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Jonas Kastberg
iris
Commits
af7b6da1
Commit
af7b6da1
authored
Jan 05, 2017
by
Ralf Jung
Browse files
Merge branch 'master' of
https://gitlab.mpisws.org/FP/iriscoq
parents
81ed7343
fb07db75
Changes
8
Hide whitespace changes
Inline
Sidebyside
README.md
View file @
af7b6da1
...
...
@@ 20,33 +20,35 @@ Run `make` to build the full development.
## Structure
*
The folder
[
prelude
](
prelude
)
contains an extended "Standard Library"
by
[
Robbert Krebbers
](
http://robbertkrebbers.nl/thesis.html
)
.
*
The folder
[
algebra
](
algebra
)
contains the COFE and CMRA
constructions as well
as the solver for recursive domain equations.
*
The folder
[
base_logic
](
base_logic
)
defines the Iris base logic and
the
primitive connectives. It also contains derived constructions that are
*
The folder
[
prelude
](
theories/
prelude
)
contains an extended "Standard Library"
by
[
Robbert Krebbers
](
http://robbertkrebbers.nl/thesis.html
)
.
*
The folder
[
algebra
](
theories/
algebra
)
contains the COFE and CMRA
constructions as well
as the solver for recursive domain equations.
*
The folder
[
base_logic
](
theories/
base_logic
)
defines the Iris base logic and
the
primitive connectives. It also contains derived constructions that are
entirely independent of the choice of resources.
*
The subfolder
[
lib
](
base_logic/lib
)
contains some generally useful
*
The subfolder
[
lib
](
theories/
base_logic/lib
)
contains some generally useful
derived constructions. Most importantly, it defines composeable
dynamic resources and ownership of them; the other constructions depend
on this setup.
*
The folder
[
program_logic
](
program_logic
)
specializes the base logic
to build
Iris, the program logic. This includes weakest preconditions that
are
defined for any language satisfying some generic axioms, and some derived
*
The folder
[
program_logic
](
theories/
program_logic
)
specializes the base logic
to build
Iris, the program logic. This includes weakest preconditions that
are
defined for any language satisfying some generic axioms, and some derived
constructions that work for any such language.
*
The folder
[
proofmode
](
proofmode
)
contains the Iris proof mode, which
extends
Coq with contexts for persistent and spatial Iris assertions. It also
contains
tactics for interactive proofs in Iris. Documentation can be found in
*
The folder
[
proofmode
](
theories/
proofmode
)
contains the Iris proof mode, which
extends
Coq with contexts for persistent and spatial Iris assertions. It also
contains
tactics for interactive proofs in Iris. Documentation can be found in
[
ProofMode.md
](
ProofMode.md
)
.
*
The folder
[
heap_lang
](
heap_lang
)
defines the MLlike concurrent heap language
*
The subfolder
[
lib
](
heap_lang/lib
)
contains a few derived constructions
within this language, e.g., parallel composition.
Most notable here is
[
lib/barrier
](
heap_lang/lib/barrier
)
, the implementation
and proof of a barrier as described in
<http://doi.acm.org/10.1145/2818638>
.
*
The folder
[
tests
](
tests
)
contains modules we use to test our infrastructure.
Users of the Iris Coq library should
*not*
depend on these modules; they may
change or disappear without any notice.
*
The folder
[
heap_lang
](
theories/heap_lang
)
defines the MLlike concurrent heap
language
*
The subfolder
[
lib
](
theories/heap_lang/lib
)
contains a few derived
constructions within this language, e.g., parallel composition.
Most notable here is
[
lib/barrier
](
theories/heap_lang/lib/barrier
)
, the
implementation and proof of a barrier as described in
<http://doi.acm.org/10.1145/2818638>
.
*
The folder
[
tests
](
theories/tests
)
contains modules we use to test our
infrastructure. Users of the Iris Coq library should
*not*
depend on these
modules; they may change or disappear without any notice.
## Documentation
...
...
theories/base_logic/lib/invariants.v
View file @
af7b6da1
...
...
@@ 28,44 +28,39 @@ Qed.
Global
Instance
inv_persistent
N
P
:
PersistentP
(
inv
N
P
).
Proof
.
rewrite
inv_eq
/
inv
;
apply
_
.
Qed
.
Lemma
fresh_inv_name
(
E
:
gset
positive
)
N
:
∃
i
,
i
∉
E
∧
i
∈
↑
N
.
Proof
.
exists
(
coPpick
(
↑
N
∖
coPset
.
of_gset
E
)).
rewrite

coPset
.
elem_of_of_gset
(
comm
and
)

elem_of_difference
.
apply
coPpick_elem_of
=>
Hfin
.
eapply
nclose_infinite
,
(
difference_finite_inv
_
_
),
Hfin
.
apply
of_gset_finite
.
Qed
.
Lemma
inv_alloc
N
E
P
:
▷
P
={
E
}=
∗
inv
N
P
.
Proof
.
rewrite
inv_eq
/
inv_def
fupd_eq
/
fupd_def
.
iIntros
"HP [Hw $]"
.
iMod
(
ownI_alloc
(
∈
↑
N
)
P
with
"[HP Hw]"
)
as
(
i
)
"(% & $ & ?)"
;
auto
.

intros
Ef
.
exists
(
coPpick
(
↑
N
∖
coPset
.
of_gset
Ef
)).
rewrite

coPset
.
elem_of_of_gset
comm

elem_of_difference
.
apply
coPpick_elem_of
=>
Hfin
.
eapply
nclose_infinite
,
(
difference_finite_inv
_
_
),
Hfin
.
apply
of_gset_finite
.

by
iFrame
.

rewrite
/
uPred_except_0
;
eauto
.
iMod
(
ownI_alloc
(
∈
↑
N
)
P
with
"[$HP $Hw]"
)
as
(
i
)
"(% & $ & ?)"
;
auto
using
fresh_inv_name
.
Qed
.
Lemma
inv_alloc_open
N
E
P
:
↑
N
⊆
E
→
True
={
E
,
E
∖↑
N
}=
∗
inv
N
P
∗
(
▷
P
={
E
∖↑
N
,
E
}=
∗
True
).
Proof
.
rewrite
inv_eq
/
inv_def
fupd_eq
/
fupd_def
.
iIntros
(
Sub
)
"[Hw HE]"
.
iMod
(
ownI_alloc_open
(
∈
↑
N
)
P
with
"Hw"
)
as
(
i
)
"(% & Hw & #Hi & HD)"
.

intros
Ef
.
exists
(
coPpick
(
↑
N
∖
coPset
.
of_gset
Ef
)).
rewrite

coPset
.
elem_of_of_gset
comm

elem_of_difference
.
apply
coPpick_elem_of
=>
Hfin
.
eapply
nclose_infinite
,
(
difference_finite_inv
_
_
),
Hfin
.
apply
of_gset_finite
.

iAssert
(
ownE
{[
i
]}
∗
ownE
(
↑
N
∖
{[
i
]})
∗
ownE
(
E
∖
↑
N
))%
I
with
"[HE]"
as
"(HEi & HEN\i & HE\N)"
.
{
rewrite

?ownE_op
;
[
set_solver

set_solver
].
rewrite
assoc_L
.
rewrite
<!
union_difference_L
;
try
done
;
set_solver
.
}
iModIntro
.
rewrite
/
uPred_except_0
.
iRight
.
iFrame
.
iSplitL
"Hw HEi"
.
+
by
iApply
"Hw"
.
+
iSplitL
"Hi"
;
[
eauto
].
iIntros
"HP [Hw HE\N]"
.
iDestruct
(
ownI_close
with
"[$Hw $Hi $HP $HD]"
)
as
"[? HEi]"
.
iModIntro
.
iRight
.
iFrame
.
iSplitL
;
[
done
].
iCombine
"HEi"
"HEN\i"
as
"HEN"
.
iCombine
"HEN"
"HE\N"
as
"HE"
.
rewrite

?ownE_op
;
[
set_solver

set_solver
].
rewrite
<!
union_difference_L
;
try
done
;
set_solver
.
rewrite
inv_eq
/
inv_def
fupd_eq
/
fupd_def
.
iIntros
(
Sub
)
"[Hw HE]"
.
iMod
(
ownI_alloc_open
(
∈
↑
N
)
P
with
"Hw"
)
as
(
i
)
"(% & Hw & #Hi & HD)"
;
auto
using
fresh_inv_name
.
iAssert
(
ownE
{[
i
]}
∗
ownE
(
↑
N
∖
{[
i
]})
∗
ownE
(
E
∖
↑
N
))%
I
with
"[HE]"
as
"(HEi & HEN\i & HE\N)"
.
{
rewrite

?ownE_op
;
[
set_solver
..].
rewrite
assoc_L
!
union_difference_L
//.
set_solver
.
}
do
2
iModIntro
.
iFrame
"HE\N"
.
iSplitL
"Hw HEi"
;
first
by
iApply
"Hw"
.
iSplitL
"Hi"
;
first
by
eauto
.
iIntros
"HP [Hw HE\N]"
.
iDestruct
(
ownI_close
with
"[$Hw $Hi $HP $HD]"
)
as
"[$ HEi]"
.
do
2
iModIntro
.
iSplitL
;
[
done
].
iCombine
"HEi"
"HEN\i"
as
"HEN"
;
iCombine
"HEN"
"HE\N"
as
"HE"
.
rewrite

?ownE_op
;
[
set_solver
..].
rewrite
!
union_difference_L
//
;
set_solver
.
Qed
.
Lemma
inv_open
E
N
P
:
...
...
theories/base_logic/lib/sts.v
View file @
af7b6da1
...
...
@@ 45,9 +45,9 @@ Section definitions.
Proof
.
solve_proper
.
Qed
.
Global
Instance
sts_ctx_persistent
`
{!
invG
Σ
}
N
φ
:
PersistentP
(
sts_ctx
N
φ
).
Proof
.
apply
_
.
Qed
.
Global
Instance
sts_own_peristent
s
:
PersistentP
(
sts_own
s
∅
).
Global
Instance
sts_own_per
s
istent
s
:
PersistentP
(
sts_own
s
∅
).
Proof
.
apply
_
.
Qed
.
Global
Instance
sts_ownS_peristent
S
:
PersistentP
(
sts_ownS
S
∅
).
Global
Instance
sts_ownS_per
s
istent
S
:
PersistentP
(
sts_ownS
S
∅
).
Proof
.
apply
_
.
Qed
.
End
definitions
.
...
...
theories/base_logic/lib/wsat.v
View file @
af7b6da1
...
...
@@ 165,5 +165,4 @@ Proof.
iApply
(
big_sepM_insert
_
I
)
;
first
done
.
iFrame
"HI"
.
by
iRight
.
Qed
.
End
wsat
.
theories/prelude/fin_maps.v
View file @
af7b6da1
...
...
@@ 119,13 +119,13 @@ Context `{FinMap K M}.
(** ** Setoids *)
Section
setoid
.
Context
`
{
Equiv
A
}.
Lemma
map_equiv_lookup_l
(
m1
m2
:
M
A
)
i
x
:
m1
≡
m2
→
m1
!!
i
=
Some
x
→
∃
y
,
m2
!!
i
=
Some
y
∧
x
≡
y
.
Proof
.
generalize
(
equiv_Some_inv_l
(
m1
!!
i
)
(
m2
!!
i
)
x
)
;
naive_solver
.
Qed
.
Context
`
{!
Equivalence
((
≡
)
:
relation
A
)}.
Global
Instance
map_equivalence
:
Equivalence
((
≡
)
:
relation
(
M
A
)).
Global
Instance
map_equivalence
:
Equivalence
((
≡
)
:
relation
A
)
→
Equivalence
((
≡
)
:
relation
(
M
A
)).
Proof
.
split
.

by
intros
m
i
.
...
...
@@ 147,7 +147,10 @@ Section setoid.
Proof
.
by
intros
???
;
apply
partial_alter_proper
;
[
constructor
].
Qed
.
Global
Instance
singleton_proper
k
:
Proper
((
≡
)
==>
(
≡
))
(
singletonM
k
:
A
→
M
A
).
Proof
.
by
intros
???
;
apply
insert_proper
.
Qed
.
Proof
.
intros
???
;
apply
insert_proper
;
[
done
].
intros
?.
rewrite
lookup_empty
;
constructor
.
Qed
.
Global
Instance
delete_proper
(
i
:
K
)
:
Proper
((
≡
)
==>
(
≡
))
(
delete
(
M
:
=
M
A
)
i
).
Proof
.
by
apply
partial_alter_proper
;
[
constructor
].
Qed
.
...
...
@@ 170,14 +173,12 @@ Section setoid.
by
do
2
destruct
1
;
first
[
apply
Hf

constructor
].
Qed
.
Global
Instance
map_leibniz
`
{!
LeibnizEquiv
A
}
:
LeibnizEquiv
(
M
A
).
Proof
.
intros
m1
m2
Hm
;
apply
map_eq
;
intros
i
.
by
unfold_leibniz
;
apply
lookup_proper
.
Qed
.
Proof
.
intros
m1
m2
Hm
;
apply
map_eq
;
intros
i
.
apply
leibniz_equiv
,
Hm
.
Qed
.
Lemma
map_equiv_empty
(
m
:
M
A
)
:
m
≡
∅
↔
m
=
∅
.
Proof
.
split
;
[
intros
Hm
;
apply
map_eq
;
intros
i

by
intros
>].
by
rewrite
lookup_empty
,
<
equiv_None
,
Hm
,
lookup_empty
.
split
;
[
intros
Hm
;
apply
map_eq
;
intros
i

intros
>].

generalize
(
Hm
i
).
by
rewrite
lookup_empty
,
equiv_None
.

intros
?.
rewrite
lookup_empty
;
constructor
.
Qed
.
Global
Instance
map_fmap_proper
`
{
Equiv
B
}
(
f
:
A
→
B
)
:
Proper
((
≡
)
==>
(
≡
))
f
→
Proper
((
≡
)
==>
(
≡
))
(
fmap
(
M
:
=
M
)
f
).
...
...
theories/prelude/list.v
View file @
af7b6da1
...
...
@@ 2753,9 +2753,8 @@ Section setoid.
by
setoid_rewrite
equiv_option_Forall2
.
Qed
.
Context
{
Hequiv
:
Equivalence
((
≡
)
:
relation
A
)}.
Global
Instance
list_equivalence
:
Equivalence
((
≡
)
:
relation
(
list
A
)).
Global
Instance
list_equivalence
:
Equivalence
((
≡
)
:
relation
A
)
→
Equivalence
((
≡
)
:
relation
(
list
A
)).
Proof
.
split
.

intros
l
.
by
apply
equiv_Forall2
.
...
...
@@ 2766,48 +2765,53 @@ Section setoid.
Proof
.
induction
1
;
f_equal
;
fold_leibniz
;
auto
.
Qed
.
Global
Instance
cons_proper
:
Proper
((
≡
)
==>
(
≡
)
==>
(
≡
))
(@
cons
A
).
Proof
using
(
Hequiv
)
.
by
constructor
.
Qed
.
Proof
.
by
constructor
.
Qed
.
Global
Instance
app_proper
:
Proper
((
≡
)
==>
(
≡
)
==>
(
≡
))
(@
app
A
).
Proof
using
(
Hequiv
)
.
induction
1
;
intros
???
;
simpl
;
try
constructor
;
auto
.
Qed
.
Proof
.
induction
1
;
intros
???
;
simpl
;
try
constructor
;
auto
.
Qed
.
Global
Instance
length_proper
:
Proper
((
≡
)
==>
(=))
(@
length
A
).
Proof
using
(
Hequiv
)
.
induction
1
;
f_equal
/=
;
auto
.
Qed
.
Proof
.
induction
1
;
f_equal
/=
;
auto
.
Qed
.
Global
Instance
tail_proper
:
Proper
((
≡
)
==>
(
≡
))
(@
tail
A
).
Proof
.
by
destruct
1
.
Qed
.
Proof
.
destruct
1
;
try
constructor
;
auto
.
Qed
.
Global
Instance
take_proper
n
:
Proper
((
≡
)
==>
(
≡
))
(@
take
A
n
).
Proof
using
(
Hequiv
)
.
induction
n
;
destruct
1
;
constructor
;
auto
.
Qed
.
Proof
.
induction
n
;
destruct
1
;
constructor
;
auto
.
Qed
.
Global
Instance
drop_proper
n
:
Proper
((
≡
)
==>
(
≡
))
(@
drop
A
n
).
Proof
using
(
Hequiv
)
.
induction
n
;
destruct
1
;
simpl
;
try
constructor
;
auto
.
Qed
.
Proof
.
induction
n
;
destruct
1
;
simpl
;
try
constructor
;
auto
.
Qed
.
Global
Instance
list_lookup_proper
i
:
Proper
((
≡
)
==>
(
≡
))
(
lookup
(
M
:
=
list
A
)
i
).
Proof
.
induction
i
;
destruct
1
;
simpl
;
f_equiv
;
auto
.
Qed
.
Proof
.
induction
i
;
destruct
1
;
simpl
;
try
constructor
;
auto
.
Qed
.
Global
Instance
list_alter_proper
f
i
:
Proper
((
≡
)
==>
(
≡
))
f
→
Proper
((
≡
)
==>
(
≡
))
(
alter
(
M
:
=
list
A
)
f
i
).
Proof
using
(
Hequiv
)
.
intros
.
induction
i
;
destruct
1
;
constructor
;
eauto
.
Qed
.
Proof
.
intros
.
induction
i
;
destruct
1
;
constructor
;
eauto
.
Qed
.
Global
Instance
list_insert_proper
i
:
Proper
((
≡
)
==>
(
≡
)
==>
(
≡
))
(
insert
(
M
:
=
list
A
)
i
).
Proof
using
(
Hequiv
)
.
intros
???
;
induction
i
;
destruct
1
;
constructor
;
eauto
.
Qed
.
Proof
.
intros
???
;
induction
i
;
destruct
1
;
constructor
;
eauto
.
Qed
.
Global
Instance
list_inserts_proper
i
:
Proper
((
≡
)
==>
(
≡
)
==>
(
≡
))
(@
list_inserts
A
i
).
Proof
using
(
Hequiv
)
.
Proof
.
intros
k1
k2
Hk
;
revert
i
.
induction
Hk
;
intros
????
;
simpl
;
try
f_equiv
;
naive_solver
.
Qed
.
Global
Instance
list_delete_proper
i
:
Proper
((
≡
)
==>
(
≡
))
(
delete
(
M
:
=
list
A
)
i
).
Proof
using
(
Hequiv
)
.
induction
i
;
destruct
1
;
try
constructor
;
eauto
.
Qed
.
Proof
.
induction
i
;
destruct
1
;
try
constructor
;
eauto
.
Qed
.
Global
Instance
option_list_proper
:
Proper
((
≡
)
==>
(
≡
))
(@
option_list
A
).
Proof
.
destruct
1
;
by
constructor
.
Qed
.
Proof
.
destruct
1
;
repeat
constructor
;
auto
.
Qed
.
Global
Instance
list_filter_proper
P
`
{
∀
x
,
Decision
(
P
x
)}
:
Proper
((
≡
)
==>
iff
)
P
→
Proper
((
≡
)
==>
(
≡
))
(
filter
(
B
:
=
list
A
)
P
).
Proof
using
(
Hequiv
)
.
intros
???.
rewrite
!
equiv_Forall2
.
by
apply
Forall2_filter
.
Qed
.
Proof
.
intros
???.
rewrite
!
equiv_Forall2
.
by
apply
Forall2_filter
.
Qed
.
Global
Instance
replicate_proper
n
:
Proper
((
≡
)
==>
(
≡
))
(@
replicate
A
n
).
Proof
using
(
Hequiv
)
.
induction
n
;
constructor
;
auto
.
Qed
.
Proof
.
induction
n
;
constructor
;
auto
.
Qed
.
Global
Instance
reverse_proper
:
Proper
((
≡
)
==>
(
≡
))
(@
reverse
A
).
Proof
.
induction
1
;
rewrite
?reverse_cons
;
repeat
(
done

f_equiv
).
Qed
.
Proof
.
induction
1
;
rewrite
?reverse_cons
;
simpl
;
[
constructor
].
apply
app_proper
;
repeat
constructor
;
auto
.
Qed
.
Global
Instance
last_proper
:
Proper
((
≡
)
==>
(
≡
))
(@
last
A
).
Proof
.
induction
1
as
[?????
[]]
;
simpl
;
repeat
(
done

f_equiv
)
.
Qed
.
Proof
.
induction
1
as
[?????
[]]
;
simpl
;
repeat
constructor
;
auto
.
Qed
.
Global
Instance
resize_proper
n
:
Proper
((
≡
)
==>
(
≡
)
==>
(
≡
))
(@
resize
A
n
).
Proof
.
induction
n
;
destruct
2
;
simpl
;
repeat
(
auto

f_equiv
).
Qed
.
Proof
.
induction
n
;
destruct
2
;
simpl
;
repeat
(
constructor

f_equiv
)
;
auto
.
Qed
.
End
setoid
.
(** * Properties of the monadic operations *)
...
...
theories/prelude/option.v
View file @
af7b6da1
...
...
@@ 115,36 +115,38 @@ End Forall2.
Instance
option_equiv
`
{
Equiv
A
}
:
Equiv
(
option
A
)
:
=
option_Forall2
(
≡
).
Section
setoids
.
Context
`
{
Equiv
A
}
{
Hequiv
:
Equivalence
((
≡
)
:
relation
A
)}
.
Context
`
{
Equiv
A
}.
Implicit
Types
mx
my
:
option
A
.
Lemma
equiv_option_Forall2
mx
my
:
mx
≡
my
↔
option_Forall2
(
≡
)
mx
my
.
Proof
using
(
Hequiv
)
.
done
.
Qed
.
Proof
.
done
.
Qed
.
Global
Instance
option_equivalence
:
Equivalence
((
≡
)
:
relation
(
option
A
)).
Global
Instance
option_equivalence
:
Equivalence
((
≡
)
:
relation
A
)
→
Equivalence
((
≡
)
:
relation
(
option
A
)).
Proof
.
apply
_
.
Qed
.
Global
Instance
Some_proper
:
Proper
((
≡
)
==>
(
≡
))
(@
Some
A
).
Proof
using
(
Hequiv
)
.
by
constructor
.
Qed
.
Proof
.
by
constructor
.
Qed
.
Global
Instance
Some_equiv_inj
:
Inj
(
≡
)
(
≡
)
(@
Some
A
).
Proof
using
(
Hequiv
)
.
by
inversion_clear
1
.
Qed
.
Proof
.
by
inversion_clear
1
.
Qed
.
Global
Instance
option_leibniz
`
{!
LeibnizEquiv
A
}
:
LeibnizEquiv
(
option
A
).
Proof
.
intros
x
y
;
destruct
1
;
f
old_leibniz
;
congruence
.
Qed
.
Proof
.
intros
x
y
;
destruct
1
;
f
_equal
;
by
apply
leibniz_equiv
.
Qed
.
Lemma
equiv_None
mx
:
mx
≡
None
↔
mx
=
None
.
Proof
.
split
;
[
by
inversion_clear
1

by
intros
>].
Qed
.
Proof
.
split
;
[
by
inversion_clear
1

intros
>
;
constructor
].
Qed
.
Lemma
equiv_Some_inv_l
mx
my
x
:
mx
≡
my
→
mx
=
Some
x
→
∃
y
,
my
=
Some
y
∧
x
≡
y
.
Proof
using
(
Hequiv
)
.
destruct
1
;
naive_solver
.
Qed
.
Proof
.
destruct
1
;
naive_solver
.
Qed
.
Lemma
equiv_Some_inv_r
mx
my
y
:
mx
≡
my
→
my
=
Some
y
→
∃
x
,
mx
=
Some
x
∧
x
≡
y
.
Proof
using
(
Hequiv
)
.
destruct
1
;
naive_solver
.
Qed
.
Proof
.
destruct
1
;
naive_solver
.
Qed
.
Lemma
equiv_Some_inv_l'
my
x
:
Some
x
≡
my
→
∃
x'
,
Some
x'
=
my
∧
x
≡
x'
.
Proof
using
(
Hequiv
).
intros
?%(
equiv_Some_inv_l
_
_
x
)
;
naive_solver
.
Qed
.
Lemma
equiv_Some_inv_r'
mx
y
:
mx
≡
Some
y
→
∃
y'
,
mx
=
Some
y'
∧
y
≡
y'
.
Proof
.
intros
?%(
equiv_Some_inv_l
_
_
x
)
;
naive_solver
.
Qed
.
Lemma
equiv_Some_inv_r'
`
{!
Equivalence
((
≡
)
:
relation
A
)}
mx
y
:
mx
≡
Some
y
→
∃
y'
,
mx
=
Some
y'
∧
y
≡
y'
.
Proof
.
intros
?%(
equiv_Some_inv_r
_
_
y
)
;
naive_solver
.
Qed
.
Global
Instance
is_Some_proper
:
Proper
((
≡
)
==>
iff
)
(@
is_Some
A
).
Proof
using
(
Hequiv
)
.
inversion_clear
1
;
split
;
eauto
.
Qed
.
Proof
.
inversion_clear
1
;
split
;
eauto
.
Qed
.
Global
Instance
from_option_proper
{
B
}
(
R
:
relation
B
)
(
f
:
A
→
B
)
:
Proper
((
≡
)
==>
R
)
f
→
Proper
(
R
==>
(
≡
)
==>
R
)
(
from_option
f
).
Proof
.
destruct
3
;
simpl
;
auto
.
Qed
.
...
...
theories/proofmode/tactics.v
View file @
af7b6da1
...
...
@@ 1280,6 +1280,7 @@ Hint Extern 1 (of_envs _ ⊢ _) =>


_
⊢
□
_
=>
iClear
"*"
;
iAlways


_
⊢
∃
_
,
_
=>
iExists
_


_
⊢
==>
_
=>
iModIntro


_
⊢
◇
_
=>
iModIntro
end
.
Hint
Extern
1
(
of_envs
_
⊢
_
)
=>
match
goal
with

_
⊢
(
_
∨
_
)%
I
=>
iLeft
end
.
...
...
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