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Rice Wine
Iris
Commits
b20fd842
Commit
b20fd842
authored
Oct 14, 2016
by
Robbert Krebbers
Browse files
Only one direction of assoc and comm for separating conjunction is needed.
parent
467c44e4
Changes
2
Hide whitespace changes
Inline
Side-by-side
algebra/upred.v
View file @
b20fd842
...
...
@@ -821,26 +821,25 @@ Proof.
split
;
intros
n'
x
?
(
x1
&
x2
&?&?&?)
;
exists
x1
,
x2
;
cofe_subst
x
;
eauto
7
using
cmra_validN_op_l
,
cmra_validN_op_r
,
uPred_in_entails
.
Qed
.
Global
Instance
True_sep
:
LeftId
(
⊣
⊢
)
True
%
I
(@
uPred_sep
M
)
.
Lemma
True_sep_1
P
:
P
⊢
True
★
P
.
Proof
.
intros
P
;
unseal
;
split
=>
n
x
Hvalid
;
split
.
-
intros
(
x1
&
x2
&?&
_
&?)
;
cofe_subst
;
eauto
using
uPred_mono
,
cmra_includedN_r
.
-
by
intros
?
;
exists
(
core
x
),
x
;
rewrite
cmra_core_l
.
unseal
;
split
;
intros
n
x
??.
exists
(
core
x
),
x
.
by
rewrite
cmra_core_l
.
Qed
.
Global
Instance
sep_comm
:
Comm
(
⊣
⊢
)
(@
uPred_sep
M
)
.
Lemma
True_sep_2
P
:
True
★
P
⊢
P
.
Proof
.
by
intros
P
Q
;
unseal
;
split
=>
n
x
?
;
spli
t
;
intros
(
x1
&
x2
&?&?&?)
;
exists
x2
,
x1
;
rewrite
(
comm
op
)
.
unseal
;
split
;
intros
n
x
?
(
x1
&
x2
&?&
_
&?)
;
cofe_subs
t
;
eauto
using
uPred_mono
,
cmra_includedN_r
.
Qed
.
Global
Instance
sep_assoc
:
Assoc
(
⊣
⊢
)
(@
uPred_sep
M
).
Lemma
sep_comm'
P
Q
:
P
★
Q
⊢
Q
★
P
.
Proof
.
unseal
;
split
;
intros
n
x
?
(
x1
&
x2
&?&?&?)
;
exists
x2
,
x1
;
by
rewrite
(
comm
op
).
Qed
.
Lemma
sep_assoc'
P
Q
R
:
(
P
★
Q
)
★
R
⊢
P
★
(
Q
★
R
).
Proof
.
intros
P
Q
R
;
unseal
;
split
=>
n
x
?
;
split
.
-
intros
(
x1
&
x2
&
Hx
&?&
y1
&
y2
&
Hy
&?&?)
;
exists
(
x1
⋅
y1
),
y2
;
split_and
?
;
auto
.
+
by
rewrite
-(
assoc
op
)
-
Hy
-
Hx
.
+
by
exists
x1
,
y1
.
-
intros
(
x1
&
x2
&
Hx
&(
y1
&
y2
&
Hy
&?&?)&?)
;
exists
y1
,
(
y2
⋅
x2
)
;
split_and
?
;
auto
.
+
by
rewrite
(
assoc
op
)
-
Hy
-
Hx
.
+
by
exists
y2
,
x2
.
unseal
;
split
;
intros
n
x
?
(
x1
&
x2
&
Hx
&(
y1
&
y2
&
Hy
&?&?)&?).
exists
y1
,
(
y2
⋅
x2
)
;
split_and
?
;
auto
.
+
by
rewrite
(
assoc
op
)
-
Hy
-
Hx
.
+
by
exists
y2
,
x2
.
Qed
.
Lemma
wand_intro_r
P
Q
R
:
(
P
★
Q
⊢
R
)
→
P
⊢
Q
-
★
R
.
Proof
.
...
...
@@ -872,6 +871,15 @@ Qed.
Global
Instance
wand_mono'
:
Proper
(
flip
(
⊢
)
==>
(
⊢
)
==>
(
⊢
))
(@
uPred_wand
M
).
Proof
.
by
intros
P
P'
HP
Q
Q'
HQ
;
apply
wand_mono
.
Qed
.
Global
Instance
sep_comm
:
Comm
(
⊣
⊢
)
(@
uPred_sep
M
).
Proof
.
intros
P
Q
;
apply
(
anti_symm
_
)
;
auto
using
sep_comm'
.
Qed
.
Global
Instance
sep_assoc
:
Assoc
(
⊣
⊢
)
(@
uPred_sep
M
).
Proof
.
intros
P
Q
R
;
apply
(
anti_symm
_
)
;
auto
using
sep_assoc'
.
by
rewrite
!(
comm
_
P
)
!(
comm
_
_
R
)
sep_assoc'
.
Qed
.
Global
Instance
True_sep
:
LeftId
(
⊣
⊢
)
True
%
I
(@
uPred_sep
M
).
Proof
.
intros
P
;
apply
(
anti_symm
_
)
;
auto
using
True_sep_1
,
True_sep_2
.
Qed
.
Global
Instance
sep_True
:
RightId
(
⊣
⊢
)
True
%
I
(@
uPred_sep
M
).
Proof
.
by
intros
P
;
rewrite
comm
left_id
.
Qed
.
Lemma
sep_elim_l
P
Q
:
P
★
Q
⊢
P
.
...
...
docs/base-logic.tex
View file @
b20fd842
...
...
@@ -289,8 +289,8 @@ Furthermore, we have the usual $\eta$ and $\beta$ laws for projections, $\lambda
\begin{mathpar}
\begin{array}
{
rMcMl
}
\TRUE
*
\prop
&
\provesIff
&
\prop
\\
\prop
*
\propB
&
\proves
Iff
&
\propB
*
\prop
\\
(
\prop
*
\propB
) *
\propC
&
\proves
Iff
&
\prop
* (
\propB
*
\propC
)
\prop
*
\propB
&
\proves
&
\propB
*
\prop
\\
(
\prop
*
\propB
) *
\propC
&
\proves
&
\prop
* (
\propB
*
\propC
)
\end{array}
\and
\infer
[$*$-mono]
...
...
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