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Jonas Kastberg
iris
Commits
4d646c6d
Commit
4d646c6d
authored
Jan 15, 2016
by
Robbert Krebbers
Browse files
Lemma about big_opM and delete.
parent
24c3871c
Changes
1
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Side-by-side
modures/ra.v
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4d646c6d
...
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@@ -146,6 +146,11 @@ Proof. unfold big_opM. by rewrite map_to_list_empty. Qed.
Lemma
big_opM_insert
(
m
:
M
A
)
i
x
:
m
!!
i
=
None
→
big_opM
(<[
i
:
=
x
]>
m
)
≡
x
⋅
big_opM
m
.
Proof
.
intros
?
;
by
rewrite
/
big_opM
map_to_list_insert
.
Qed
.
Lemma
big_opM_delete
(
m
:
M
A
)
i
x
:
m
!!
i
=
Some
x
→
x
⋅
big_opM
(
delete
i
m
)
≡
big_opM
m
.
Proof
.
intros
.
by
rewrite
-{
2
}(
insert_delete
m
i
x
)
//
big_opM_insert
?lookup_delete
.
Qed
.
Lemma
big_opM_singleton
i
x
:
big_opM
({[
i
↦
x
]}
:
M
A
)
≡
x
.
Proof
.
rewrite
-
insert_empty
big_opM_insert
/=
;
last
auto
using
lookup_empty
.
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...
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