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iris
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Tej Chajed
iris
Commits
4a934341
Commit
4a934341
authored
8 years ago
by
Robbert Krebbers
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More IntoX and FromX proofmode instances.
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proofmode/class_instances.v
+35
-1
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proofmode/class_instances.v
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and
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proofmode/class_instances.v
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4a934341
...
...
@@ -113,6 +113,9 @@ Global Instance into_wand_iff_r P Q : IntoWand (P ↔ Q) Q P.
Proof
.
apply
and_elim_r'
,
impl_wand
.
Qed
.
Global
Instance
into_wand_always
R
P
Q
:
IntoWand
R
P
Q
→
IntoWand
(
□
R
)
P
Q
.
Proof
.
rewrite
/
IntoWand
=>
->
.
apply
always_elim
.
Qed
.
Global
Instance
into_wand_later
{
M
}
(
R
P
Q
:
uPred
M
)
:
IntoWand
R
P
Q
→
IntoWand
R
(
▷
P
)
(
▷
Q
)
|
100
.
Proof
.
rewrite
/
IntoWand
=>
->
.
by
rewrite
-
later_wand
-
later_intro
.
Qed
.
Global
Instance
into_wand_bupd
R
P
Q
:
IntoWand
R
P
Q
→
IntoWand
R
(|
==>
P
)
(|
==>
Q
)
|
100
.
Proof
.
rewrite
/
IntoWand
=>
->
.
apply
wand_intro_l
.
by
rewrite
bupd_wand_r
.
Qed
.
...
...
@@ -126,6 +129,8 @@ Proof. intros. by rewrite /FromAnd always_and_sep_l. Qed.
Global
Instance
from_and_sep_persistent_r
P1
P2
:
PersistentP
P2
→
FromAnd
(
P1
∗
P2
)
P1
P2
|
10
.
Proof
.
intros
.
by
rewrite
/
FromAnd
always_and_sep_r
.
Qed
.
Global
Instance
from_and_pure
φ
ψ
:
@
FromAnd
M
⌜
φ
∧
ψ
⌝
⌜
φ
⌝
⌜
ψ
⌝.
Proof
.
by
rewrite
/
FromAnd
pure_and
.
Qed
.
Global
Instance
from_and_always
P
Q1
Q2
:
FromAnd
P
Q1
Q2
→
FromAnd
(
□
P
)
(
□
Q1
)
(
□
Q2
)
.
Proof
.
rewrite
/
FromAnd
=>
<-.
by
rewrite
always_and
.
Qed
.
...
...
@@ -140,6 +145,8 @@ Global Instance from_sep_ownM (a b1 b2 : M) :
FromOp
a
b1
b2
→
FromSep
(
uPred_ownM
a
)
(
uPred_ownM
b1
)
(
uPred_ownM
b2
)
.
Proof
.
intros
.
by
rewrite
/
FromSep
-
ownM_op
from_op
.
Qed
.
Global
Instance
from_sep_pure
φ
ψ
:
@
FromSep
M
⌜
φ
∧
ψ
⌝
⌜
φ
⌝
⌜
ψ
⌝.
Proof
.
by
rewrite
/
FromSep
pure_and
sep_and
.
Qed
.
Global
Instance
from_sep_always
P
Q1
Q2
:
FromSep
P
Q1
Q2
→
FromSep
(
□
P
)
(
□
Q1
)
(
□
Q2
)
.
Proof
.
rewrite
/
FromSep
=>
<-.
by
rewrite
always_sep
.
Qed
.
...
...
@@ -210,6 +217,13 @@ Global Instance into_and_and_persistent_r P Q :
PersistentP
Q
→
IntoAnd
false
(
P
∧
Q
)
P
Q
.
Proof
.
intros
;
by
rewrite
/
IntoAnd
/=
always_and_sep_r
.
Qed
.
Global
Instance
into_and_pure
p
φ
ψ
:
@
IntoAnd
M
p
⌜
φ
∧
ψ
⌝
⌜
φ
⌝
⌜
ψ
⌝.
Proof
.
apply
mk_into_and_sep
.
by
rewrite
pure_and
always_and_sep_r
.
Qed
.
Global
Instance
into_and_always
p
P
Q1
Q2
:
IntoAnd
true
P
Q1
Q2
→
IntoAnd
p
(
□
P
)
(
□
Q1
)
(
□
Q2
)
.
Proof
.
rewrite
/
IntoAnd
=>
->
.
destruct
p
;
by
rewrite
?always_and
always_and_sep_r
.
Qed
.
Global
Instance
into_and_later
p
P
Q1
Q2
:
IntoAnd
p
P
Q1
Q2
→
IntoAnd
p
(
▷
P
)
(
▷
Q1
)
(
▷
Q2
)
.
Proof
.
rewrite
/
IntoAnd
=>
->
.
destruct
p
;
by
rewrite
?later_and
?later_sep
.
Qed
.
...
...
@@ -330,6 +344,8 @@ Proof. done. Qed.
Global
Instance
from_or_bupd
P
Q1
Q2
:
FromOr
P
Q1
Q2
→
FromOr
(|
==>
P
)
(|
==>
Q1
)
(|
==>
Q2
)
.
Proof
.
rewrite
/
FromOr
=>
<-.
apply
or_elim
;
apply
bupd_mono
;
auto
with
I
.
Qed
.
Global
Instance
from_or_pure
φ
ψ
:
@
FromOr
M
⌜
φ
∨
ψ
⌝
⌜
φ
⌝
⌜
ψ
⌝.
Proof
.
by
rewrite
/
FromOr
pure_or
.
Qed
.
Global
Instance
from_or_always
P
Q1
Q2
:
FromOr
P
Q1
Q2
→
FromOr
(
□
P
)
(
□
Q1
)
(
□
Q2
)
.
Proof
.
rewrite
/
FromOr
=>
<-.
by
rewrite
always_or
.
Qed
.
...
...
@@ -340,6 +356,11 @@ Proof. rewrite /FromOr=><-. by rewrite later_or. Qed.
(* IntoOr *)
Global
Instance
into_or_or
P
Q
:
IntoOr
(
P
∨
Q
)
P
Q
.
Proof
.
done
.
Qed
.
Global
Instance
into_or_pure
φ
ψ
:
@
IntoOr
M
⌜
φ
∨
ψ
⌝
⌜
φ
⌝
⌜
ψ
⌝.
Proof
.
by
rewrite
/
IntoOr
pure_or
.
Qed
.
Global
Instance
into_or_always
P
Q1
Q2
:
IntoOr
P
Q1
Q2
→
IntoOr
(
□
P
)
(
□
Q1
)
(
□
Q2
)
.
Proof
.
rewrite
/
IntoOr
=>
->
.
by
rewrite
always_or
.
Qed
.
Global
Instance
into_or_later
P
Q1
Q2
:
IntoOr
P
Q1
Q2
→
IntoOr
(
▷
P
)
(
▷
Q1
)
(
▷
Q2
)
.
Proof
.
rewrite
/
IntoOr
=>
->
.
by
rewrite
later_or
.
Qed
.
...
...
@@ -352,13 +373,26 @@ Global Instance from_exist_bupd {A} P (Φ : A → uPred M) :
Proof
.
rewrite
/
FromExist
=>
<-.
apply
exist_elim
=>
a
.
by
rewrite
-
(
exist_intro
a
)
.
Qed
.
Global
Instance
from_exist_pure
{
A
}
(
φ
:
A
→
Prop
)
:
@
FromExist
M
A
⌜∃
x
,
φ
x
⌝
(
λ
a
,
⌜
φ
a
⌝
)
%
I
.
Proof
.
by
rewrite
/
FromExist
pure_exist
.
Qed
.
Global
Instance
from_exist_always
{
A
}
P
(
Φ
:
A
→
uPred
M
)
:
FromExist
P
Φ
→
FromExist
(
□
P
)
(
λ
a
,
□
(
Φ
a
))
%
I
.
Proof
.
rewrite
/
FromExist
=>
<-.
apply
exist_elim
=>
x
.
apply
always_mono
,
exist_intro
.
Qed
.
Global
Instance
from_exist_later
{
A
}
P
(
Φ
:
A
→
uPred
M
)
:
FromExist
P
Φ
→
FromExist
(
▷
P
)
(
λ
a
,
▷
(
Φ
a
))
%
I
.
Proof
.
rewrite
/
FromExist
=>
<-.
apply
exist_elim
=>
x
.
apply
later_mono
,
exist_intro
.
Qed
.
Proof
.
rewrite
/
FromExist
=>
<-.
apply
exist_elim
=>
x
.
apply
later_mono
,
exist_intro
.
Qed
.
(* IntoExist *)
Global
Instance
into_exist_exist
{
A
}
(
Φ
:
A
→
uPred
M
)
:
IntoExist
(
∃
a
,
Φ
a
)
Φ
.
Proof
.
done
.
Qed
.
Global
Instance
into_exist_pure
{
A
}
(
φ
:
A
→
Prop
)
:
@
IntoExist
M
A
⌜∃
x
,
φ
x
⌝
(
λ
a
,
⌜
φ
a
⌝
)
%
I
.
Proof
.
by
rewrite
/
IntoExist
pure_exist
.
Qed
.
Global
Instance
into_exist_later
{
A
}
P
(
Φ
:
A
→
uPred
M
)
:
IntoExist
P
Φ
→
Inhabited
A
→
IntoExist
(
▷
P
)
(
λ
a
,
▷
(
Φ
a
))
%
I
.
Proof
.
rewrite
/
IntoExist
=>
HP
?
.
by
rewrite
HP
later_exist
.
Qed
.
...
...
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