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 Th9:
  LIN x,y,z & LIN x,y,t implies x,y // z,t
proof
  assume that
A1: LIN x,y,z and
A2: LIN x,y,t;
  now
A3: x,y // x,t by A2;
A4: x,y // x,z by A1;
    assume x<>y;
    then x,z // x,t by A4,A3,Th4;
    then z,x // z,t by DIRAF:40;
    then x,z // z,t by Th3;
    hence thesis by A4,A3,Th4;
  end;
  hence thesis by Th2;
end;
