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David Swasey
coq-stdpp
Commits
bd4a6a84
Commit
bd4a6a84
authored
Mar 06, 2018
by
Robbert Krebbers
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Prove `map_fmap_empty_inv`.
parent
4c60de24
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theories/fin_maps.v
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bd4a6a84
...
...
@@ -261,6 +261,11 @@ Proof.
Qed
.
Lemma
map_fmap_empty
{
A
B
}
(
f
:
A
→
B
)
:
f
<$>
(
∅
:
M
A
)
=
∅
.
Proof
.
by
apply
map_eq
;
intros
i
;
rewrite
lookup_fmap
,
!
lookup_empty
.
Qed
.
Lemma
map_fmap_empty_inv
{
A
B
}
(
f
:
A
→
B
)
m
:
f
<$>
m
=
∅
→
m
=
∅
.
Proof
.
intros
Hm
.
apply
map_eq
;
intros
i
.
generalize
(
f_equal
(
lookup
i
)
Hm
).
by
rewrite
lookup_fmap
,
!
lookup_empty
,
fmap_None
.
Qed
.
Lemma
map_subset_alt
{
A
}
(
m1
m2
:
M
A
)
:
m1
⊂
m2
↔
m1
⊆
m2
∧
∃
i
,
m1
!!
i
=
None
∧
is_Some
(
m2
!!
i
).
...
...
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