
!!
j
).
Proof
.
unfold
is_Some
;
setoid_rewrite
lookup_delete_Some
;
naive_solver
.
Qed
.
Lemma
lookup_delete_None
{
A
}
(
m
:
M
A
)
i
j
:
delete
i
m
!!
j
=
None
↔
i
=
j
∨
m
!!
j
=
None
.
Proof
.
...
...
@@ -411,6 +414,9 @@ Proof.
rewrite
?
lookup_insert
,
?
lookup_insert_ne
;
intuition
congruence
.
*
intros
[[
->
->
]
|
[
??
]];
[
apply
lookup_insert
|
].
by
rewrite
lookup_insert_ne
.
Qed
.
Lemma
lookup_insert_is_Some
{
A
}
(
m
:
M
A
)
i
j
x
:
is_Some
(
<
[
i
:=
x
]
>
m
!!
j
)
↔
i
=
j
∨
i
≠
j
∧
is_Some
(
m
!!
j
).
Proof
.
unfold
is_Some
;
setoid_rewrite
lookup_insert_Some
;
naive_solver
.
Qed
.
Lemma
lookup_insert_None
{
A
}
(
m
:
M
A
)
i
j
x
:
<
[
i
:=
x
]
>
m
!!
j
=
None
↔
m
!!
j
=
None
∧
i
≠
j
.
Proof
.
...
...
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