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Dan Frumin
iris-coq
Commits
add800d8
Commit
add800d8
authored
Jul 01, 2016
by
Jacques-Henri Jourdan
Browse files
Local updates for sums
parent
9af65178
Changes
1
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Inline
Side-by-side
algebra/csum.v
View file @
add800d8
...
...
@@ -292,6 +292,32 @@ Proof. eauto using csum_updateP_l. Qed.
Lemma
csum_updateP
'_
r
(
P
:
B
→
Prop
)
b
:
b
~~>:
P
→
Cinr
b
~~>:
λ
m
'
,
∃
b
'
,
m
'
=
Cinr
b
'
∧
P
b
'
.
Proof
.
eauto
using
csum_updateP_r
.
Qed
.
Lemma
csum_local_update_l
(
a1
a2
:
A
)
af
:
(
∀
af
'
,
af
=
Cinl
<
$
>
af
'
→
a1
~
l
~>
a2
@
af
'
)
→
Cinl
a1
~
l
~>
Cinl
a2
@
af
.
Proof
.
intros
Ha
.
split
;
destruct
af
as
[[
af
'
|
|
]
|
]
=>
//=.
-
by
eapply
(
Ha
(
Some
af
'
)).
-
by
eapply
(
Ha
None
).
-
destruct
(
Ha
(
Some
af
'
)
(
reflexivity
_
))
as
[
_
Ha
'
].
intros
n
[[
mz
|
mz
|
]
|
]
?
;
inversion
1
;
subst
;
constructor
.
by
apply
(
Ha
'
n
(
Some
mz
)).
by
apply
(
Ha
'
n
None
).
-
destruct
(
Ha
None
(
reflexivity
_
))
as
[
_
Ha
'
].
intros
n
[[
mz
|
mz
|
]
|
]
?
;
inversion
1
;
subst
;
constructor
.
by
apply
(
Ha
'
n
(
Some
mz
)).
by
apply
(
Ha
'
n
None
).
Qed
.
Lemma
csum_local_update_r
(
b1
b2
:
B
)
bf
:
(
∀
bf
'
,
bf
=
Cinr
<
$
>
bf
'
→
b1
~
l
~>
b2
@
bf
'
)
→
Cinr
b1
~
l
~>
Cinr
b2
@
bf
.
Proof
.
intros
Hb
.
split
;
destruct
bf
as
[[
|
bf
'
|
]
|
]
=>
//=.
-
by
eapply
(
Hb
(
Some
bf
'
)).
-
by
eapply
(
Hb
None
).
-
destruct
(
Hb
(
Some
bf
'
)
(
reflexivity
_
))
as
[
_
Hb
'
].
intros
n
[[
mz
|
mz
|
]
|
]
?
;
inversion
1
;
subst
;
constructor
.
by
apply
(
Hb
'
n
(
Some
mz
)).
by
apply
(
Hb
'
n
None
).
-
destruct
(
Hb
None
(
reflexivity
_
))
as
[
_
Hb
'
].
intros
n
[[
mz
|
mz
|
]
|
]
?
;
inversion
1
;
subst
;
constructor
.
by
apply
(
Hb
'
n
(
Some
mz
)).
by
apply
(
Hb
'
n
None
).
Qed
.
End
cmra
.
Arguments
csumR
:
clear
implicits
.
...
...
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