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;
