> Could you elaborate on this? I would assume that once you have nfi and 
nfri you can easily convert between the two styles.

The conversion ist still possible. But nfi uses both ax-10 and ax-12, sth 
that I'd like to avoid if possible. This in some cases inevitably lead to 
different proofs for both versions.

Wolf

[email protected] schrieb am Sonntag, 12. September 2021 um 16:03:44 UTC+2:

> > (a) There is more friction in the transition between hb* and nf* style 
> theorems
>
> Could you elaborate on this? I would assume that once you have nfi and 
> nfri you can easily convert between the two styles.
>
> On Sun, Sep 12, 2021 at 9:16 AM 'ookami' via Metamath <
> [email protected]> wrote:
>
>> Hi,
>>
>> I recently uploaded a couple of theorems to my Mathbox, starting with 
>> http://us2.metamath.org:88/mpeuni/wl-section-nf.htm, that demonstrate 
>> how things could have developed, if one had picked 
>> http://us2.metamath.org:88/mpeuni/nf2.html instead of 
>> http://us2.metamath.org:88/mpeuni/df-nf.html as the defining term for 
>> 'Not Free (Ⅎ)'.
>> The results show, that one can expect in predicate logic an overall 
>> reduction of the usage of http://us2.metamath.org:88/mpeuni/ax-10.html, 
>> and perhaps a marginal decrease in use of 
>> http://us2.metamath.org:88/mpeuni/ax-12.html.
>> This certainly positive result is due to the more symmetric structure of 
>> nf2 wrt to negation, and the avoidance of mixed quantified and not 
>> quantified variables. But it comes with a price, too. (a) There is more 
>> friction in the transition between hb* and nf* style theorems; (b) Axioms 
>> like ax-5 need the old style for full exploitation, so there is a sort of 
>> disruption in technique present.
>> You will find more details in a 
>> http://us2.metamath.org:88/mpeuni/wl-section-nf.html.
>> But these are my thoughts. Let me hear how you think about a change of 
>> definition of 'Not Free'.
>> Wolf Lammen
>>
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