reserve AS for AffinSpace;
reserve a,a9,b,b9,c,d,o,p,q,r,s,x,y,z,t,u,w for Element of AS;

theorem
  not LIN o,a,b & LIN o,b,b9 & a,b // a,b9 implies b=b9
proof
  assume that
A1: not LIN o,a,b and
A2: LIN o,b,b9 and
A3: a,b // a,b9;
  LIN a,b,b9 by A3;
  then
A4: LIN b,b9,a by Th5;
A5: LIN b,b9,b by Th6;
  assume
A6: b<>b9;
  LIN b,b9,o by A2,Th5;
  hence contradiction by A1,A6,A4,A5,Th7;
end;
