reserve n for Nat,
        lambda,lambda2,mu,mu2 for Real,
        x1,x2 for Element of REAL n,
        An,Bn,Cn for Point of TOP-REAL n,
        a for Real;
 reserve Pn,PAn,PBn for Element of REAL n,
         Ln for Element of line_of_REAL n;

theorem Th6:
  Ln is being_line or ex Pn being Element of REAL n st Ln={Pn}
  proof
    assume
A1: not Ln is being_line;
    Ln in line_of_REAL n;
    then Ln in the set of all Line(x1,x2) where
             x1,x2 is Element of REAL n by EUCLIDLP:def 4;
    then consider x1,x2 be Element of REAL n such that
A2: Ln = Line(x1,x2);
    x1 = x2 by A1,A2;
    then Ln = {x1} by A2,Th3;
    hence thesis;
  end;
