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143fbc52
Commit
143fbc52
authored
Oct 06, 2016
by
Robbert Krebbers
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Prove that the dec_agree CMRA is total.
parent
59829441
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algebra/dec_agree.v
algebra/dec_agree.v
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algebra/dec_agree.v
View file @
143fbc52
...
@@ 31,21 +31,19 @@ Instance dec_agree_pcore : PCore (dec_agree A) := Some.
...
@@ 31,21 +31,19 @@ Instance dec_agree_pcore : PCore (dec_agree A) := Some.
Definition
dec_agree_ra_mixin
:
RAMixin
(
dec_agree
A
).
Definition
dec_agree_ra_mixin
:
RAMixin
(
dec_agree
A
).
Proof
.
Proof
.
split
.
apply
ra_total_mixin
;
apply
_

eauto
.

apply
_
.

intros
x
y
cx
?
[=<]
;
eauto
.

apply
_
.

intros
[?]
[?]
[?]
;
by
repeat
(
simplify_eq
/=

case_match
).

intros
[?]
[?]
[?]
;
by
repeat
(
simplify_eq
/=

case_match
).

intros
[?]
[?]
;
by
repeat
(
simplify_eq
/=

case_match
).

intros
[?]
[?]
;
by
repeat
(
simplify_eq
/=

case_match
).

intros
[?]
?
[=<]
;
by
repeat
(
simplify_eq
/=

case_match
).

intros
[?]
;
by
repeat
(
simplify_eq
/=

case_match
).

intros
[?]
;
by
repeat
(
simplify_eq
/=

case_match
).

intros
[?]
[?]
??
[=<]
;
eauto
.

by
intros
[?]
[?]
?.

by
intros
[?]
[?]
?.
Qed
.
Qed
.
Canonical
Structure
dec_agreeR
:
cmraT
:
=
Canonical
Structure
dec_agreeR
:
cmraT
:
=
discreteR
(
dec_agree
A
)
dec_agree_ra_mixin
.
discreteR
(
dec_agree
A
)
dec_agree_ra_mixin
.
Global
Instance
dec_agree_total
:
CMRATotal
dec_agreeR
.
Proof
.
intros
x
.
by
exists
x
.
Qed
.
(* Some properties of this CMRA *)
(* Some properties of this CMRA *)
Global
Instance
dec_agree_persistent
(
x
:
dec_agreeR
)
:
Persistent
x
.
Global
Instance
dec_agree_persistent
(
x
:
dec_agreeR
)
:
Persistent
x
.
Proof
.
by
constructor
.
Qed
.
Proof
.
by
constructor
.
Qed
.
...
@@ 59,8 +57,10 @@ Proof. destruct x; by rewrite /= ?decide_True. Qed.
...
@@ 59,8 +57,10 @@ Proof. destruct x; by rewrite /= ?decide_True. Qed.
Lemma
dec_agree_op_inv
(
x1
x2
:
dec_agree
A
)
:
✓
(
x1
⋅
x2
)
→
x1
=
x2
.
Lemma
dec_agree_op_inv
(
x1
x2
:
dec_agree
A
)
:
✓
(
x1
⋅
x2
)
→
x1
=
x2
.
Proof
.
destruct
x1
,
x2
;
by
repeat
(
simplify_eq
/=

case_match
).
Qed
.
Proof
.
destruct
x1
,
x2
;
by
repeat
(
simplify_eq
/=

case_match
).
Qed
.
Lemma
DecAgree_included
a
b
:
DecAgree
a
≼
DecAgree
b
→
a
=
b
.
Lemma
DecAgree_included
a
b
:
DecAgree
a
≼
DecAgree
b
↔
a
=
b
.
Proof
.
intros
[[
c
]
[=]%
leibniz_equiv_iff
].
by
simplify_option_eq
.
Qed
.
Proof
.
split
.
intros
[[
c
]
[=]%
leibniz_equiv
].
by
simplify_option_eq
.
by
intros
>.
Qed
.
End
dec_agree
.
End
dec_agree
.
Arguments
dec_agreeC
:
clear
implicits
.
Arguments
dec_agreeC
:
clear
implicits
.
...
...
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