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Joshua Yanovski
iris-coq
Commits
ce61436f
Commit
ce61436f
authored
Feb 10, 2016
by
Robbert Krebbers
Browse files
Seperate derived rules for own and valid in upred.
parent
6c686e78
Changes
1
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Side-by-side
algebra/upred.v
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ce61436f
...
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@@ -826,17 +826,19 @@ 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
)
.
Proof
.
move
=>
x
n
Hv
[
a
'
?
];
cofe_subst
;
eauto
using
cmra_validN_op_l
.
Qed
.
Lemma
valid_intro
{
A
:
cmraT
}
(
a
:
A
)
:
✓
a
→
True
⊑
(
✓
a
)
.
Lemma
own_valid
(
a
:
M
)
:
uPred_own
a
⊑
✓
a
.
Proof
.
intros
x
n
Hv
[
a
'
?
];
cofe_subst
;
eauto
using
cmra_validN_op_l
.
Qed
.
Lemma
valid_intro
{
A
:
cmraT
}
(
a
:
A
)
:
✓
a
→
True
⊑
✓
a
.
Proof
.
by
intros
?
x
n
?
_
;
simpl
;
apply
cmra_valid_validN
.
Qed
.
Lemma
valid_elim
{
A
:
cmraT
}
(
a
:
A
)
:
¬
✓
{
1
}
a
→
(
✓
a
)
⊑
False
.
Lemma
valid_elim
{
A
:
cmraT
}
(
a
:
A
)
:
¬
✓
{
1
}
a
→
✓
a
⊑
False
.
Proof
.
intros
Ha
x
[
|
n
]
??
;
[
|
apply
Ha
,
cmra_validN_le
with
(
S
n
)];
auto
.
Qed
.
Lemma
valid_mono
{
A
B
:
cmraT
}
(
a
:
A
)
(
b
:
B
)
:
(
∀
n
,
✓
{
n
}
a
→
✓
{
n
}
b
)
→
(
✓
a
)
⊑
(
✓
b
)
.
(
∀
n
,
✓
{
n
}
a
→
✓
{
n
}
b
)
→
✓
a
⊑
✓
b
.
Proof
.
by
intros
?
x
n
?
;
simpl
;
auto
.
Qed
.
Lemma
always_valid
{
A
:
cmraT
}
(
a
:
A
)
:
(
□
(
✓
a
))
%
I
≡
(
✓
a
:
uPred
M
)
%
I
.
Proof
.
done
.
Qed
.
(
*
Own
and
valid
derived
*
)
Lemma
own_invalid
(
a
:
M
)
:
¬
✓
{
1
}
a
→
uPred_own
a
⊑
False
.
Proof
.
by
intros
;
rewrite
own_valid
valid_elim
.
Qed
.
...
...
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