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Rodolphe Lepigre
Iris
Commits
e88994af
Commit
e88994af
authored
Dec 03, 2017
by
Robbert Krebbers
Browse files
Rename `wand_impl_plainly` → `impl_wand_plainly` and swap direction.
To be consistent with the lemma for the persistence modality.
parent
7298dd39
Changes
1
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Inline
Side-by-side
theories/base_logic/derived.v
View file @
e88994af
...
...
@@ -566,9 +566,9 @@ Proof.
apply
plainly_intro'
,
impl_intro_r
.
by
rewrite
plainly_and_sep_l'
plainly_elim
wand_elim_l
.
Qed
.
Lemma
wand_impl
_plainly
P
Q
:
(
■
P
-
∗
Q
)
⊣
⊢
(
■
P
→
Q
).
Lemma
impl_wand
_plainly
P
Q
:
(
■
P
→
Q
)
⊣
⊢
(
■
P
-
∗
Q
).
Proof
.
apply
(
anti_symm
(
⊢
))
;
[
|
by
rewrite
-
impl_wand_1
].
apply
(
anti_symm
(
⊢
))
;
[
by
rewrite
-
impl_wand_1
|
].
apply
impl_intro_l
.
by
rewrite
plainly_and_sep_l'
wand_elim_r
.
Qed
.
Lemma
plainly_entails_l'
P
Q
:
(
P
⊢
■
Q
)
→
P
⊢
■
Q
∗
P
.
...
...
@@ -1029,7 +1029,7 @@ Qed.
Global
Instance
wand_plain
P
Q
:
Plain
P
→
Plain
Q
→
Plain
(
P
-
∗
Q
)%
I
.
Proof
.
rewrite
/
Plain
=>
HP
HQ
.
by
rewrite
{
2
}
HP
-{
1
}(
plainly_elim
P
)
!
wand_impl
_plainly
-
plainly_impl_plainly
-
HQ
.
by
rewrite
{
2
}
HP
-{
1
}(
plainly_elim
P
)
-!
impl_wand
_plainly
-
plainly_impl_plainly
-
HQ
.
Qed
.
Global
Instance
plainly_plain
P
:
Plain
(
■
P
).
Proof
.
by
intros
;
apply
plainly_intro'
.
Qed
.
...
...
@@ -1079,7 +1079,7 @@ Global Instance wand_persistent P Q :
Plain
P
→
Persistent
Q
→
Persistent
(
P
-
∗
Q
)%
I
.
Proof
.
rewrite
/
Plain
/
Persistent
=>
HP
HQ
.
by
rewrite
{
2
}
HP
-{
1
}(
plainly_elim
P
)
!
wand_impl
_plainly
-
persistently_impl_plainly
-
HQ
.
by
rewrite
{
2
}
HP
-{
1
}(
plainly_elim
P
)
-!
impl_wand
_plainly
-
persistently_impl_plainly
-
HQ
.
Qed
.
Global
Instance
plainly_persistent
P
:
Persistent
(
■
P
).
Proof
.
by
rewrite
/
Persistent
persistently_plainly
.
Qed
.
...
...
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