Skip to content
GitLab
Menu
Projects
Groups
Snippets
Loading...
Help
Help
Support
Community forum
Keyboard shortcuts
?
Submit feedback
Contribute to GitLab
Sign in / Register
Toggle navigation
Menu
Open sidebar
Pierre-Marie Pédrot
Iris
Commits
f01839f7
Commit
f01839f7
authored
Apr 12, 2017
by
Ralf Jung
Browse files
add Aleš's proof that agree is not complete
parent
1c1ae879
Changes
1
Hide whitespace changes
Inline
Side-by-side
theories/algebra/agree.v
View file @
f01839f7
...
...
@@ -6,6 +6,27 @@ Local Arguments valid _ _ !_ /.
Local
Arguments
op
_
_
_
!
_
/.
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
{
agree_car
:
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