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Tej Chajed
iris
Commits
a3413622
Commit
a3413622
authored
Feb 20, 2016
by
Ralf Jung
Browse files
remove a needless lemma
parent
02639dd4
Changes
1
Hide whitespace changes
Inline
Side-by-side
algebra/upred.v
View file @
a3413622
...
...
@@ -984,8 +984,6 @@ Lemma always_always P `{!AlwaysStable P} : (□ P)%I ≡ P.
Proof
.
apply
(
anti_symm
(
⊑
))
;
auto
using
always_elim
.
Qed
.
Lemma
always_intro
P
Q
`
{!
AlwaysStable
P
}
:
P
⊑
Q
→
P
⊑
□
Q
.
Proof
.
rewrite
-(
always_always
P
)
;
apply
always_intro'
.
Qed
.
Lemma
always_entails
P
Q
`
{!
AlwaysStable
P
}
:
P
⊑
□
Q
→
P
⊑
Q
.
Proof
.
rewrite
-(
always_always
P
).
move
=>->.
by
rewrite
always_elim
.
Qed
.
Lemma
always_and_sep_l
P
Q
`
{!
AlwaysStable
P
}
:
(
P
∧
Q
)%
I
≡
(
P
★
Q
)%
I
.
Proof
.
by
rewrite
-(
always_always
P
)
always_and_sep_l'
.
Qed
.
Lemma
always_and_sep_r
P
Q
`
{!
AlwaysStable
Q
}
:
(
P
∧
Q
)%
I
≡
(
P
★
Q
)%
I
.
...
...
@@ -1001,7 +999,7 @@ Proof. by rewrite -(always_always Q); apply always_entails_r'. Qed.
Lemma
l
ö
b_strong_sep
P
Q
:
(
P
★
▷
(
P
-
★
Q
))
⊑
Q
→
P
⊑
Q
.
Proof
.
move
/
wand_intro_l
=>
Hl
ö
b
.
rewrite
-[
P
](
left_id
True
(
∧
))%
I
.
apply
impl_elim_l'
.
apply
:
always_e
ntails
.
apply
l
ö
b_strong
.
apply
impl_elim_l'
.
rewrite
-[(
_
→
_
)%
I
]
always_e
lim
.
apply
l
ö
b_strong
.
rewrite
left_id
-
always_wand_impl
-
always_later
Hl
ö
b
.
done
.
Qed
.
...
...
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