Skip to content
Projects
Groups
Snippets
Help
Loading...
Help
Support
Keyboard shortcuts
?
Submit feedback
Contribute to GitLab
Sign in / Register
Toggle navigation
I
Iris
Project overview
Project overview
Details
Activity
Releases
Repository
Repository
Files
Commits
Branches
Tags
Contributors
Graph
Compare
Issues
81
Issues
81
List
Boards
Labels
Milestones
Merge Requests
10
Merge Requests
10
CI / CD
CI / CD
Pipelines
Jobs
Schedules
Analytics
CI / CD Analytics
Repository Analytics
Value Stream Analytics
Wiki
Wiki
Members
Members
Collapse sidebar
Close sidebar
Activity
Graph
Create a new issue
Jobs
Commits
Issue Boards
Open sidebar
Iris
Iris
Commits
143fbc52
Commit
143fbc52
authored
Oct 06, 2016
by
Robbert Krebbers
Browse files
Options
Browse Files
Download
Email Patches
Plain Diff
Prove that the dec_agree CMRA is total.
parent
59829441
Changes
1
Hide whitespace changes
Inline
Sidebyside
Showing
1 changed file
with
8 additions
and
8 deletions
+8
8
algebra/dec_agree.v
algebra/dec_agree.v
+8
8
No files found.
algebra/dec_agree.v
View file @
143fbc52
...
...
@@ 31,21 +31,19 @@ Instance dec_agree_pcore : PCore (dec_agree A) := Some.
Definition
dec_agree_ra_mixin
:
RAMixin
(
dec_agree
A
).
Proof
.
split
.

apply
_
.

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

apply
_
.
apply
ra_total_mixin
;
apply
_

eauto
.

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
[?]
[?]
?.
Qed
.
Canonical
Structure
dec_agreeR
:
cmraT
:
=
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 *)
Global
Instance
dec_agree_persistent
(
x
:
dec_agreeR
)
:
Persistent
x
.
Proof
.
by
constructor
.
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
.
Proof
.
destruct
x1
,
x2
;
by
repeat
(
simplify_eq
/=

case_match
).
Qed
.
Lemma
DecAgree_included
a
b
:
DecAgree
a
≼
DecAgree
b
→
a
=
b
.
Proof
.
intros
[[
c
]
[=]%
leibniz_equiv_iff
].
by
simplify_option_eq
.
Qed
.
Lemma
DecAgree_included
a
b
:
DecAgree
a
≼
DecAgree
b
↔
a
=
b
.
Proof
.
split
.
intros
[[
c
]
[=]%
leibniz_equiv
].
by
simplify_option_eq
.
by
intros
>.
Qed
.
End
dec_agree
.
Arguments
dec_agreeC
:
clear
implicits
.
...
...
Write
Preview
Markdown
is supported
0%
Try again
or
attach a new file
Attach a file
Cancel
You are about to add
0
people
to the discussion. Proceed with caution.
Finish editing this message first!
Cancel
Please
register
or
sign in
to comment