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stdpp
Commits
ec71b502
Commit
ec71b502
authored
May 25, 2017
by
Robbert Krebbers
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Version of map_fold_insert for Leibniz equality.
parent
2db8a61c
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theories/fin_maps.v
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theories/fin_maps.v
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ec71b502
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@@ -947,6 +947,14 @@ Proof.
-
by
eapply
elem_of_map_to_list
,
elem_of_list_lookup_2
.
Qed
.
Lemma
map_fold_insert_L
{
A
B
}
(
f
:
K
→
A
→
B
→
B
)
(
b
:
B
)
(
i
:
K
)
(
x
:
A
)
(
m
:
M
A
)
:
(
∀
j1
j2
z1
z2
y
,
j1
≠
j2
→
<[
i
:
=
x
]>
m
!!
j1
=
Some
z1
→
<[
i
:
=
x
]>
m
!!
j2
=
Some
z2
→
f
j1
z1
(
f
j2
z2
y
)
=
f
j2
z2
(
f
j1
z1
y
))
→
m
!!
i
=
None
→
map_fold
f
b
(<[
i
:
=
x
]>
m
)
=
f
i
x
(
map_fold
f
b
m
).
Proof
.
apply
map_fold_insert
;
apply
_
.
Qed
.
Lemma
map_fold_ind
{
A
B
}
(
P
:
B
→
M
A
→
Prop
)
(
f
:
K
→
A
→
B
→
B
)
(
b
:
B
)
:
P
b
∅
→
(
∀
i
x
m
r
,
m
!!
i
=
None
→
P
r
m
→
P
(
f
i
x
r
)
(<[
i
:
=
x
]>
m
))
→
...
...
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