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Tej Chajed
iris
Commits
ef7ea67f
Commit
ef7ea67f
authored
Feb 04, 2016
by
Robbert Krebbers
Browse files
Some cleanup in upred.
parent
f402c1cc
Changes
1
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Inline
Sidebyside
logic/upred.v
View file @
ef7ea67f
...
...
@@ 812,9 +812,7 @@ 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
).
Proof
.
by
intros
?
x
n
?
_;
simpl
;
apply
cmra_valid_validN
.
Qed
.
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
with
lia
.
Qed
.
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
).
Proof
.
by
intros
?
x
n
?
;
simpl
;
auto
.
Qed
.
...
...
@@ 832,26 +830,20 @@ Global Instance uPred_big_and_perm : Proper ((≡ₚ) ==> (≡)) (@uPred_big_and
Proof
.
induction
1
as
[
P
Ps
Qs
?
IH

P
Q
Ps
]
;
simpl
;
auto
.
*
by
rewrite
IH
.
*
by
rewrite
!
(
associative
_
)
(
commutative
_
P
).
*
by
rewrite
!
associative
(
commutative
_
P
).
*
etransitivity
;
eauto
.
Qed
.
Global
Instance
uPred_big_sep_perm
:
Proper
((
≡
ₚ
)
==>
(
≡
))
(@
uPred_big_sep
M
).
Proof
.
induction
1
as
[
P
Ps
Qs
?
IH

P
Q
Ps
]
;
simpl
;
auto
.
*
by
rewrite
IH
.
*
by
rewrite
!
(
associative
_
)
(
commutative
_
P
).
*
by
rewrite
!
associative
(
commutative
_
P
).
*
etransitivity
;
eauto
.
Qed
.
Lemma
uPred_big_and_app
Ps
Qs
:
(
Π
∧
(
Ps
++
Qs
))%
I
≡
(
Π
∧
Ps
∧
Π
∧
Qs
)%
I
.
Proof
.
by
induction
Ps
as
[
P
Ps
IH
]
;
rewrite
/=
?(
left_id
_
_
)
?(
associative
_
)
?IH
.
Qed
.
Proof
.
by
induction
Ps
as
[??
IH
]
;
rewrite
/=
?left_id

?associative
?IH
.
Qed
.
Lemma
uPred_big_sep_app
Ps
Qs
:
(
Π★
(
Ps
++
Qs
))%
I
≡
(
Π★
Ps
★
Π★
Qs
)%
I
.
Proof
.
by
induction
Ps
as
[
P
Ps
IH
]
;
rewrite
/=
?(
left_id
_
_
)
?(
associative
_
)
?IH
.
Qed
.
Proof
.
by
induction
Ps
as
[??
IH
]
;
rewrite
/=
?left_id

?associative
?IH
.
Qed
.
Lemma
uPred_big_sep_and
Ps
:
(
Π★
Ps
)
⊑
(
Π
∧
Ps
).
Proof
.
by
induction
Ps
as
[
P
Ps
IH
]
;
simpl
;
auto
.
Qed
.
Lemma
uPred_big_and_elem_of
Ps
P
:
P
∈
Ps
→
(
Π
∧
Ps
)
⊑
P
.
...
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