
    wgA                     	   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$ ed%      fd& ed'      fd( ed)      fd* ed+      fd, ed-      fd. ed/      fd0 ed1      fd2 ed3      fd4 ed      fd5 ed6      fd7 ed8      fd9 ed      fd: ed;      fd< ed=      fd> ed?      fd@ edA      fdB edC      fdD ed      fdE edF      fdG ed      fdH edI      fdJ ed      fdK edL      fdM edN      fdO edP      fdQ edR      fdS edT      fdU edV      fdW edX      fdY ed      fdZ ed[      fd\ ed]      fd^ ed_      fd` ed      fda edb      fdc edd      fde edf      fdg edh      fdi edj      fdk ed      fdl edm      fdn ed      f      Zi doh dpdqdrhdsh dtduh dvdwh dxdyh dzd{h d|d}h d~dh ddh ddh ddh ddh ddh ddrh ddh ddh dh dh dh dh dh dh dh dh dh dh dh dh dh ddZg h ddfh ddfd>dYhdfh ddfd d$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$d0hdSfdd>hdWfh dd\fh ddZfdKdShdZfd(d0hdZfh dd^fh ddgfd,d<hdefd,d0hdefddhdifh ddlfh ddlfdd hdlfdKdOhdlfZi dg ddg ddg dg dg ddg ddg ddddgdg ddg ddg ddg ddg ddg dd"g dd g dd&g di d$g dd*g dd(g dd.g d,g dd2g dd0g dd5g dd7dgd<g dd:g dd@g dd>g ddBg d¢dGg dâdEg dĢdHg dŢi dMg dƢdKg dǢdQg dȢdOg dɢdUg dʢdSg dˢdYdgdWg d̢d\g d͢dZg d΢d`g dϢd^ddgdcg dТdag dѢdgg ddeg dҢdig dӢg dԢg d՜Zeeeeed֜Zy)zC
Do NOT manually edit this file.
Instead, run ./bin/ask_update.py.
)	algebraicantihermitiancommutativecomplex	compositeevenextended_negativeextended_nonnegativeextended_nonpositiveextended_nonzeroextended_positiveextended_realfinite	hermitian	imaginaryinfiniteinteger
irrationalnegative
nonintegernonnegativenonpositivenonzerooddpositiveprimerationalrealtranscendental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>   )
                               )
                        )r]      rT   rU   rV   r[   r\   )	rS   r]   r^   r_   r`   ra   rb   rc   rd   )               )ri   rT   rU   rV   rW   rX   rY   r\   )rU   !   rV         rX   "   rY         r`   ra   rb   rc   rd       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   	   rl   rW   rn   rY   rp   rc   #   r[   r\   )rT   rV   rm   rW   rY   rp   r\   )r^   re   r_   rU   rk      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         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   $   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   )defined_factsfull_implicationsprereq
beta_rulesbeta_triggersN)	__doc__rx   dictsetry   rz   r{   r|   generated_assumptionsr/       e/home/mcse/projects/flask/flask-venv/lib/python3.12/site-packages/sympy/core/assumptions_generated.py<module>r      s)  
D  q#  	  q 3 !	  	q, c $	  -q4 s %	   5q> C "	  ?qF S #	  Gq@  	  AqN  	  Oqx #  	  yqt 3 !	  uq| S 	  }qb c 	  cql !# (	 # mqL "3 )	 $ MqV $S +	 & Wqh %c ,	 ' iq| $S +	 & 	}qR %c ,	 ' Sqb   '	 " cqr !# (	 # 	sqH !# (	 # Iqd "3 )	 $ eqr c $	  sq~ s %	   qn s 	  oqx  	  yqf	 #  	  g	qn	 3 !	  o	qR
 #  	  S
qN 3 !	  OqV  	  WqD #  	  EqN  	  Oqp  	  qqB 3 !	  Cqn C "	  oqv  	  wqf #  	  gqn 3 !	  oqJ C "	  KqR C "	  Sqp S #	  qq@ C "	  Aqb S #	  cqn  	  oqJ  	  KqZ C 	  [qF S 	  GqN  	  Oqz #  	  {qF c 	  GqB s 	  CqJ  	  Kqh #  	  iq| S 	  	}qR c 	  Sqt s %	   uqT  &	 ! Uq\ S 	  ]q\ c 	  ]q q hx	
  x	
& 'x	
0  1x	
j  kx	
Z  [x	
V  Wx	
~  x	
`  ax	
~  x	
\  ]x	
@  Ax	
b  cx	
V  Wx	
D  Ex	
h  ix	
d	  e	x	
R
  S
x	
~
&0&&((0<*0 sx	
x| <| B| (| N#%|" %&@A#%#|* #$;<&(+|2 #$;<&(3|: /"$;|B N#%C|F %&@A#%G|N ?+ "O|R S "S|Z /[|b >*c|j <k|n ./o|r "#34s|z 12{|B >*C|F %&67G|N >*O|R %&67S|Z !"23[|b ()c|j >k|r <s|v ./w|z "#34{|B @C|J AK|R 23S|V /0W|^ -. "_|f [g|j @k|n %&DEo|r 23s|
z6?696 b6 B	6
 16 ;6 +6 "a6 26 Z6 !"@6  !I6 $%>6 #$\6 $%>6  #$\!6"  !?#6$  R%6& !"@'6(  !I)6* b+6, @-6. (/60 6162 3364 "566 9768 )96: 5;6< Y=6> X?6@ )A6B C6D HE6F 5G6H [I6J 5K6L [M6N (O6P ]Q6R QCS6T MU6V )W6X .Y6Z j[6\ b!W]6^ :_6` Wa6b .c6d [e6f _g6h /k6r +8N_zM[ r   