reserve ADG for Uniquely_Two_Divisible_Group;
reserve a,b,c,d,a9,b9,c9,p,q for Element of ADG;
reserve x,y for set;
reserve AS for non empty AffinStruct;

theorem
  for AS holds (ex a,b being Element of AS st a<>b) & (for a,b,c being
  Element of AS st a,b // c,c holds a=b) & (for a,b,c,d,p,q being Element of AS
  st a,b // p,q & c,d // p,q holds a,b // c,d) & (for a,b,c being Element of AS
ex d being Element of AS st a,b // c,d) & (for a,b,c,a9,b9,c9 being Element of
AS st a,b // a9,b9 & a,c // a9,c9 holds b,c // b9,c9) & (for a,c being Element
of AS ex b being Element of AS st a,b // b,c) & (for a,b,c,b9 being Element of
  AS st a,b // b,c & a,b9 // b9,c holds b = b9) & (for a,b,c,d being Element of
  AS st a,b // c,d holds a,c // b,d) iff AS is AffVect by Def5,STRUCT_0:def 10;
