reserve n for Nat;
reserve i for Integer;
reserve r,s,t for Real;
reserve An,Bn,Cn,Dn for Point of TOP-REAL n;
reserve L1,L2 for Element of line_of_REAL n;
reserve A,B,C for Point of TOP-REAL 2;

theorem
  A <> B & A <> C implies |.A - B.| + |.A - C.| <> 0
  proof
    assume A <> B & A <> C;
    then |.A - B.| <> 0 & |.A - C.| <> 0 by EUCLID_6:42;
    hence thesis;
  end;
