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Joshua Yanovski
iriscoq
Commits
f01839f7
Commit
f01839f7
authored
Apr 12, 2017
by
Ralf Jung
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add Aleš's proof that agree is not complete
parent
1c1ae879
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theories/algebra/agree.v
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theories/algebra/agree.v
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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
Ale
š
:
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
A
ₙ
be
the
set
of
all
binary
strings
of
length
n
.
Thus
for
A
ₙ
to
be
a
subset
of
T
we
have
them
continue
as
a
stream
of
zeroes
.
Now
A
ₙ
is
a
finite
non

empty
subset
of
T
.
Moreover
{
A
ₙ
}
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
;
...
...
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