Skip to content
GitLab
Projects
Groups
Snippets
Help
Loading...
Help
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
0
Issues
0
List
Boards
Labels
Service Desk
Milestones
Merge Requests
0
Merge Requests
0
CI / CD
CI / CD
Pipelines
Jobs
Schedules
Operations
Operations
Environments
Analytics
Analytics
CI / CD
Repository
Value Stream
Wiki
Wiki
Snippets
Snippets
Members
Members
Collapse sidebar
Close sidebar
Activity
Graph
Create a new issue
Jobs
Commits
Issue Boards
Open sidebar
Pierre-Marie Pédrot
Iris
Commits
f01839f7
Commit
f01839f7
authored
Apr 12, 2017
by
Ralf Jung
Browse files
Options
Browse Files
Download
Email Patches
Plain Diff
add Aleš's proof that agree is not complete
parent
1c1ae879
Changes
1
Hide whitespace changes
Inline
Side-by-side
Showing
1 changed file
with
21 additions
and
0 deletions
+21
-0
theories/algebra/agree.v
theories/algebra/agree.v
+21
-0
No files found.
theories/algebra/agree.v
View file @
f01839f7
...
@@ -6,6 +6,27 @@ Local Arguments valid _ _ !_ /.
...
@@ -6,6 +6,27 @@ Local Arguments valid _ _ !_ /.
Local
Arguments
op
_
_
_
!
_
/.
Local
Arguments
op
_
_
_
!
_
/.
Local
Arguments
pcore
_
_
!
_
/.
Local
Arguments
pcore
_
_
!
_
/.
(** Define an agreement construction such that Agree A is discrete when A is discrete.
Notice that this construction is NOT complete. The fullowing is due to Aleš:
Proposition: Ag(T) is not necessarily complete.
Proof.
Let T be the set of binary streams (infinite sequences) with the usual
ultrametric, measuring how far they agree.
Let Aₙ be the set of all binary strings of length n. Thus for Aₙ to be a
subset of T we have them continue as a stream of zeroes.
Now Aₙ is a finite non-empty subset of T. Moreover {Aₙ} is a Cauchy sequence
in the defined (Hausdorff) metric.
However the limit (if it were to exist as an element of Ag(T)) would have to
be the set of all binary streams, which is not exactly finite.
Thus Ag(T) is not necessarily complete.
*)
Record
agree
(
A
:
Type
)
:
Type
:
=
Agree
{
Record
agree
(
A
:
Type
)
:
Type
:
=
Agree
{
agree_car
:
A
;
agree_car
:
A
;
agree_with
:
list
A
;
agree_with
:
list
A
;
...
...
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