Ë
    7^(hA§  ã                   ó¨	  — d Z g d¢Z eg d ed«      f‘d ed«      f‘d ed«      f‘d ed	«      f‘d
 ed«      f‘d ed«      f‘d ed«      f‘d ed«      f‘d ed«      f‘d ed«      f‘d ed«      f‘d ed«      f‘d ed«      f‘d ed«      f‘d ed«      f‘d ed«      f‘d  ed!«      f‘d" ed#«      f‘d$ ed%«      f‘d& ed'«      f‘d( ed)«      f‘d* ed+«      f‘d, ed-«      f‘d. ed/«      f‘d0 ed1«      f‘d2 ed3«      f‘d4 ed«      f‘d5 ed6«      f‘d7 ed8«      f‘d9 ed«      f‘d: ed;«      f‘d< ed=«      f‘d> ed?«      f‘d@ edA«      f‘dB edC«      f‘dD ed«      f‘dE edF«      f‘dG ed«      f‘dH edI«      f‘dJ ed«      f‘dK edL«      f‘dM edN«      f‘dO edP«      f‘dQ edR«      f‘dS edT«      f‘dU edV«      f‘dW edX«      f‘dY ed«      f‘dZ ed[«      f‘d\ ed]«      f‘d^ ed_«      f‘d` ed«      f‘da edb«      f‘dc edd«      f‘de edf«      f‘dg edh«      f‘di edj«      f‘dk ed«      f‘dl edm«      f‘dn ed«      f‘«      Zi doh dp£“dqdrh“dsh dt£“duh dv£“dwh dx£“dyh dz£“d{h d|£“d}h d~£“dh d€£“d�h d‚£“dƒh d„£“d…h d†£“d‡h dˆ£“d‰h dŠ£“drh d‹£“dŒh d�£“dŽh d�£“h d�£h d‘£h d’£h d“£h d”£h d•£h d–£h d—£h d˜£h d™£h dš£h d›£h dœ£d�œ¥Zg h dž£df‘h dŸ£df‘d>dYhdf‘h d £df‘d d$hdf‘dd,hdf‘d*d,hd f‘d,dnhd$f‘h d¡£d(f‘dd$hd(f‘d<dghd.f‘h d¢£d.f‘d,dghd:f‘dcdehdBf‘h d££dEf‘dOdShdEf‘dd0hdEf‘d,d@hdHf‘dGdehdKf‘dd0hdKf‘d\dehdOf‘d d0hdOf‘d$d0hdSf‘dd>hdWf‘h d¤£d\f‘h d¥£dZf‘dKdShdZf‘d(d0hdZf‘h d¦£d^f‘h d§£dgf‘d,d<hdef‘d,d0hdef‘ddhdif‘h d¨£dlf‘h d©£dlf‘dd hdlf‘dKdOhdlf‘Zi dg dª¢“dg d«¢“dg “dg “dg d¬¢“dg d­¢“dg d®¢“dd¯d°g“dg d±¢“dg d²¢“dg d³¢“dg d´¢“dg dµ¢“dg d¶¢“d"g d·¢“d g d¸¢“d&g d¹¢“i d$g dº¢“d*g d»¢“d(g d¼¢“d.g “d,g d½¢“d2g d¾¢“d0g d«¢“d5g d¬¢“d7d¿g“d<g d«¢“d:g d¾¢“d@g dÀ¢“d>g dÁ¢“dBg dÂ¢“dGg dÃ¢“dEg dÄ¢“dHg dÅ¢“¥i dMg dÆ¢“dKg dÇ¢“dQg dÈ¢“dOg dÉ¢“dUg dÊ¢“dSg dË¢“dYd°g“dWg dÌ¢“d\g dÍ¢“dZg dÎ¢“d`g dÏ¢“d^d¯d°g“dcg dÐ¢“dag dÑ¢“dgg d¬¢“deg dÒ¢“dig dÓ¢“¥g dÔ¢g dÕœ¥ZeeeeedÖœZy×)ØzC
Do NOT manually edit this file.
Instead, run ./bin/ask_update.py.
)Ú	algebraicÚantihermitianÚcommutativeÚcomplexÚ	compositeÚevenÚextended_negativeÚextended_nonnegativeÚextended_nonpositiveÚextended_nonzeroÚextended_positiveÚextended_realÚfiniteÚ	hermitianÚ	imaginaryÚinfiniteÚintegerÚ
irrationalÚnegativeÚ
nonintegerÚnonnegativeÚnonpositiveÚnonzeroÚoddÚpositiveÚprimeÚrationalÚrealÚtranscendentalÚzero©r   T)©r   T©r   T©r   T©r   F©r   F©r   F)©r   F©r   F©r   F©r   F©r   F©r   F©r   F©r   T© )r   F)©r   Fr!   )r   F)r&   ©r   Fr'   r(   ©r   F©r	   F©r
   F©r   F©r   F©r   Fr0   r)   ©r   F©r   F©r   F©r   F©r   F©r   Fr*   ©r   Fr+   r,   ©r   Fr%   r-   r"   )r!   r#   r$   r1   )r&   r'   r(   r0   r)   r8   r9   r;   r<   r=   r*   r>   r+   r,   r?   r%   r-   )r   T)r    r!   r"   r2   ©r	   Tr4   ©r   T©r   T©r   Tr#   ©r   Tr0   r$   ©r   Tr8   r9   r:   ©r   Tr<   ©r   T©r   Tr+   ©r   T©r   Tr%   r-   r'   ©r   T)r    r!   r"   rC   r#   rD   r0   r$   rE   r8   r:   r*   rI   rJ   r%   r(   )r-   ©r   T)r!   r'   r3   ©r
   TrA   r6   rC   r0   r;   r>   r+   r-   r2   )r9   r@   )r!   r2   rC   r0   r9   r3   )r'   r6   r;   r>   r+   r-   rM   )r!   r'   r6   rC   r0   r>   r+   r4   )r2   r9   r<   r-   rA   )r!   rC   r0   r-   r5   )r'   r2   r6   r9   r=   r>   r+   rB   )
r!   r2   r@   r4   rA   rC   r0   r9   r<   r-   r6   )r'   r>   r+   rC   )r!   r0   r7   )r'   r(   r2   r3   r4   r5   r6   r)   r8   r9   r:   r;   r<   r=   r*   r>   r+   r,   r?   r-   r#   )r$   ©r   F)r&   r1   r'   r(   r0   ©r   Tr)   r8   r9   r;   r<   r=   r*   r>   r+   r,   r?   r%   r-   rD   )r   F)r'   r(   r)   r8   r9   r;   r<   r=   r*   r>   r+   r,   r?   r-   )r   T)r.   r!   r"   r'   r(   r2   r3   r4   r5   r6   r7   r#   r$   r)   r8   r9   r:   r;   r<   r=   r*   r>   r+   r,   r?   r-   r0   rO   )r&   r1   r'   r(   rN   r0   r)   r8   r9   r;   r<   r=   r*   r>   r+   r,   r?   r%   r-   r$   )r#   rE   )r    r!   r"   rC   r#   rD   r0   r$   r8   r:   rI   rJ   r%   r)   )r'   r(   r*   r+   r-   )r   T)r!   r"   r'   r(   rA   rC   r#   rD   r0   r$   r)   ©r   TrG   r*   r+   r,   rJ   r-   r8   )r   T)r!   r"   r'   rL   r3   rM   rA   r6   rC   r#   rD   r0   r$   r;   ©r   TrG   r>   r+   rJ   r-   r9   rP   )
r!   r'   r(   rA   rC   r0   r)   r*   r+   r-   r:   rF   )r!   r"   r2   r@   rC   r#   rD   r0   r$   r9   rJ   r;   )r'   r>   r+   r-   rQ   )r!   r"   r'   rM   r6   rC   r#   rD   r0   r$   r>   r+   rJ   r<   )r9   r-   rG   )
r!   r"   rA   rC   r#   rD   r0   r$   rJ   r-   r=   )r'   r9   r>   r+   )r   T)r    r!   r"   r(   rA   rC   r#   rD   r0   r$   rE   r8   r:   rG   rI   rJ   r%   r-   r*   rH   )r!   r"   r2   r@   r4   rA   rB   rC   r#   rD   r0   r$   r9   rF   r<   rG   rJ   r-   r>   )r'   r+   )r   T)r    r!   r"   r'   r2   r@   r4   rA   rB   rC   r#   rD   r0   r$   rE   r8   r9   r:   rF   r<   rG   rH   rI   rJ   r%   r-   r+   rI   )r    r!   r"   rC   r#   rD   r0   r$   r8   rJ   r%   r,   )r'   r(   r)   r*   r+   r-   rJ   )r!   r"   rC   r#   rD   r0   r$   r?   )r'   r(   r)   r8   r9   r;   r<   r=   r*   r>   r+   r,   r-   )r   T)r&   r!   r"   r'   r(   r#   r$   r)   r*   r+   r,   r-   r%   ©r   T)r    r!   r"   r'   rK   r2   r@   rM   r5   r6   rC   r#   rD   r0   r$   rE   r8   r9   r:   rF   rQ   r=   r*   r>   r+   rI   rJ   r%   r-   r   >   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   >   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r	   r
   r   >   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   >   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r	   r
   r   >   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   >   r   r   r   r   r   r   r   r   r   r   r   r	   r
   r	   >   r   r   r   r   r   r   r   r   r   r   r   r
   >   r   r   r   r   r   r   r   r   r   r   r   r   >   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   >   r   r   r   r   r   r   r   r   r   r   r   r	   r
   r   >   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r	   r
   r   >   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   >   r   r   r   r   r   r   r   r   r   r   r   r   r   r   >   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r	   r
   r   >   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   >   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   >   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   >   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r	   r
   >
   r   r   r   r   r   r   r   r   r   r   >   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r	   >   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r
   >   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   >   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   >   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r	   r
   >   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r	   r
   >   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   >   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   >   r   r   r   r   r   r   r   r   r   r   r   r   >   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r	   r
   )r   r   r   r   r   r   r   r   r   r   r   r   r   >   rK   r+   rH   >   r+   rH   r'   >   r-   rC   r6   >   r-   rC   r2   >   r-   r2   r6   >   rJ   r-   r>   >   rK   r+   r'   >   rJ   r-   r9   >   rK   rH   r'   >   r-   r9   r>   >   rC   r2   r6   >   rJ   r9   r>   )
é    é   é   é   é   é   é   é   é   é   )é
   é   é   é   é   é   é   é   )r]   é   rT   rU   rV   r[   r\   )	rS   r]   r^   r_   r`   ra   rb   rc   rd   )é   é   é   é   é   )ri   rT   rU   rV   rW   rX   rY   r\   )rU   é!   rV   é   é   rX   é"   rY   é   é   r`   ra   rb   rc   rd   é    rg   rh   r\   )rT   rk   rV   rm   rW   rn   rY   rp   )
r^   re   r_   rW   rX   ro   ra   rb   rd   r[   )rT   rU   rl   rW   rX   ro   r\   )r^   re   r_   rk   rV   é	   rl   rW   rn   rY   rp   rc   é#   r[   r\   )rT   rV   rm   rW   rY   rp   r\   )r^   re   r_   rU   rk   é   rm   rW   rX   rn   ro   rb   rs   r[   r\   )rT   rk   rl   rm   rW   rn   ro   rp   )r^   re   r_   rU   rV   rt   rr   rl   rm   rW   rX   rY   rd   r[   )rT   rU   rk   rl   rW   rX   rn   ro   )
r^   re   r_   rW   rY   rp   r`   rc   rd   r[   )
r^   re   r_   rU   rk   rV   rl   rm   r[   r\   )rT   rU   rV   r[   r\   rS   )rT   rU   rV   rW   rX   rY   r[   r\   )ri   rj   rU   rk   rV   rl   rm   rX   rn   rY   ro   rp   r`   ra   rb   rc   rd   r\   )rS   rU   rV   rt   rr   rl   rm   rX   rY   é   é   ro   rp   r`   ra   rb   rc   )rW   rn   rY   rp   )rS   rZ   r[   )r^   re   r_   rU   rV   rt   rr   rl   rm   rW   rX   rY   rd   )rT   rU   rV   rW   rX   ro   r\   )rS   rk   rV   rr   rl   rn   rY   rv   ro   r`   rb   rd   rs   é$   rZ   r[   r\   )rT   rU   rV   rW   rY   rp   r\   )rS   rU   rk   rt   rm   rX   rn   ru   rp   ra   rc   rd   rs   rw   rZ   r[   r\   )rW   rn   ro   rp   )rS   rU   rV   rt   rr   rl   rm   rX   rY   ru   rv   ro   rp   r`   ra   rb   rc   rZ   r[   )rU   rV   rt   rr   rl   rm   rX   rY   ru   rv   ro   rp   r`   ra   rb   rc   )rW   rX   rn   ro   )rS   rq   rf   rg   rZ   r[   )rq   rf   rh   )	rT   rU   rV   rW   rX   rY   rZ   r[   r\   )rU   rk   rV   rl   rm   rX   rn   rY   ro   rp   r`   ra   rb   rc   rd   r[   r\   )rS   rU   rk   rV   rl   rm   rX   rn   rY   ro   rp   r`   ra   rb   rc   rd   rZ   r[   r\   )r]   r^   r_   rT   rU   rV   rW   rX   rY   r`   ra   rb   rc   rd   rZ   r[   r\   )rT   rU   rV   rW   rX   rY   r\   )r-   rR   )Údefined_factsÚfull_implicationsÚprereqÚ
beta_rulesÚbeta_triggersN)	Ú__doc__rx   ÚdictÚsetry   rz   r{   r|   Úgenerated_assumptionsr/   ó    ú^/var/www/skyplay_api_hub/venv/lib/python3.12/site-packages/sympy/core/assumptions_generated.pyú<module>rƒ      s)  ðñò
€ñD ð qà™#ð  	ó ð ðqð ™3ð !	ó ð 	ðqð, ™cð $	ó ð ð-qð4 ™sð %	ó  ð ð5qð> ™Cð "	ó ð ð?qðF ™Sð #	ó ð ðGqð@ ™ð 	ó ð ðAqðN ™ð 	ó ð ðOqðx ™#ð  	ó ð ðyqðt ™3ð !	ó ð ðuqð| ‘Sð 	ó ð ð}qðb ‘cð 	ó ð ðcqðl !¡#ð (	ó #ð ðmqðL "¡3ð )	ó $ð ðMqðV $¡Sð +	ó &ð ðWqðh %¡cð ,	ó 'ð ðiqð| $¡Sð +	ó &ð 	ð}qðR %¡cð ,	ó 'ð ðSqðb  ¡ð '	ó "ð ðcqðr !¡#ð (	ó #ð 	ðsqðH !¡#ð (	ó #ð ðIqðd "¡3ð )	ó $ð ðeqðr ™cð $	ó ð ðsqð~ ™sð %	ó  ð ðqðn ‘sð 	ó ð ðoqðx ™ð 	ó ð ðyqðf	 ™#ð  	ó ð ðg	qðn	 ™3ð !	ó ð ðo	qðR
 ™#ð  	ó ð ðS
qðN ™3ð !	ó ð ðOqðV ™ð 	ó ð ðWqðD ™#ð  	ó ð ðEqðN ™ð 	ó ð ðOqðp ™ð 	ó ð ðqqðB ™3ð !	ó ð ðCqðn ™Cð "	ó ð ðoqðv ™ð 	ó ð ðwqðf ™#ð  	ó ð ðgqðn ™3ð !	ó ð ðoqðJ ™Cð "	ó ð ðKqðR ™Cð "	ó ð ðSqðp ™Sð #	ó ð ðqqð@ ™Cð "	ó ð ðAqðb ™Sð #	ó ð ðcqðn ™ð 	ó ð ðoqðJ ™ð 	ó ð ðKqðZ ‘Cð 	ó ð ð[qðF ‘Sð 	ó ð ðGqðN ™ð 	ó ð ðOqðz ™#ð  	ó ð ð{qðF ‘cð 	ó ð ðGqðB ‘sð 	ó ð ðCqðJ ™ð 	ó ð ðKqðh ™#ð  	ó ð ðiqð| ‘Sð 	ó ð 	ð}qðR ‘cð 	ó ð ðSqðt ™sð %	ó  ð ðuqðT ¡ð &	ó !ð ðUqð\ ‘Sð 	ó ð ð]qð\ ‘cð 	ó ð ð]qó qÐ ðhx	
ð ò ðx	
ð& Øðð'x	
ð0 ò ð1x	
ðj ò ðkx	
ðZ ò ð[x	
ðV ò ðWx	
ð~ ò ðx	
ð` ò ðax	
ð~ ò ðx	
ð\ ò ð]x	
ð@ ò ðAx	
ðb ò ðcx	
ðV ò ðWx	
ðD ò ðEx	
ðh ò ðix	
ðd	 ò ðe	x	
ðR
 ò ðS
x	
ò~
ò&ò0òò&ò&ò(ò(ò0ò<ò*ò0ò òsx	
€ðx|ò <Øðð|ò BØðð|ð ˜Ð(Øðð|ò NØ#ð%ð|ð" %Ð&@ÐAØ#ð%ð#|ð* #Ð$;Ð<Ø&ð(ð+|ð2 #Ð$;Ð<Ø&ð(ð3|ð: ˜Ð/Ø"ð$ð;|òB NØ#ð%ðC|ðF %Ð&@ÐAØ#ð%ðG|ðN ˜?Ð+Ø ð"ðO|òR SØ ð"ðS|ðZ ˜Ð/Øðð[|ðb ˜>Ð*Øððc|òj <Øððk|ðn Ð.Ð/Øððo|ðr "Ð#3Ð4Øððs|ðz Ð1Ð2Øðð{|ðB ˜>Ð*ØððC|ðF %Ð&6Ð7ØððG|ðN ˜>Ð*ØððO|ðR %Ð&6Ð7ØððS|ðZ !Ð"2Ð3Øðð[|ðb Ð(Ð)Øððc|òj >Øððk|òr <Øððs|ðv Ð.Ð/Øððw|ðz "Ð#3Ð4Øðð{|òB @ØððC|òJ AØððK|ðR Ð2Ð3ØððS|ðV Ð/Ð0ØððW|ð^ Ð-Ð.Ø ð"ð_|òf [Øððg|òj @Øððk|ðn %Ð&DÐEØððo|ðr Ð2Ð3Øððs|€
ðz6ØÒ?ð6àÒ9ð6ð ˜bð6ð ˜Bð	6ð
 Ò1ð6ð Ò;ð6ð š+ð6ð ˜"˜a˜ð6ð Ò2ð6ð ÒZð6ð !Ò"@ð6ð  Ò!Ið6ð $Ò%>ð6ð #Ò$\ð6ð $Ò%>ð6ð  #Ò$\ð!6ð"  Ò!?ñ#6ð$ Ò Rð%6ð& !Ò"@ð'6ð(  Ò!Ið)6ð* ˜bð+6ð, Ò@ð-6ð. Ò(ð/6ð0 Ò6ð16ð2 Ò3ð36ð4 ˜"˜ð56ð6 Ò9ð76ð8 Ò)ð96ð: Ò5ð;6ð< ÒYð=6ð> ÒXð?6ð@ Ò)ðA6ðB šðC6ðD ÒHòE6ðF Ò5ðG6ðH Ò[ðI6ðJ Ò5ðK6ðL Ò[ðM6ðN Ò(ðO6ðP Ò]ðQ6ðR �Q�CðS6ðT ÒMðU6ðV Ò)ðW6ðX Ò.ðY6ðZ ’jð[6ð\ �b˜!�Wð]6ð^ Ò:ð_6ð` ÒWða6ðb Ò.ðc6ðd Ò[ðe6ðf Ò_ñg6òh /Øòk6€ðr +8ÐN_Ø¨zÈMñ[Ñ r�   