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 Th31:
  L1,L2 are_coplane
  proof
    reconsider OO = |[0,0]|, Ox = |[1,0]|, Oy = |[0,1]| as Element of REAL 2
          by EUCLID:22;
    REAL 2 = plane(OO,Ox,Oy) by Th12;
    hence thesis by EUCLIDLP:def 12;
  end;
