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;
reserve A,B,C for Point of TOP-REAL 2;
reserve x,y,z,y1,y2 for Element of REAL 2;
reserve L,L1,L2,L3,L4 for Element of line_of_REAL 2;
reserve D,E,F for Point of TOP-REAL 2;
reserve b,c,d,r,s for Real;

theorem Th37:
  L is being_line & A in L & B in L & A <> B implies L = Line(A,B)
  proof
    assume
A1: L is being_line & A in L & B in L & A <> B;
    reconsider x1=A,x2=B as Element of REAL 2 by EUCLID:22;
    L = Line(x1,x2) by A1,EUCLID_4:10,EUCLID_4:11;
    hence thesis by Th4;
  end;
