reserve f for non empty FinSequence of TOP-REAL 2,
  i,j,k,k1,k2,n,i1,i2,j1,j2 for Nat,
  r,s,r1,r2 for Real,
  p,q,p1,q1 for Point of TOP-REAL 2,
  G for Go-board;

theorem Th2:
  |.r-s.| = 0 iff r = s
proof
  hereby
    assume |.r-s.| = 0;
    then r - s = 0 by ABSVALUE:2;
    hence r = s;
  end;
  assume r = s;
  hence thesis by ABSVALUE:2;
end;
