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Simon Spies
Iris
Commits
c798ff4f
Commit
c798ff4f
authored
Mar 15, 2017
by
Ralf Jung
Browse files
make fractional lemmas use AsFractional
parent
010154e2
Changes
1
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Inline
Sidebyside
theories/base_logic/lib/fractional.v
View file @
c798ff4f
...
@@ 22,21 +22,14 @@ Section fractional.
...
@@ 22,21 +22,14 @@ Section fractional.
Implicit
Types
Φ
:
Qp
→
uPred
M
.
Implicit
Types
Φ
:
Qp
→
uPred
M
.
Implicit
Types
p
q
:
Qp
.
Implicit
Types
p
q
:
Qp
.
Lemma
fractional_split
`
{!
Fractional
Φ
}
p
q
:
Lemma
fractional_split
P
P1
P2
Φ
q1
q2
:
Φ
(
p
+
q
)%
Qp
⊢
Φ
p
∗
Φ
q
.
AsFractional
P
Φ
(
q1
+
q2
)
→
AsFractional
P1
Φ
q1
→
AsFractional
P2
Φ
q2
→
Proof
.
by
rewrite
fractional
.
Qed
.
P
⊣
⊢
P1
∗
P2
.
Lemma
fractional_combine
`
{!
Fractional
Φ
}
p
q
:
Proof
.
move
=>[>
>]
[>
_
]
[>
_
].
done
.
Qed
.
Φ
p
∗
Φ
q
⊢
Φ
(
p
+
q
)%
Qp
.
Lemma
fractional_half
P
P12
Φ
q
:
Proof
.
by
rewrite
fractional
.
Qed
.
AsFractional
P
Φ
q
→
AsFractional
P12
Φ
(
q
/
2
)
→
Lemma
fractional_half_equiv
`
{!
Fractional
Φ
}
p
:
P
⊣
⊢
P12
∗
P12
.
Φ
p
⊣
⊢
Φ
(
p
/
2
)%
Qp
∗
Φ
(
p
/
2
)%
Qp
.
Proof
.
rewrite
{
1
}(
Qp_div_2
q
)=>[>>][>
_
].
done
.
Qed
.
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
.
(** Fractional and logical connectives *)
(** Fractional and logical connectives *)
Global
Instance
persistent_fractional
P
:
Global
Instance
persistent_fractional
P
:
...
@@ 132,25 +125,25 @@ Section fractional.
...
@@ 132,25 +125,25 @@ Section fractional.
AsFractional
P
Φ
(
q1
+
q2
)
→
AsFractional
P1
Φ
q1
→
AsFractional
P2
Φ
q2
→
AsFractional
P
Φ
(
q1
+
q2
)
→
AsFractional
P1
Φ
q1
→
AsFractional
P2
Φ
q2
→
IntoAnd
b
P
P1
P2
.
IntoAnd
b
P
P1
P2
.
Proof
.
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
Ideally, it'd not even be possible to make the mistake that
was originally made here, which is to give this instance for
was originally made here, which is to give this instance for
"false" only, thus breaking some intro patterns. *)
"false" only, thus breaking some intro patterns. *)
intros
H1
H2
H3
.
apply
mk_into_and_sep
.
revert
H1
H2
H3
.
intros
H1
H2
H3
.
apply
mk_into_and_sep
.
rewrite
[
P
]
fractional_split
//.
by
rewrite
/
IntoAnd
=>[>
>]
[>
_
]
[>
_
].
Qed
.
Qed
.
Global
Instance
into_and_fractional_half
b
P
Q
Φ
q
:
Global
Instance
into_and_fractional_half
b
P
Q
Φ
q
:
AsFractional
P
Φ
q
→
AsFractional
Q
Φ
(
q
/
2
)
→
AsFractional
P
Φ
q
→
AsFractional
Q
Φ
(
q
/
2
)
→
IntoAnd
b
P
Q
Q

100
.
IntoAnd
b
P
Q
Q

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

frame_fractional_hyps_l
Q
p
p'
r
:

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