reserve AFV for WeakAffVect;
reserve a,b,c,d,e,f,a9,b9,c9,d9,f9,p,q,r,o,x99 for Element of AFV;
reserve a,b,c for Element of GroupVect(AFV,o);
reserve a,b for Element of GroupVect(AFV,o);

theorem Th46:
  for a ex b st b + b = a
proof
  let a;
  reconsider a99=a as Element of AFV;
  consider b9 being Element of AFV such that
A1: o,b9 // b9,a99 by Def1;
  reconsider b=b9 as Element of GroupVect(AFV,o);
  a99 = Padd(o,b9,b9) by A1,Def5
    .= b+b by Def6;
  hence thesis;
end;
