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stdpp
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3544168c
Commit
3544168c
authored
Sep 06, 2017
by
Robbert Krebbers
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Put delete_singleton lemmas together.
parent
d9dd7c5e
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theories/fin_maps.v
theories/fin_maps.v
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theories/fin_maps.v
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3544168c
...
...
@@ -396,8 +396,6 @@ Proof.
Qed
.
Lemma
delete_empty
{
A
}
i
:
delete
i
(
∅
:
M
A
)
=
∅
.
Proof
.
rewrite
<-(
partial_alter_self
∅
)
at
2
.
by
rewrite
lookup_empty
.
Qed
.
Lemma
delete_singleton
{
A
}
i
(
x
:
A
)
:
delete
i
{[
i
:
=
x
]}
=
∅
.
Proof
.
setoid_rewrite
<-
partial_alter_compose
.
apply
delete_empty
.
Qed
.
Lemma
delete_commute
{
A
}
(
m
:
M
A
)
i
j
:
delete
i
(
delete
j
m
)
=
delete
j
(
delete
i
m
).
Proof
.
destruct
(
decide
(
i
=
j
)).
by
subst
.
by
apply
partial_alter_commute
.
Qed
.
...
...
@@ -578,8 +576,10 @@ Proof.
Qed
.
Lemma
singleton_non_empty
{
A
}
i
(
x
:
A
)
:
{[
i
:
=
x
]}
≠
∅
.
Proof
.
apply
insert_non_empty
.
Qed
.
Lemma
delete_singleton
{
A
}
i
(
x
:
A
)
:
delete
i
{[
i
:
=
x
]}
=
∅
.
Proof
.
setoid_rewrite
<-
partial_alter_compose
.
apply
delete_empty
.
Qed
.
Lemma
delete_singleton_ne
{
A
}
i
j
(
x
:
A
)
:
j
≠
i
→
delete
i
{[
j
:
=
x
]}
=
{[
j
:
=
x
]}.
j
≠
i
→
delete
i
{[
j
:
=
x
]}
=
{[
j
:
=
x
]}.
Proof
.
intro
.
apply
delete_notin
.
by
apply
lookup_singleton_ne
.
Qed
.
(** ** Properties of the map operations *)
...
...
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