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Jeehoon Kang
iriscoq
Commits
c798ff4f
Commit
c798ff4f
authored
Mar 15, 2017
by
Ralf Jung
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make fractional lemmas use AsFractional
parent
010154e2
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21
theories/base_logic/lib/fractional.v
theories/base_logic/lib/fractional.v
+14
21
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theories/base_logic/lib/fractional.v
View file @
c798ff4f
...
...
@@ 22,21 +22,14 @@ Section fractional.
Implicit
Types
Φ
:
Qp
→
uPred
M
.
Implicit
Types
p
q
:
Qp
.
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
:
Φ
p
∗
Φ
q
⊢
Φ
(
p
+
q
)
%
Qp
.
Proof
.
by
rewrite
fractional
.
Qed
.
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
:
Φ
p
⊢
Φ
(
p
/
2
)
%
Qp
∗
Φ
(
p
/
2
)
%
Qp
.
Proof
.
by
rewrite
fractional_half_equiv
.
Qed
.
Lemma
half_fractional
`
{!
Fractional
Φ
}
p
q
:
Φ
(
p
/
2
)
%
Qp
∗
Φ
(
p
/
2
)
%
Qp
⊢
Φ
p
.
Proof
.
by
rewrite

fractional_half_equiv
.
Qed
.
Lemma
fractional_split
P
P1
P2
Φ
q1
q2
:
AsFractional
P
Φ
(
q1
+
q2
)
→
AsFractional
P1
Φ
q1
→
AsFractional
P2
Φ
q2
→
P
⊣⊢
P1
∗
P2
.
Proof
.
move
=>
[
>
>
]
[
>
_
]
[
>
_
].
done
.
Qed
.
Lemma
fractional_half
P
P12
Φ
q
:
AsFractional
P
Φ
q
→
AsFractional
P12
Φ
(
q
/
2
)
→
P
⊣⊢
P12
∗
P12
.
Proof
.
rewrite
{
1
}
(
Qp_div_2
q
)
=>
[
>>
][
>
_
].
done
.
Qed
.
(
**
Fractional
and
logical
connectives
*
)
Global
Instance
persistent_fractional
P
:
...
...
@@ 132,25 +125,25 @@ Section fractional.
AsFractional
P
Φ
(
q1
+
q2
)
→
AsFractional
P1
Φ
q1
→
AsFractional
P2
Φ
q2
→
IntoAnd
b
P
P1
P2
.
Proof
.
(
*
TODO
:
We
need
a
better
way
to
handle
this
boolean
here
.
(
*
TODO
:
We
need
a
better
way
to
handle
this
boolean
here
;
always
applying
mk_into_and_sep
(
which
only
works
after
introducing
all
assumptions
)
is
rather
annoying
.
Ideally
,
it
'
d
not
even
be
possible
to
make
the
mistake
that
was
originally
made
here
,
which
is
to
give
this
instance
for
"false"
only
,
thus
breaking
some
intro
patterns
.
*
)
intros
H1
H2
H3
.
apply
mk_into_and_sep
.
revert
H1
H2
H3
.
by
rewrite
/
IntoAnd
=>
[
>
>
]
[
>
_
]
[
>
_
].
intros
H1
H2
H3
.
apply
mk_into_and_sep
.
rewrite
[
P
]
fractional_split
//.
Qed
.
Global
Instance
into_and_fractional_half
b
P
Q
Φ
q
:
AsFractional
P
Φ
q
→
AsFractional
Q
Φ
(
q
/
2
)
→
IntoAnd
b
P
Q
Q

100.
Proof
.
intros
H1
H2
.
apply
mk_into_and_sep
.
revert
H1
H2
.
by
rewrite
/
IntoAnd
{
1
}
(
Qp_div_2
q
)
=>
[
>>
][
>
_
].
intros
H1
H2
.
apply
mk_into_and_sep
.
rewrite
[
P
]
fractional_half
//.
Qed
.
(
*
The
instance
[
frame_fractional
]
can
be
tried
at
all
the
nodes
of
the
proof
search
.
The
proof
search
then
fails
almost
always
on
[
AsFractional
R
Φ
r
],
but
the
slowdown
is
still
noticeable
.
For
that
reason
,
we
factorize
the
three
instances
that
could
ave
been
that
reason
,
we
factorize
the
three
instances
that
could
h
ave
been
defined
for
that
purpose
into
one
.
*
)
Inductive
FrameFractionalHyps
R
Φ
RES
:
Qp
→
Qp
→
Prop
:=

frame_fractional_hyps_l
Q
p
p
'
r
:
...
...
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