OK, thanks everyone!  So FILTER is what I must use.

I think I’m going to use ``(FILTER (\e. e = X) L = [X])`` to assert the unique 
appearance of X in list L, and after I split the list using MEM_SPLIT, my 
target props (~MEM X l1) could be re-expressed by EVERY and FILTER, then it may 
be provable for me.

—Chun

> Il giorno 05 ott 2017, alle ore 17:03, Scott Owens <[email protected]> ha 
> scritto:
> 
> Among others, LENGTH (FILTER (\e. X = e)) = 1
> 
> Scott
> 
>> On 2017/10/05, at 15:55, Chun Tian (binghe) <[email protected]> wrote:
>> 
>> But my list is not ALL_DISTINCT … there’re duplicated elements for sure, 
>> just the appearance of certain element is only one. —Chun
>> 
>>> Il giorno 05 ott 2017, alle ore 16:48, Konrad Slind 
>>> <[email protected]> ha scritto:
>>> 
>>> Hi Chun Tian,
>>> 
>>> The constant ALL_DISTINCT in listTheory is what you are looking for, I 
>>> think.
>>> 
>>> Konrad.
>>> 
>>> 
>>> On Thu, Oct 5, 2017 at 9:03 AM, Chun Tian (binghe) <[email protected]> 
>>> wrote:
>>> Hi,
>>> 
>>> (I'm new to HOL's listTheory). Suppose I have a list L which contains 
>>> possibly duplicated elements, and I want to express certain element X is 
>>> unique (i.e. has only one copy) in that list.  How can I do this?  It seems 
>>> "?!" doesn't work here, e.g. ``?!e. MEM e L /\ (e = X)``.
>>> 
>>> Regards,
>>> 
>>> Chun Tian
>>> 
>>> --
>>> Chun Tian (binghe)
>>> University of Bologna (Italy)
>>> 
>>> 
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>> 
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