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Pierre Roux
Iris
Commits
20789d80
Verified
Commit
20789d80
authored
3 years ago
by
Paolo G. Giarrusso
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1 changed file
iris/proofmode/frame_instances.v
+20
-10
20 additions, 10 deletions
iris/proofmode/frame_instances.v
with
20 additions
and
10 deletions
iris/proofmode/frame_instances.v
+
20
−
10
View file @
20789d80
...
...
@@ -68,13 +68,15 @@ Global Instance make_embed_default `{BiEmbed PROP PROP'} P :
Proof
.
by
rewrite
/
MakeEmbed
.
Qed
.
Global
Instance
frame_embed
`{
BiEmbed
PROP
PROP'
}
p
P
Q
(
Q'
:
PROP'
)
R
:
Frame
p
R
P
Q
→
MakeEmbed
Q
Q'
→
Frame
p
⎡
R
⎤
⎡
P
⎤
Q'
|
2
.
(* Same prio as default. *)
Frame
p
R
P
Q
→
MakeEmbed
Q
Q'
→
Frame
p
⎡
R
⎤
⎡
P
⎤
Q'
|
2
.
(* Same prio as default. *)
Proof
.
rewrite
/
Frame
/
MakeEmbed
=>
<-
<-.
rewrite
embed_sep
embed_intuitionistically_if_2
=>
//.
Qed
.
Global
Instance
frame_pure_embed
`{
BiEmbed
PROP
PROP'
}
p
P
Q
(
Q'
:
PROP'
)
φ
:
Frame
p
⌜
φ
⌝
P
Q
→
MakeEmbed
Q
Q'
→
Frame
p
⌜
φ
⌝
⎡
P
⎤
Q'
|
2
.
(* Same prio as default. *)
Frame
p
⌜
φ
⌝
P
Q
→
MakeEmbed
Q
Q'
→
Frame
p
⌜
φ
⌝
⎡
P
⎤
Q'
|
2
.
(* Same prio as default. *)
Proof
.
rewrite
/
Frame
/
MakeEmbed
-
embed_pure
.
apply
(
frame_embed
p
P
Q
)
.
Qed
.
Global
Instance
make_sep_emp_l
P
:
KnownLMakeSep
emp
P
P
.
...
...
@@ -213,7 +215,8 @@ Proof. by rewrite /MakeAffinely. Qed.
Global
Instance
frame_affinely
p
R
P
Q
Q'
:
TCOr
(
TCEq
p
true
)
(
Affine
R
)
→
Frame
p
R
P
Q
→
MakeAffinely
Q
Q'
→
Frame
p
R
(
<
affine
>
P
)
Q'
.
(* Default prio > 1 *)
Frame
p
R
P
Q
→
MakeAffinely
Q
Q'
→
Frame
p
R
(
<
affine
>
P
)
Q'
.
(* Default prio > 1 *)
Proof
.
rewrite
/
Frame
/
MakeAffinely
=>
-
[
->
|?]
<-
<-
/=
;
by
rewrite
-
{
1
}(
affine_affinely
(_
R
))
affinely_sep_2
.
...
...
@@ -236,7 +239,8 @@ Global Instance make_intuitionistically_default P :
Proof
.
by
rewrite
/
MakeIntuitionistically
.
Qed
.
Global
Instance
frame_intuitionistically
R
P
Q
Q'
:
Frame
true
R
P
Q
→
MakeIntuitionistically
Q
Q'
→
Frame
true
R
(
□
P
)
Q'
|
2
.
(* Same prio as default. *)
Frame
true
R
P
Q
→
MakeIntuitionistically
Q
Q'
→
Frame
true
R
(
□
P
)
Q'
|
2
.
(* Same prio as default. *)
Proof
.
rewrite
/
Frame
/
MakeIntuitionistically
=>
<-
<-
/=.
rewrite
-
intuitionistically_sep_2
intuitionistically_idemp
//.
...
...
@@ -253,7 +257,8 @@ Global Instance make_absorbingly_default P : MakeAbsorbingly P (<absorb> P) | 10
Proof
.
by
rewrite
/
MakeAbsorbingly
.
Qed
.
Global
Instance
frame_absorbingly
p
R
P
Q
Q'
:
Frame
p
R
P
Q
→
MakeAbsorbingly
Q
Q'
→
Frame
p
R
(
<
absorb
>
P
)
Q'
|
2
.
(* Same prio as default. *)
Frame
p
R
P
Q
→
MakeAbsorbingly
Q
Q'
→
Frame
p
R
(
<
absorb
>
P
)
Q'
|
2
.
(* Same prio as default. *)
Proof
.
rewrite
/
Frame
/
MakeAbsorbingly
=>
<-
<-
/=.
by
rewrite
absorbingly_sep_r
.
Qed
.
...
...
@@ -270,7 +275,8 @@ Global Instance make_persistently_default P :
Proof
.
by
rewrite
/
MakePersistently
.
Qed
.
Global
Instance
frame_persistently
R
P
Q
Q'
:
Frame
true
R
P
Q
→
MakePersistently
Q
Q'
→
Frame
true
R
(
<
pers
>
P
)
Q'
|
2
.
(* Same prio as default. *)
Frame
true
R
P
Q
→
MakePersistently
Q
Q'
→
Frame
true
R
(
<
pers
>
P
)
Q'
|
2
.
(* Same prio as default. *)
Proof
.
rewrite
/
Frame
/
MakePersistently
=>
<-
<-
/=.
rewrite
-
persistently_and_intuitionistically_sep_l
.
...
...
@@ -311,7 +317,8 @@ Qed.
Global
Instance
frame_eq_embed
`{
!
BiEmbed
PROP
PROP'
,
!
BiInternalEq
PROP
,
!
BiInternalEq
PROP'
,
!
BiEmbedInternalEq
PROP
PROP'
}
p
P
Q
(
Q'
:
PROP'
)
{
A
:
ofe
}
(
a
b
:
A
)
:
Frame
p
(
a
≡
b
)
P
Q
→
MakeEmbed
Q
Q'
→
Frame
p
(
a
≡
b
)
⎡
P
⎤
Q'
.
(* Default prio > 1 *)
Frame
p
(
a
≡
b
)
P
Q
→
MakeEmbed
Q
Q'
→
Frame
p
(
a
≡
b
)
⎡
P
⎤
Q'
.
(* Default prio > 1 *)
Proof
.
rewrite
/
Frame
/
MakeEmbed
-
embed_internal_eq
.
apply
(
frame_embed
p
P
Q
)
.
Qed
.
Global
Instance
make_laterN_true
n
:
@
KnownMakeLaterN
PROP
n
True
True
|
0
.
...
...
@@ -324,14 +331,16 @@ Proof. by rewrite /MakeLaterN. Qed.
Global
Instance
frame_later
p
R
R'
P
Q
Q'
:
TCNoBackTrack
(
MaybeIntoLaterN
true
1
R'
R
)
→
Frame
p
R
P
Q
→
MakeLaterN
1
Q
Q'
→
Frame
p
R'
(
▷
P
)
Q'
.
(* Default prio > 1 *)
Frame
p
R
P
Q
→
MakeLaterN
1
Q
Q'
→
Frame
p
R'
(
▷
P
)
Q'
.
(* Default prio > 1 *)
Proof
.
rewrite
/
Frame
/
MakeLaterN
/
MaybeIntoLaterN
=>
-
[
->
]
<-
<-.
by
rewrite
later_intuitionistically_if_2
later_sep
.
Qed
.
Global
Instance
frame_laterN
p
n
R
R'
P
Q
Q'
:
TCNoBackTrack
(
MaybeIntoLaterN
true
n
R'
R
)
→
Frame
p
R
P
Q
→
MakeLaterN
n
Q
Q'
→
Frame
p
R'
(
▷^
n
P
)
Q'
.
(* Default prio > 1 *)
Frame
p
R
P
Q
→
MakeLaterN
n
Q
Q'
→
Frame
p
R'
(
▷^
n
P
)
Q'
.
(* Default prio > 1 *)
Proof
.
rewrite
/
Frame
/
MakeLaterN
/
MaybeIntoLaterN
=>
-
[
->
]
<-
<-.
by
rewrite
laterN_intuitionistically_if_2
laterN_sep
.
...
...
@@ -350,7 +359,8 @@ Global Instance make_except_0_default P : MakeExcept0 P (◇ P) | 100.
Proof
.
by
rewrite
/
MakeExcept0
.
Qed
.
Global
Instance
frame_except_0
p
R
P
Q
Q'
:
Frame
p
R
P
Q
→
MakeExcept0
Q
Q'
→
Frame
p
R
(
◇
P
)
Q'
|
2
.
(* Same prio as default *)
Frame
p
R
P
Q
→
MakeExcept0
Q
Q'
→
Frame
p
R
(
◇
P
)
Q'
|
2
.
(* Same prio as default *)
Proof
.
rewrite
/
Frame
/
MakeExcept0
=>
<-
<-.
by
rewrite
except_0_sep
-
(
except_0_intro
(
□
?p
R
))
.
...
...
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