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stdpp
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653cb9db
Commit
653cb9db
authored
Jul 15, 2020
by
Ralf Jung
Committed by
Robbert
Jul 15, 2020
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add map_filter_insert_not_delete
by Tej
parent
5bdd73dd
Changes
2
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2 changed files
with
56 additions
and
0 deletions
+56
0
theories/fin_maps.v
theories/fin_maps.v
+45
0
theories/list.v
theories/list.v
+11
0
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theories/fin_maps.v
View file @
653cb9db
...
...
@@ 1132,6 +1132,17 @@ Section map_filter.
+
rewrite
Eq
,
Hm
,
lookup_insert
.
naive_solver
.
+
by
rewrite
lookup_insert_ne
.
Qed
.
Lemma
map_filter_lookup_Some_11
m
i
x
:
filter
P
m
!!
i
=
Some
x
→
m
!!
i
=
Some
x
.
Proof
.
apply
map_filter_lookup_Some
.
Qed
.
Lemma
map_filter_lookup_Some_12
m
i
x
:
filter
P
m
!!
i
=
Some
x
→
P
(
i
,
x
).
Proof
.
apply
map_filter_lookup_Some
.
Qed
.
Lemma
map_filter_lookup_Some_2
m
i
x
:
m
!!
i
=
Some
x
→
P
(
i
,
x
)
→
filter
P
m
!!
i
=
Some
x
.
Proof
.
intros
.
by
apply
map_filter_lookup_Some
.
Qed
.
Lemma
map_filter_lookup_None
m
i
:
filter
P
m
!!
i
=
None
↔
m
!!
i
=
None
∨
∀
x
,
m
!!
i
=
Some
x
→
¬
P
(
i
,
x
).
...
...
@@ 1139,6 +1150,14 @@ Section map_filter.
rewrite
eq_None_not_Some
.
unfold
is_Some
.
setoid_rewrite
map_filter_lookup_Some
.
naive_solver
.
Qed
.
Lemma
map_filter_lookup_None_1
m
i
:
filter
P
m
!!
i
=
None
→
m
!!
i
=
None
∨
∀
x
,
m
!!
i
=
Some
x
→
¬
P
(
i
,
x
).
Proof
.
apply
map_filter_lookup_None
.
Qed
.
Lemma
map_filter_lookup_None_2
m
i
:
m
!!
i
=
None
∨
(
∀
x
:
A
,
m
!!
i
=
Some
x
→
¬
P
(
i
,
x
))
→
filter
P
m
!!
i
=
None
.
Proof
.
apply
map_filter_lookup_None
.
Qed
.
Lemma
map_filter_lookup_eq
m1
m2
:
(
∀
k
x
,
P
(
k
,
x
)
→
m1
!!
k
=
Some
x
↔
m2
!!
k
=
Some
x
)
→
...
...
@@ 1170,6 +1189,14 @@ Section map_filter.
(
∀
y
,
¬
P
(
i
,
y
))
→
filter
P
(<[
i
:
=
x
]>
m
)
=
filter
P
m
.
Proof
.
intros
HP
.
by
apply
map_filter_insert_not'
.
Qed
.
Lemma
map_filter_insert_not_delete
m
i
x
:
¬
P
(
i
,
x
)
→
filter
P
(<[
i
:
=
x
]>
m
)
=
filter
P
(
delete
i
m
).
Proof
.
intros
.
rewrite
<
insert_delete
by
done
.
rewrite
map_filter_insert_not'
;
[
done
..].
rewrite
lookup_delete
;
done
.
Qed
.
Lemma
map_filter_delete
m
i
:
filter
P
(
delete
i
m
)
=
delete
i
(
filter
P
m
).
Proof
.
apply
map_eq
.
intros
j
.
apply
option_eq
;
intros
y
.
...
...
@@ 1200,6 +1227,24 @@ Section map_filter.
Qed
.
End
map_filter
.
Lemma
map_filter_fmap
{
A
A2
}
(
P
:
K
*
A
→
Prop
)
`
{!
∀
x
,
Decision
(
P
x
)}
(
f
:
A2
→
A
)
(
m
:
M
A2
)
:
filter
P
(
f
<$>
m
)
=
f
<$>
filter
(
λ
'
(
k
,
v
),
P
(
k
,
(
f
v
)))
m
.
Proof
.
apply
map_eq
.
intros
i
.
apply
option_eq
;
intros
x
.
repeat
(
rewrite
lookup_fmap
,
fmap_Some

setoid_rewrite
map_filter_lookup_Some
).
naive_solver
.
Qed
.
Lemma
map_filter_iff
{
A
}
(
P1
P2
:
K
*
A
→
Prop
)
`
{!
∀
x
,
Decision
(
P1
x
),
!
∀
x
,
Decision
(
P2
x
)}
(
m
:
M
A
)
:
(
∀
x
,
P1
x
↔
P2
x
)
→
filter
P1
m
=
filter
P2
m
.
Proof
.
intros
HPiff
.
rewrite
!
map_filter_alt
.
f_equal
.
apply
list_filter_iff
.
done
.
Qed
.
(** ** Properties of the [map_Forall] predicate *)
Section
map_Forall
.
Context
{
A
}
(
P
:
K
→
A
→
Prop
).
...
...
theories/list.v
View file @
653cb9db
...
...
@@ 1791,6 +1791,17 @@ Section filter.
Qed
.
End
filter
.
Lemma
list_filter_iff
(
P1
P2
:
A
→
Prop
)
`
{!
∀
x
,
Decision
(
P1
x
),
!
∀
x
,
Decision
(
P2
x
)}
(
l
:
list
A
)
:
(
∀
x
,
P1
x
↔
P2
x
)
→
filter
P1
l
=
filter
P2
l
.
Proof
.
intros
HPiff
.
induction
l
as
[
a
l
IH
]
;
[
done
].
destruct
(
decide
(
P1
a
)).

rewrite
!
filter_cons_True
by
naive_solver
.
by
rewrite
IH
.

rewrite
!
filter_cons_False
by
naive_solver
.
by
rewrite
IH
.
Qed
.
(** ** Properties of the [prefix] and [suffix] predicates *)
Global
Instance
:
PreOrder
(@
prefix
A
).
Proof
.
...
...
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