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Marianna Rapoport
iris-coq
Commits
82511560
Commit
82511560
authored
Feb 05, 2016
by
Ralf Jung
Browse files
show that we always own something
parent
79d2785b
Changes
1
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Inline
Side-by-side
program_logic/upred.v
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82511560
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@@ -786,7 +786,7 @@ Proof. intros; rewrite -always_and_sep_l; auto. Qed.
Lemma
always_entails_r
P
Q
:
(
P
⊑
□
Q
)
→
P
⊑
(
P
★
□
Q
).
Proof
.
intros
;
rewrite
-
always_and_sep_r
;
auto
.
Qed
.
(* Own *)
(* Own
and valid
*)
Lemma
own_op
(
a1
a2
:
M
)
:
uPred_own
(
a1
⋅
a2
)
≡
(
uPred_own
a1
★
uPred_own
a2
)%
I
.
Proof
.
...
...
@@ -805,6 +805,8 @@ Proof.
Qed
.
Lemma
always_own
(
a
:
M
)
:
unit
a
≡
a
→
(
□
uPred_own
a
)%
I
≡
uPred_own
a
.
Proof
.
by
intros
<-
;
rewrite
always_own_unit
.
Qed
.
Lemma
own_something
:
True
⊑
∃
a
,
uPred_own
a
.
Proof
.
intros
x
[|
n
]
??
;
[
done
|].
by
exists
x
;
simpl
.
Qed
.
Lemma
own_empty
`
{
Empty
M
,
!
CMRAIdentity
M
}
:
True
⊑
uPred_own
∅
.
Proof
.
intros
x
[|
n
]
??
;
[
done
|].
by
exists
x
;
rewrite
(
left_id
_
_
).
Qed
.
Lemma
own_valid
(
a
:
M
)
:
uPred_own
a
⊑
(
✓
a
).
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