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979b6b5b
Commit
979b6b5b
authored
Feb 08, 2016
by
Robbert Krebbers
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Transport an equality between CMRAs.
parent
7a070280
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algebra/cmra.v
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979b6b5b
...
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@@ -393,6 +393,35 @@ Section cmra_monotone.
Proof
.
rewrite
!
cmra_valid_validN
;
eauto
using
validN_preserving
.
Qed
.
End
cmra_monotone
.
(** * Transporting a CMRA equality *)
Definition
cmra_transport
{
A
B
:
cmraT
}
(
H
:
A
=
B
)
(
x
:
A
)
:
B
:
=
eq_rect
A
id
x
_
H
.
Section
cmra_transport
.
Context
{
A
B
:
cmraT
}
(
H
:
A
=
B
).
Notation
T
:
=
(
cmra_transport
H
).
Global
Instance
cmra_transport_ne
n
:
Proper
(
dist
n
==>
dist
n
)
T
.
Proof
.
by
intros
???
;
destruct
H
.
Qed
.
Global
Instance
cmra_transport_proper
:
Proper
((
≡
)
==>
(
≡
))
T
.
Proof
.
by
intros
???
;
destruct
H
.
Qed
.
Lemma
cmra_transport_op
x
y
:
T
(
x
⋅
y
)
=
T
x
⋅
T
y
.
Proof
.
by
destruct
H
.
Qed
.
Lemma
cmra_transport_unit
x
:
T
(
unit
x
)
=
unit
(
T
x
).
Proof
.
by
destruct
H
.
Qed
.
Lemma
cmra_transport_validN
n
x
:
✓
{
n
}
(
T
x
)
↔
✓
{
n
}
x
.
Proof
.
by
destruct
H
.
Qed
.
Lemma
cmra_transport_valid
x
:
✓
(
T
x
)
↔
✓
x
.
Proof
.
by
destruct
H
.
Qed
.
Global
Instance
cmra_transport_timeless
x
:
Timeless
x
→
Timeless
(
T
x
).
Proof
.
by
destruct
H
.
Qed
.
Lemma
cmra_transport_updateP
(
P
:
A
→
Prop
)
(
Q
:
B
→
Prop
)
x
:
x
~~>
:
P
→
(
∀
y
,
P
y
→
Q
(
T
y
))
→
T
x
~~>
:
Q
.
Proof
.
destruct
H
;
eauto
using
cmra_updateP_weaken
.
Qed
.
Lemma
cmra_transport_updateP'
(
P
:
A
→
Prop
)
x
:
x
~~>
:
P
→
T
x
~~>
:
λ
y
,
∃
y'
,
y
=
cmra_transport
H
y'
∧
P
y'
.
Proof
.
eauto
using
cmra_transport_updateP
.
Qed
.
End
cmra_transport
.
(** * Instances *)
(** ** Discrete CMRA *)
Class
RA
A
`
{
Equiv
A
,
Unit
A
,
Op
A
,
Valid
A
,
Minus
A
}
:
=
{
...
...
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