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Rice Wine
Iris
Commits
a50d23b9
Commit
a50d23b9
authored
8 years ago
by
Robbert Krebbers
Committed by
Ralf Jung
8 years ago
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Omit spacing when pretty printing `N.@x` to reflect its tight precedence.
parent
274209c2
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base_logic/lib/namespaces.v
+8
-7
8 additions, 7 deletions
base_logic/lib/namespaces.v
with
8 additions
and
7 deletions
base_logic/lib/namespaces.v
+
8
−
7
View file @
a50d23b9
...
...
@@ -19,7 +19,8 @@ Definition nclose_aux : { x | x = @nclose_def }. by eexists. Qed.
Instance
nclose
:
UpClose
namespace
coPset
:=
proj1_sig
nclose_aux
.
Definition
nclose_eq
:
@
nclose
=
@
nclose_def
:=
proj2_sig
nclose_aux
.
Infix
".@"
:=
ndot
(
at
level
19
,
left
associativity
)
:
C_scope
.
Notation
"N .@ x"
:=
(
ndot
N
x
)
(
at
level
19
,
left
associativity
,
format
"N .@ x"
)
:
C_scope
.
Notation
"(.@)"
:=
ndot
(
only
parsing
)
:
C_scope
.
Instance
ndisjoint
:
Disjoint
namespace
:=
λ
N1
N2
,
nclose
N1
⊥
nclose
N2
.
...
...
@@ -41,7 +42,7 @@ Section namespace.
by
apply
elem_coPset_suffixes
;
exists
xH
;
rewrite
(
left_id_L
_
_)
.
Qed
.
Lemma
nclose_subseteq
N
x
:
↑
N
.
@
x
⊆
(
↑
N
:
coPset
)
.
Lemma
nclose_subseteq
N
x
:
↑
N
.
@
x
⊆
(
↑
N
:
coPset
)
.
Proof
.
intros
p
;
rewrite
nclose_eq
/
nclose
!
ndot_eq
!
elem_coPset_suffixes
.
intros
[
q
->
]
.
destruct
(
list_encode_suffix
N
(
ndot_def
N
x
))
as
[
q'
?]
.
...
...
@@ -49,25 +50,25 @@ Section namespace.
by
exists
(
q
++
q'
)
%
positive
;
rewrite
<-
(
assoc_L
_);
f_equal
.
Qed
.
Lemma
nclose_subseteq'
E
N
x
:
↑
N
⊆
E
→
↑
N
.
@
x
⊆
E
.
Lemma
nclose_subseteq'
E
N
x
:
↑
N
⊆
E
→
↑
N
.
@
x
⊆
E
.
Proof
.
intros
.
etrans
;
eauto
using
nclose_subseteq
.
Qed
.
Lemma
ndot_nclose
N
x
:
encode
(
N
.
@
x
)
∈
↑
N
.
Lemma
ndot_nclose
N
x
:
encode
(
N
.
@
x
)
∈
↑
N
.
Proof
.
apply
nclose_subseteq
with
x
,
encode_nclose
.
Qed
.
Lemma
nclose_infinite
N
:
¬
set_finite
(
↑
N
:
coPset
)
.
Proof
.
rewrite
nclose_eq
.
apply
coPset_suffixes_infinite
.
Qed
.
Lemma
ndot_ne_disjoint
N
x
y
:
x
≠
y
→
N
.
@
x
⊥
N
.
@
y
.
Lemma
ndot_ne_disjoint
N
x
y
:
x
≠
y
→
N
.
@
x
⊥
N
.
@
y
.
Proof
.
intros
Hxy
a
.
rewrite
!
nclose_eq
!
elem_coPset_suffixes
!
ndot_eq
.
intros
[
qx
->
]
[
qy
Hqy
]
.
revert
Hqy
.
by
intros
[
=
?
%
encode_inj
]
%
list_encode_suffix_eq
.
Qed
.
Lemma
ndot_preserve_disjoint_l
N
E
x
:
↑
N
⊥
E
→
↑
N
.
@
x
⊥
E
.
Lemma
ndot_preserve_disjoint_l
N
E
x
:
↑
N
⊥
E
→
↑
N
.
@
x
⊥
E
.
Proof
.
intros
.
pose
proof
(
nclose_subseteq
N
x
)
.
set_solver
.
Qed
.
Lemma
ndot_preserve_disjoint_r
N
E
x
:
E
⊥
↑
N
→
E
⊥
↑
N
.
@
x
.
Lemma
ndot_preserve_disjoint_r
N
E
x
:
E
⊥
↑
N
→
E
⊥
↑
N
.
@
x
.
Proof
.
intros
.
by
apply
symmetry
,
ndot_preserve_disjoint_l
.
Qed
.
Lemma
ndisj_subseteq_difference
N
E
F
:
E
⊥
↑
N
→
E
⊆
F
→
E
⊆
F
∖
↑
N
.
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