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Tej Chajed
iris
Commits
aec7c174
Commit
aec7c174
authored
Dec 12, 2016
by
Robbert Krebbers
Browse files
Some tweaks.
parent
fa7dc440
Changes
1
Hide whitespace changes
Inline
Side-by-side
theories/base_logic/lib/fractional.v
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aec7c174
...
...
@@ -19,24 +19,23 @@ Section fractional.
Implicit
Types
Φ
:
Qp
→
uPred
M
.
Implicit
Types
p
q
:
Qp
.
Lemma
fractional_split
`
{
Fractional
_
Φ
}
p
q
:
Lemma
fractional_split
`
{
!
Fractional
Φ
}
p
q
:
Φ
(
p
+
q
)%
Qp
⊢
Φ
p
∗
Φ
q
.
Proof
.
by
rewrite
fractional
.
Qed
.
Lemma
fractional_combine
`
{
Fractional
_
Φ
}
p
q
:
Lemma
fractional_combine
`
{
!
Fractional
Φ
}
p
q
:
Φ
p
∗
Φ
q
⊢
Φ
(
p
+
q
)%
Qp
.
Proof
.
by
rewrite
fractional
.
Qed
.
Lemma
fractional_half_equiv
`
{
Fractional
_
Φ
}
p
:
Lemma
fractional_half_equiv
`
{
!
Fractional
Φ
}
p
:
Φ
p
⊣
⊢
Φ
(
p
/
2
)%
Qp
∗
Φ
(
p
/
2
)%
Qp
.
Proof
.
by
rewrite
-(
fractional
(
p
/
2
)
(
p
/
2
))
Qp_div_2
.
Qed
.
Lemma
fractional_half
`
{
Fractional
_
Φ
}
p
:
Lemma
fractional_half
`
{
!
Fractional
Φ
}
p
:
Φ
p
⊢
Φ
(
p
/
2
)%
Qp
∗
Φ
(
p
/
2
)%
Qp
.
Proof
.
by
rewrite
fractional_half_equiv
.
Qed
.
Lemma
half_fractional
`
{
Fractional
_
Φ
}
p
q
:
Lemma
half_fractional
`
{
!
Fractional
Φ
}
p
q
:
Φ
(
p
/
2
)%
Qp
∗
Φ
(
p
/
2
)%
Qp
⊢
Φ
p
.
Proof
.
by
rewrite
-
fractional_half_equiv
.
Qed
.
(** Fractional and logical connectives *)
Global
Instance
persistent_fractional
P
:
PersistentP
P
→
Fractional
(
λ
_
,
P
).
Proof
.
intros
HP
q
q'
.
by
apply
uPred_derived
.
always_sep_dup
.
Qed
.
...
...
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