Sindbad~EG File Manager

Length of proof is 17.  Level of proof is 6.
 
---------------- PROOF ----------------
 
107 [] -M(xa,xm,xb)|M(xb,xm,xa).
111 [] -M(xp,xa,xr)| -M(xp,xa,xq)|xr=xq.
117 [] s(xa,xp)=xp|xp!=xa.
123 [] -M(xp,xa,xq)| -M(xp,xb,xq)|xa=xb.
124 [] s(xa,xp)!=s(xb,xp)|xa=xb.
174 [] M(xa,midpoint(xa,xb),xb).
182 [] -perp(xa,xb,xp,xq)|perp(xa,xb,xq,xp).
213 [] xa=xb|Col(xa,xb,midpoint(xp,reflect(xa,xb,xp))).
214 [] xa=xb|xp=reflect(xa,xb,xp)|perp(xa,xb,xp,reflect(xa,xb,xp)).
215 [] xa=xb| -Col(xa,xb,midpoint(xp,xp1))| -perp(xa,xb,xp,xp1)|xp1=reflect(xa,xb,xp).
293 [] a!=b.
294 [] reflect(a,b,p)=p1.
295 [] reflect(a,b,p1)!=p.
296 [] m=midpoint(p,p1).
297 [] midpoint(p,p1)=m.
359 [para_from,294.1.1,214.3.4,unit_del,293] p=reflect(a,b,p)|perp(a,b,p,p1).
360 [para_from,294.1.1,213.2.3.2,demod,297,unit_del,293] Col(a,b,m).
361 [binary,295.1,124.2] s(reflect(a,b,p1),x)!=s(p,x).
376 [para_from,296.1.2,174.1.2] M(p,m,p1).
377 [binary,359.2,182.1] p=reflect(a,b,p)|perp(a,b,p1,p).
424 [binary,376.1,107.1] M(p1,m,p).
431 [para_into,377.1.2,294.1.1] p=p1|perp(a,b,p1,p).
445 [hyper,123,174,424] midpoint(p1,p)=m.
447 [hyper,111,424,424] p=p.
450 [ur,111,424,295] -M(p1,m,reflect(a,b,p1)).
453 [para_into,424.1.3,377.1.1] M(p1,m,reflect(a,b,p))|perp(a,b,p1,p).
472 [para_from,445.1.2,360.1.3] Col(a,b,midpoint(p1,p)).
478 [binary,447.1,117.2] s(p,p)=p.
481 [para_into,453.1.3.3,431.1.1,unit_del,450,factor_simp] perp(a,b,p1,p).
488 [binary,472.1,215.2,unit_del,293,481] p=reflect(a,b,p1).
518 [para_from,478.1.1,361.1.2] s(reflect(a,b,p1),p)!=p.
544 [binary,488.1,117.2] s(reflect(a,b,p1),p)=p.
545 [binary,544.1,518.1] $F.