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Marianna Rapoport
iris-coq
Commits
0d69828b
Commit
0d69828b
authored
Nov 18, 2015
by
Robbert Krebbers
Browse files
Owning units.
parent
764f0e4b
Changes
1
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Inline
Side-by-side
iris/logic.v
View file @
0d69828b
...
...
@@ -471,6 +471,15 @@ Proof.
rewrite
(
associative
op
),
<-(
commutative
op
z1
),
<-!(
associative
op
),
<-
Hy2
.
by
rewrite
(
associative
op
),
(
commutative
op
z1
),
<-
Hy1
.
Qed
.
Lemma
uPred_own_unit
(
a
:
M
)
:
uPred_own
(
unit
a
)
≡
(
□
uPred_own
(
unit
a
))%
I
.
Proof
.
intros
x
n
;
split
;
[
intros
[
a'
Hx
]|
by
apply
uPred_always_necessity
].
assert
(
∃
a''
,
unit
(
unit
a
⋅
a'
)
≡
unit
(
unit
a
)
⋅
a''
)
as
[
a''
Ha
]
by
(
rewrite
<-
ra_included_spec
;
auto
using
ra_unit_weaken
).
by
exists
a''
;
rewrite
Hx
,
Ha
,
ra_unit_idempotent
.
Qed
.
Lemma
uPred_own_empty
`
{
Empty
M
,
!
RAEmpty
M
}
:
True
%
I
⊆
uPred_own
∅
.
Proof
.
intros
x
[|
n
]
??
;
[
done
|].
by
exists
x
;
rewrite
(
left_id
_
_
).
Qed
.
Lemma
uPred_own_valid
(
a
:
M
)
:
uPred_own
a
⊆
uPred_valid
a
.
Proof
.
intros
x
n
Hv
[
a'
Hx
]
;
simpl
;
rewrite
Hx
in
Hv
;
eauto
using
cmra_valid_op_l
.
...
...
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