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Joshua Yanovski
iriscoq
Commits
4a154f08
Commit
4a154f08
authored
Mar 20, 2017
by
Robbert Krebbers
Browse files
Remove duplicate lemmas for agree.
parent
0b908b36
Changes
3
Hide whitespace changes
Inline
Sidebyside
theories/algebra/agree.v
View file @
4a154f08
...
...
@@ 292,6 +292,7 @@ Proof.

simpl
.
destruct
Ha
as
[
>
Ha
];
set_solver
.

simpl
.
set_solver
+
.
Qed
.
Lemma
agree_op_invN
n
(
x1
x2
:
agree
A
)
:
✓
{
n
}
(
x1
⋅
x2
)
→
x1
≡
{
n
}
≡
x2
.
Proof
.
intros
Hxy
.
split
;
apply
agree_op_inv_inclN
;
first
done
.
by
rewrite
comm
.
...
...
@@ 325,13 +326,7 @@ Proof. rewrite /CMRATotal; eauto. Qed.
Global
Instance
agree_persistent
(
x
:
agree
A
)
:
Persistent
x
.
Proof
.
by
constructor
.
Qed
.
Lemma
agree_op_inv
(
x1
x2
:
agree
A
)
:
✓
(
x1
⋅
x2
)
→
x1
≡
x2
.
Proof
.
intros
?
.
apply
equiv_dist
=>
n
.
by
apply
agree_op_invN
,
cmra_valid_validN
.
Qed
.
Global
Instance
agree_discrete
:
Discrete
A
→
CMRADiscrete
agreeR
.
Global
Instance
agree_discrete
:
Discrete
A
→
CMRADiscrete
agreeR
.
Proof
.
intros
HD
.
split
.

intros
x
y
Hxy
n
.
eapply
list_setequiv_subrel
;
last
exact
Hxy
.
clear

HD
.
...
...
@@ 354,22 +349,18 @@ Global Instance to_agree_proper : Proper ((≡) ==> (≡)) to_agree := ne_proper
Global
Instance
to_agree_injN
n
:
Inj
(
dist
n
)
(
dist
n
)
(
to_agree
).
Proof
.
intros
a
b
[
Hxy
%
list_setincl_singleton_rev
_
].
done
.
Qed
.
Global
Instance
to_agree_inj
:
Inj
(
≡
)
(
≡
)
(
to_agree
).
Proof
.
intros
a
b
?
.
apply
equiv_dist
=>
n
.
apply
to_agree_injN
.
by
apply
equiv_dist
.
Qed
.
Proof
.
intros
a
b
?
.
apply
equiv_dist
=>
n
.
by
apply
to_agree_injN
,
equiv_dist
.
Qed
.
Lemma
to_agree_uninjN
n
(
x
:
agree
A
)
:
✓
{
n
}
x
→
∃
y
:
A
,
to_agree
y
≡
{
n
}
≡
x
.
Proof
.
intros
Hl
.
exists
(
agree_car
x
).
rewrite
/
dist
/
agree_dist
/=
.
split
.
intros
Hl
.
exists
(
agree_car
x
).
rewrite
/
dist
/
agree_dist
/=
.
split
.

apply
:
list_setincl_singleton_in
.
set_solver
+
.

apply
(
list_agrees_iff_setincl
_
);
first
set_solver
+
.
done
.
Qed
.
Lemma
to_agree_uninj
(
x
:
agree
A
)
:
✓
x
→
∃
y
:
A
,
to_agree
y
≡
x
.
Proof
.
intros
Hl
.
exists
(
agree_car
x
).
rewrite
/
dist
/
agree_dist
/=
.
split
.
intros
Hl
.
exists
(
agree_car
x
).
rewrite
/
dist
/
agree_dist
/=
.
split
.

apply
:
list_setincl_singleton_in
.
set_solver
+
.

apply
(
list_agrees_iff_setincl
_
);
first
set_solver
+
.
eapply
list_agrees_subrel
;
last
exact
:
Hl
;
[
apply
_.
.

].
...
...
@@ 383,22 +374,7 @@ Proof.
(
*
TODO
:
This
could
become
a
generic
lemma
about
list_setincl
.
*
)
destruct
(
Hincl
a
)
as
(
?
&
>%
elem_of_list_singleton
&
?
);
first
set_solver
+
.
done
.

intros
Hab
.
rewrite
Hab
.
eexists
.
symmetry
.
eapply
agree_idemp
.
Qed
.
Lemma
to_agree_comp_validN
n
(
a
b
:
A
)
:
✓
{
n
}
(
to_agree
a
⋅
to_agree
b
)
↔
a
≡
{
n
}
≡
b
.
Proof
.
split
.

(
*
TODO
:
can
this
be
derived
from
other
stuff
?
Otherwise
,
should
probably
become
sth
.
generic
about
list_agrees
.
*
)
intros
Hv
.
apply
Hv
;
simpl
;
set_solver
.

intros
>
.
rewrite
agree_idemp
.
done
.
Qed
.
Lemma
to_agree_comp_valid
(
a
b
:
A
)
:
✓
(
to_agree
a
⋅
to_agree
b
)
↔
a
≡
b
.
Proof
.
rewrite
cmra_valid_validN
equiv_dist
.
by
setoid_rewrite
to_agree_comp_validN
.

by
intros
>
.
Qed
.
Global
Instance
agree_cancelable
(
x
:
agree
A
)
:
Cancelable
x
.
...
...
@@ 409,12 +385,22 @@ Proof.
destruct
(
to_agree_uninjN
n
z
)
as
[
z
'
EQz
].
{
eapply
(
cmra_validN_op_r
n
x
z
).
by
rewrite

Heq
.
}
assert
(
Hx
'
y
'
:
x
'
≡
{
n
}
≡
y
'
).
{
apply
to_agree
_comp_valid
N
.
by
rewrite
EQx
EQy
.
}
{
apply
(
inj
to_agree
),
agree_op_inv
N
.
by
rewrite
EQx
EQy
.
}
assert
(
Hx
'z
'
:
x
'
≡
{
n
}
≡
z
'
).
{
apply
to_agree
_comp_valid
N
.
by
rewrite
EQx
EQz

Heq
.
}
{
apply
(
inj
to_agree
),
agree_op_inv
N
.
by
rewrite
EQx
EQz

Heq
.
}
by
rewrite

EQy

EQz

Hx
'
y
'

Hx
'z
'
.
Qed
.
Lemma
agree_op_inv
(
x1
x2
:
agree
A
)
:
✓
(
x1
⋅
x2
)
→
x1
≡
x2
.
Proof
.
intros
?
.
apply
equiv_dist
=>
n
.
by
apply
agree_op_invN
,
cmra_valid_validN
.
Qed
.
Lemma
agree_op_inv
'
(
a1
a2
:
A
)
:
✓
(
to_agree
a1
⋅
to_agree
a2
)
→
a1
≡
a2
.
Proof
.
by
intros
?%
agree_op_inv
%
(
inj
_
).
Qed
.
Lemma
agree_op_invL
'
`
{!
LeibnizEquiv
A
}
(
a1
a2
:
A
)
:
✓
(
to_agree
a1
⋅
to_agree
a2
)
→
a1
=
a2
.
Proof
.
by
intros
?%
agree_op_inv
'
%
leibniz_equiv
.
Qed
.
(
**
Internalized
properties
*
)
Lemma
agree_equivI
{
M
}
a
b
:
to_agree
a
≡
to_agree
b
⊣⊢
(
a
≡
b
:
uPred
M
).
Proof
.
...
...
theories/base_logic/lib/gen_heap.v
View file @
4a154f08
...
...
@@ 95,7 +95,7 @@ Section gen_heap.
apply
wand_intro_r
.
rewrite
mapsto_eq

own_op

auth_frag_op
own_valid
discrete_valid
.
f_equiv
=>
/
auth_own_valid
/=
.
rewrite
op_singleton
singleton_valid
pair_op
.
by
intros
[
_
?%
agree_op_inv
%
(
inj
to_agree
)
%
leibniz_equiv
].
by
intros
[
_
?%
agree_op_inv
L
'
].
Qed
.
Global
Instance
ex_mapsto_fractional
l
:
Fractional
(
λ
q
,
l
↦
{
q
}

)
%
I
.
...
...
theories/tests/one_shot.v
View file @
4a154f08
...
...
@@ 75,11 +75,10 @@ Proof.
{
by
wp_match
.
}
wp_match
.
wp_bind
(
!
_
)
%
E
.
iInv
N
as
">[[Hl Hγ]H]"
"Hclose"
;
last
iDestruct
"H"
as
(
m
'
)
"[Hl Hγ]"
.
{
iCombine
"Hγ"
"Hγ'"
as
"Hγ"
.
by
iDestruct
(
own_valid
with
"Hγ"
)
as
%?
.
}
{
by
iDestruct
(
own_valid
_2
with
"Hγ
Hγ'
"
)
as
%?
.
}
wp_load
.
iCombine
"Hγ"
"Hγ'"
as
"Hγ"
.
iDestruct
(
own_valid
with
"Hγ"
)
as
%?%
agree_op_inv
%
to_agree_inj
.
fold_leibniz
.
subst
.
iMod
(
"Hclose"
with
"[Hl]"
)
as
"_"
.
iDestruct
(
own_valid_2
with
"Hγ Hγ'"
)
as
%?%
agree_op_invL
'
;
subst
.
iMod
(
"Hclose"
with
"[Hl]"
)
as
"_"
.
{
iNext
;
iRight
;
by
eauto
.
}
iModIntro
.
wp_match
.
iApply
wp_assert
.
wp_op
=>?
;
simplify_eq
/=
;
eauto
.
Qed
.
...
...
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