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Iris
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af8c793f
Commit
af8c793f
authored
Nov 15, 2016
by
Robbert Krebbers
Browse files
Prove map_to_list {[i:=x]} = [(i,x)].
parent
712e8666
Changes
1
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prelude/fin_maps.v
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af8c793f
...
...
@@ -687,6 +687,12 @@ Proof.
rewrite
elem_of_map_to_list
in
Hlookup
.
congruence
.
-
by
rewrite
!
map_of_to_list
.
Qed
.
Lemma
map_to_list_singleton
{
A
}
i
(
x
:
A
)
:
map_to_list
{[
i
:
=
x
]}
=
[(
i
,
x
)].
Proof
.
apply
Permutation_singleton
.
unfold
singletonM
,
map_singleton
.
by
rewrite
map_to_list_insert
,
map_to_list_empty
by
auto
using
lookup_empty
.
Qed
.
Lemma
map_to_list_contains
{
A
}
(
m1
m2
:
M
A
)
:
m1
⊆
m2
→
map_to_list
m1
`
contains
`
map_to_list
m2
.
Proof
.
...
...
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