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Dan Frumin
iris-coq
Commits
100a7b9d
Commit
100a7b9d
authored
Dec 15, 2015
by
Robbert Krebbers
Browse files
Extensionality of map on setoid equality on finite maps.
parent
92a22d63
Changes
1
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prelude/fin_maps.v
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100a7b9d
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@@ -536,6 +536,12 @@ Proof. apply map_eq; intros i; by rewrite lookup_fmap, option_fmap_id. Qed.
Lemma
map_fmap_compose
{
A
B
C
}
(
f
:
A
→
B
)
(
g
:
B
→
C
)
(
m
:
M
A
)
:
g
∘
f
<
$
>
m
=
g
<
$
>
f
<
$
>
m
.
Proof
.
apply
map_eq
;
intros
i
;
by
rewrite
!
lookup_fmap
,
option_fmap_compose
.
Qed
.
Lemma
map_fmap_setoid_ext
`
{
Equiv
A
,
Equiv
B
}
(
f1
f2
:
A
→
B
)
m
:
(
∀
i
x
,
m
!!
i
=
Some
x
→
f1
x
≡
f2
x
)
→
f1
<
$
>
m
≡
f2
<
$
>
m
.
Proof
.
intros
Hi
i
;
rewrite
!
lookup_fmap
.
destruct
(
m
!!
i
)
eqn
:?
;
constructor
;
eauto
.
Qed
.
Lemma
map_fmap_ext
{
A
B
}
(
f1
f2
:
A
→
B
)
m
:
(
∀
i
x
,
m
!!
i
=
Some
x
→
f1
x
=
f2
x
)
→
f1
<
$
>
m
=
f2
<
$
>
m
.
Proof
.
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