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Marianna Rapoport
iris-coq
Commits
04d0796d
Commit
04d0796d
authored
Feb 23, 2016
by
Ralf Jung
Browse files
show some dec_agree properties
parent
7b0417ad
Changes
1
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Side-by-side
algebra/dec_agree.v
View file @
04d0796d
...
...
@@ -48,4 +48,20 @@ Qed.
Canonical
Structure
dec_agreeRA
:
cmraT
:
=
discreteRA
dec_agree_ra
.
End
dec_agree
.
\ No newline at end of file
(* Some properties of this CMRA *)
Lemma
dec_agree_idemp
(
x
:
dec_agree
A
)
:
x
⋅
x
≡
x
.
Proof
.
destruct
x
as
[
x
|]
;
simpl
;
repeat
(
case_match
;
simpl
)
;
try
subst
;
congruence
.
Qed
.
Lemma
dec_agree_op_inv
(
x1
x2
:
dec_agree
A
)
:
✓
(
x1
⋅
x2
)
→
x1
≡
x2
.
Proof
.
destruct
x1
as
[
x1
|],
x2
as
[
x2
|]
;
simpl
;
repeat
(
case_match
;
simpl
)
;
by
subst
.
Qed
.
Lemma
dec_agree_equivI
{
M
}
a
b
:
(
DecAgree
a
≡
DecAgree
b
)%
I
≡
(
a
=
b
:
uPred
M
)%
I
.
Proof
.
split
.
by
case
.
by
destruct
1
.
Qed
.
Lemma
dec_agree_validI
{
M
}
(
x
y
:
dec_agreeRA
)
:
✓
(
x
⋅
y
)
⊑
(
x
=
y
:
uPred
M
).
Proof
.
intros
r
n
_
?.
by
apply
:
dec_agree_op_inv
.
Qed
.
End
dec_agree
.
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