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Tej Chajed
iris
Commits
6326a24c
Commit
6326a24c
authored
Jan 30, 2016
by
Ralf Jung
Browse files
since we use unicode, let's write Löb's name correctly
parent
2d0a5475
Changes
1
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Inline
Side-by-side
modures/logic.v
View file @
6326a24c
...
...
@@ -672,7 +672,7 @@ Proof.
intros
x
[|
n
]
??
;
simpl
in
*
;
[
done
|].
apply
uPred_weaken
with
x
(
S
n
)
;
eauto
using
cmra_valid_S
.
Qed
.
Lemma
l
u
b
P
:
(
▷
P
→
P
)
⊑
P
.
Lemma
l
ö
b
P
:
(
▷
P
→
P
)
⊑
P
.
Proof
.
intros
x
n
?
HP
;
induction
n
as
[|
n
IH
]
;
[
by
apply
HP
|].
apply
HP
,
IH
,
uPred_weaken
with
x
(
S
n
)
;
eauto
using
cmra_valid_S
.
...
...
@@ -709,6 +709,14 @@ Proof.
Qed
.
Lemma
later_wand
P
Q
:
▷
(
P
-
★
Q
)
⊑
(
▷
P
-
★
▷
Q
).
Proof
.
apply
wand_intro_r
;
rewrite
-
later_sep
;
apply
later_mono
,
wand_elim_l
.
Qed
.
Lemma
l
ö
b_all_1
{
A
}
(
P
Q
:
A
→
uPred
M
)
:
(
∀
a
,
(
▷
(
∀
b
,
P
b
→
Q
b
)
∧
P
a
)
⊑
Q
a
)
→
∀
a
,
P
a
⊑
Q
a
.
Proof
.
intros
Hl
ö
b
a
.
apply
impl_entails
.
transitivity
(
∀
a
,
P
a
→
Q
a
)%
I
;
last
first
.
{
by
rewrite
(
forall_elim
_
a
).
}
clear
a
.
etransitivity
;
last
by
eapply
l
ö
b
.
apply
impl_intro_l
,
forall_intro
=>
a
.
rewrite
right_id
.
by
apply
impl_intro_r
.
Qed
.
(* Always *)
Lemma
always_const
φ
:
(
□
■
φ
:
uPred
M
)%
I
≡
(
■
φ
)%
I
.
...
...
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