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stdpp
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498fe5f9
Commit
498fe5f9
authored
Nov 30, 2018
by
Robbert Krebbers
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Bit of clean up.
parent
1cbda487
Pipeline
#13181
passed with stage
in 7 minutes and 44 seconds
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theories/fin_maps.v
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theories/fin_maps.v
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498fe5f9
...
...
@@ -1032,7 +1032,7 @@ Proof.
Qed
.
(** ** The filter operation *)
Section
map_
F
ilter
.
Section
map_
f
ilter
.
Context
{
A
}
(
P
:
K
*
A
→
Prop
)
`
{!
∀
x
,
Decision
(
P
x
)}.
Implicit
Types
m
:
M
A
.
...
...
@@ -1085,7 +1085,7 @@ Section map_Filter.
Lemma
map_filter_empty
:
filter
P
(
∅
:
M
A
)
=
∅
.
Proof
.
apply
map_fold_empty
.
Qed
.
End
map_
F
ilter
.
End
map_
f
ilter
.
(** ** Properties of the [map_Forall] predicate *)
Section
map_Forall
.
...
...
@@ -1521,19 +1521,16 @@ Proof.
Qed
.
Global
Instance
:
IdemP
(=@{
M
A
})
(
∪
).
Proof
.
intros
A
?.
by
apply
union_with_idemp
.
Qed
.
Lemma
lookup_union
{
A
}
(
m1
m2
:
M
A
)
i
:
(
m1
∪
m2
)
!!
i
=
union_with
(
λ
x
_
,
Some
x
)
(
m1
!!
i
)
(
m2
!!
i
).
Proof
.
apply
lookup_union_with
.
Qed
.
Lemma
lookup_union_Some_raw
{
A
}
(
m1
m2
:
M
A
)
i
x
:
(
m1
∪
m2
)
!!
i
=
Some
x
↔
m1
!!
i
=
Some
x
∨
(
m1
!!
i
=
None
∧
m2
!!
i
=
Some
x
).
Proof
.
unfold
union
,
map_union
,
union_with
,
map_union_with
.
rewrite
(
lookup_merge
_
).
destruct
(
m1
!!
i
),
(
m2
!!
i
)
;
compute
;
intuition
congruence
.
Qed
.
Proof
.
rewrite
lookup_union
.
destruct
(
m1
!!
i
),
(
m2
!!
i
)
;
naive_solver
.
Qed
.
Lemma
lookup_union_None
{
A
}
(
m1
m2
:
M
A
)
i
:
(
m1
∪
m2
)
!!
i
=
None
↔
m1
!!
i
=
None
∧
m2
!!
i
=
None
.
Proof
.
unfold
union
,
map_union
,
union_with
,
map_union_with
.
rewrite
(
lookup_merge
_
).
destruct
(
m1
!!
i
),
(
m2
!!
i
)
;
compute
;
intuition
congruence
.
Qed
.
Proof
.
rewrite
lookup_union
.
destruct
(
m1
!!
i
),
(
m2
!!
i
)
;
naive_solver
.
Qed
.
Lemma
map_positive_l
{
A
}
(
m1
m2
:
M
A
)
:
m1
∪
m2
=
∅
→
m1
=
∅
.
Proof
.
intros
Hm
.
apply
map_empty
.
intros
i
.
apply
(
f_equal
(!!
i
))
in
Hm
.
...
...
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