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f72340bc
Commit
f72340bc
authored
Sep 20, 2016
by
Robbert Krebbers
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More derived auth properties.
parent
0024ac1f
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#2720
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in 9 minutes and 25 seconds
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algebra/auth.v
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f72340bc
...
...
@@ -111,6 +111,8 @@ Proof.
destruct
x
as
[[[?|]|]
?]
;
simpl
;
try
done
.
setoid_rewrite
<-
cmra_discrete_included_iff
;
naive_solver
eauto
using
0
.
Qed
.
Lemma
auth_valid_discrete_2
`
{
CMRADiscrete
A
}
a
b
:
✓
(
●
a
⋅
◯
b
)
↔
b
≼
a
∧
✓
a
.
Proof
.
by
rewrite
auth_valid_discrete
/=
left_id
.
Qed
.
Lemma
authoritative_valid
x
:
✓
x
→
✓
authoritative
x
.
Proof
.
by
destruct
x
as
[[[]|]].
Qed
.
...
...
@@ -189,6 +191,10 @@ Lemma auth_frag_op a b : ◯ (a ⋅ b) ≡ ◯ a ⋅ ◯ b.
Proof
.
done
.
Qed
.
Lemma
auth_both_op
a
b
:
Auth
(
Excl'
a
)
b
≡
●
a
⋅
◯
b
.
Proof
.
by
rewrite
/
op
/
auth_op
/=
left_id
.
Qed
.
Lemma
auth_frag_mono
a
b
:
a
≼
b
→
◯
a
≼
◯
b
.
Proof
.
intros
[
c
->].
rewrite
auth_frag_op
.
apply
cmra_included_l
.
Qed
.
Lemma
auth_auth_valid
a
:
✓
a
→
✓
(
●
a
).
Proof
.
intros
;
split
;
simpl
;
auto
using
ucmra_unit_leastN
.
Qed
.
Lemma
auth_update
a
af
b
:
a
~l
~>
b
@
Some
af
→
●
(
a
⋅
af
)
⋅
◯
a
~~>
●
(
b
⋅
af
)
⋅
◯
b
.
...
...
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