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Rice Wine
Iris
Commits
39a5e48f
Commit
39a5e48f
authored
Jun 08, 2017
by
Robbert Krebbers
Browse files
More frac_auth stuff.
parent
3cb9abac
Changes
1
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Inline
Side-by-side
theories/algebra/frac_auth.v
View file @
39a5e48f
...
...
@@ -84,6 +84,11 @@ Section frac_auth.
Lemma
frag_auth_op
q1
q2
a1
a2
:
◯
!{
q1
+
q2
}
(
a1
⋅
a2
)
≡
◯
!{
q1
}
a1
⋅
◯
!{
q2
}
a2
.
Proof
.
done
.
Qed
.
Lemma
frac_auth_frag_validN_op_1_l
n
q
a
b
:
✓
{
n
}
(
◯
!{
1
}
a
⋅
◯
!{
q
}
b
)
→
False
.
Proof
.
rewrite
-
frag_auth_op
frac_auth_frag_validN
=>
-[/
exclusiveN_l
[]].
Qed
.
Lemma
frac_auth_frag_valid_op_1_l
q
a
b
:
✓
(
◯
!{
1
}
a
⋅
◯
!{
q
}
b
)
→
False
.
Proof
.
rewrite
-
frag_auth_op
frac_auth_frag_valid
=>
-[/
exclusive_l
[]].
Qed
.
Global
Instance
into_op_frac_auth
(
q
q1
q2
:
frac
)
(
a
a1
a2
:
A
)
:
IntoOp
q
q1
q2
→
IntoOp
a
a1
a2
→
IntoOp
(
◯
!{
q
}
a
)
(
◯
!{
q1
}
a1
)
(
◯
!{
q2
}
a2
).
Proof
.
by
rewrite
/
IntoOp
=>
/
leibniz_equiv_iff
->
->.
Qed
.
...
...
@@ -92,15 +97,15 @@ Section frac_auth.
Proof
.
by
rewrite
/
FromOp
=>
/
leibniz_equiv_iff
<-
<-.
Qed
.
Global
Instance
into_op_frac_auth_persistent
(
q
q1
q2
:
frac
)
(
a
:
A
)
:
IntoOp
q
q1
q2
→
Persistent
a
→
IntoOp
(
◯
!{
q
}
a
)
(
◯
!{
q1
}
a
)
(
◯
!{
q2
}
a
).
Persistent
a
→
IntoOp
q
q1
q2
→
IntoOp
(
◯
!{
q
}
a
)
(
◯
!{
q1
}
a
)
(
◯
!{
q2
}
a
).
Proof
.
rewrite
/
IntoOp
=>
/
leibniz_equiv_iff
->
?
.
rewrite
/
IntoOp
=>
?
/
leibniz_equiv_iff
->.
by
rewrite
-
frag_auth_op
-
persistent_dup
.
Qed
.
Global
Instance
from_op_frac_auth_persistent
(
q
q1
q2
:
frac
)
(
a
:
A
)
:
FromOp
q
q1
q2
→
Persistent
a
→
FromOp
(
◯
!{
q
}
a
)
(
◯
!{
q1
}
a
)
(
◯
!{
q2
}
a
).
Persistent
a
→
FromOp
q
q1
q2
→
FromOp
(
◯
!{
q
}
a
)
(
◯
!{
q1
}
a
)
(
◯
!{
q2
}
a
).
Proof
.
rewrite
/
FromOp
=>
/
leibniz_equiv_iff
<-
?
.
rewrite
/
FromOp
=>
?
/
leibniz_equiv_iff
<-.
by
rewrite
-
frag_auth_op
-
persistent_dup
.
Qed
.
...
...
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