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David Swasey
coq-stdpp
Commits
60c8d501
Commit
60c8d501
authored
Jun 05, 2015
by
Robbert Krebbers
Browse files
Add fin_map_dom lemmas for Leibniz equality.
parent
3cbd41e4
Changes
1
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Inline
Side-by-side
theories/fin_map_dom.v
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60c8d501
...
...
@@ -111,4 +111,27 @@ Proof.
rewrite
!
elem_of_dom
,
lookup_fmap
,
<-!
not_eq_None_Some
.
destruct
(
m
!!
i
)
;
naive_solver
.
Qed
.
Context
`
{!
LeibnizEquiv
D
}.
Lemma
dom_empty_L
{
A
}
:
dom
D
(@
empty
(
M
A
)
_
)
=
∅
.
Proof
.
unfold_leibniz
;
apply
dom_empty
.
Qed
.
Lemma
dom_empty_inv_L
{
A
}
(
m
:
M
A
)
:
dom
D
m
=
∅
→
m
=
∅
.
Proof
.
by
intros
;
apply
dom_empty_inv
;
unfold_leibniz
.
Qed
.
Lemma
dom_alter_L
{
A
}
f
(
m
:
M
A
)
i
:
dom
D
(
alter
f
i
m
)
=
dom
D
m
.
Proof
.
unfold_leibniz
;
apply
dom_alter
.
Qed
.
Lemma
dom_insert_L
{
A
}
(
m
:
M
A
)
i
x
:
dom
D
(<[
i
:
=
x
]>
m
)
=
{[
i
]}
∪
dom
D
m
.
Proof
.
unfold_leibniz
;
apply
dom_insert
.
Qed
.
Lemma
dom_singleton_L
{
A
}
(
i
:
K
)
(
x
:
A
)
:
dom
D
{[(
i
,
x
)]}
=
{[
i
]}.
Proof
.
unfold_leibniz
;
apply
dom_singleton
.
Qed
.
Lemma
dom_delete_L
{
A
}
(
m
:
M
A
)
i
:
dom
D
(
delete
i
m
)
=
dom
D
m
∖
{[
i
]}.
Proof
.
unfold_leibniz
;
apply
dom_delete
.
Qed
.
Lemma
dom_union_L
{
A
}
(
m1
m2
:
M
A
)
:
dom
D
(
m1
∪
m2
)
=
dom
D
m1
∪
dom
D
m2
.
Proof
.
unfold_leibniz
;
apply
dom_union
.
Qed
.
Lemma
dom_intersection_L
{
A
}
(
m1
m2
:
M
A
)
:
dom
D
(
m1
∩
m2
)
=
dom
D
m1
∩
dom
D
m2
.
Proof
.
unfold_leibniz
;
apply
dom_intersection
.
Qed
.
Lemma
dom_difference_L
{
A
}
(
m1
m2
:
M
A
)
:
dom
D
(
m1
∖
m2
)
=
dom
D
m1
∖
dom
D
m2
.
Proof
.
unfold_leibniz
;
apply
dom_difference
.
Qed
.
Lemma
dom_fmap_L
{
A
B
}
(
f
:
A
→
B
)
m
:
dom
D
(
f
<$>
m
)
=
dom
D
m
.
Proof
.
unfold_leibniz
;
apply
dom_fmap
.
Qed
.
End
fin_map_dom
.
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