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 Th7:
  Ln is being_line implies not ex Pn being Element of REAL n st Ln={Pn}
  proof
    assume
A1: Ln is being_line;
    given x be Element of REAL n such that
A2: Ln = {x};
    consider x1,x2 be Element of REAL n such that
A3: x1 <> x2 and
A4: Ln = Line(x1,x2) by A1;
    x1 in {x} & x2 in {x} by A2,A4,EUCLID_4:9;
    then x1 = x & x2 = x by TARSKI:def 1;
    hence contradiction by A3;
  end;
