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George Pirlea
Iris
Commits
be74ad29
Commit
be74ad29
authored
Nov 21, 2016
by
Robbert Krebbers
Browse files
Prove f <$> to_gmap x X = to_gmap (f x) X.
parent
700a60a0
Changes
1
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prelude/gmap.v
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be74ad29
...
...
@@ -159,6 +159,12 @@ Proof.
elem_of_singleton
;
destruct
(
decide
(
i
=
j
))
;
intuition
.
Qed
.
Lemma
fmap_to_gmap
`
{
Countable
K
}
{
A
B
}
(
f
:
A
→
B
)
(
X
:
gset
K
)
(
x
:
A
)
:
f
<$>
to_gmap
x
X
=
to_gmap
(
f
x
)
X
.
Proof
.
apply
map_eq
;
intros
j
.
rewrite
lookup_fmap
,
!
lookup_to_gmap
.
by
simplify_option_eq
.
Qed
.
Lemma
to_gmap_dom
`
{
Countable
K
}
{
A
B
}
(
m
:
gmap
K
A
)
(
y
:
B
)
:
to_gmap
y
(
dom
_
m
)
=
const
y
<$>
m
.
Proof
.
...
...
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