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87957de9
Commit
87957de9
authored
Feb 09, 2016
by
Robbert Krebbers
Browse files
Stronger version of auth_update w.r.t. step indexes.
parent
efd82c63
Changes
1
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Inline
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algebra/auth.v
View file @
87957de9
...
@@ 148,11 +148,11 @@ Lemma auth_frag_op a b : ◯ (a ⋅ b) ≡ ◯ a ⋅ ◯ b.
...
@@ 148,11 +148,11 @@ Lemma auth_frag_op a b : ◯ (a ⋅ b) ≡ ◯ a ⋅ ◯ b.
Proof
.
done
.
Qed
.
Proof
.
done
.
Qed
.
Lemma
auth_update
a
a'
b
b'
:
Lemma
auth_update
a
a'
b
b'
:
(
∀
n
af
,
✓
{
n
}
a
→
a
={
n
}=
a'
⋅
af
→
b
={
n
}=
b'
⋅
af
∧
✓
{
n
}
b
)
→
(
∀
n
af
,
✓
{
S
n
}
a
→
a
={
S
n
}=
a'
⋅
af
→
b
={
S
n
}=
b'
⋅
af
∧
✓
{
S
n
}
b
)
→
●
a
⋅
◯
a'
~~>
●
b
⋅
◯
b'
.
●
a
⋅
◯
a'
~~>
●
b
⋅
◯
b'
.
Proof
.
Proof
.
move
=>
Hab
[[]
bf1
]
n
//
=>[[
bf2
Ha
]
?]
;
do
2
red
;
simpl
in
*.
move
=>
Hab
[[
?

]
bf1
]
n
//
=>[[
bf2
Ha
]
?]
;
do
2
red
;
simpl
in
*.
destruct
(
Hab
(
S
n
)
(
bf1
⋅
bf2
))
as
[
Ha'
?]
;
auto
.
destruct
(
Hab
n
(
bf1
⋅
bf2
))
as
[
Ha'
?]
;
auto
.
{
by
rewrite
Ha
left_id
associative
.
}
{
by
rewrite
Ha
left_id
associative
.
}
split
;
[
by
rewrite
Ha'
left_id
associative
;
apply
cmra_includedN_l

done
].
split
;
[
by
rewrite
Ha'
left_id
associative
;
apply
cmra_includedN_l

done
].
Qed
.
Qed
.
...
...
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