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stdpp
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a26ede46
Commit
a26ede46
authored
Sep 23, 2016
by
Robbert Krebbers
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Relate map_to_list to nil.
parent
8f263269
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theories/fin_maps.v
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theories/fin_maps.v
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a26ede46
...
...
@@ -707,6 +707,11 @@ Lemma map_to_list_empty_inv_alt {A} (m : M A) : map_to_list m ≡ₚ [] → m =
Proof
.
rewrite
<-
map_to_list_empty
.
apply
map_to_list_inj
.
Qed
.
Lemma
map_to_list_empty_inv
{
A
}
(
m
:
M
A
)
:
map_to_list
m
=
[]
→
m
=
∅
.
Proof
.
intros
Hm
.
apply
map_to_list_empty_inv_alt
.
by
rewrite
Hm
.
Qed
.
Lemma
map_to_list_empty'
{
A
}
(
m
:
M
A
)
:
map_to_list
m
=
[]
↔
m
=
∅
.
Proof
.
split
.
apply
map_to_list_empty_inv
.
intros
->.
apply
map_to_list_empty
.
Qed
.
Lemma
map_to_list_insert_inv
{
A
}
(
m
:
M
A
)
l
i
x
:
map_to_list
m
≡
ₚ
(
i
,
x
)
::
l
→
m
=
<[
i
:
=
x
]>(
map_of_list
l
).
Proof
.
...
...
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