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 Th14:
  |[1,0]| <> |[0,1]| & |[1,0]| <> |[0,0]| & |[0,1]| <> |[0,0]|
  proof
    |[1,0]|`1 = 1 & |[1,0]|`2 = 0 & |[0,1]|`1 = 0 & |[0,1]|`2 = 1 &
    |[0,0]|`1 = 0 & |[0,0]|`2 = 0 by EUCLID:52;
    hence thesis;
  end;
