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);
reserve AFV for AffVect,
  o for Element of AFV;

theorem
  for AS being strict AffinStruct holds (AS is AffVect iff ex ADG being
  Proper_Uniquely_Two_Divisible_Group st AS = AV(ADG) )
proof
  let AS be strict AffinStruct;
  now
    assume AS is AffVect;
    then reconsider AS9 = AS as AffVect;
    set o = the Element of AS9;
    take ADG = GroupVect(AS9,o);
    AS9 = AV(ADG) by Th50;
    hence ex ADG being Proper_Uniquely_Two_Divisible_Group st AS = AV(ADG);
  end;
  hence thesis;
end;
