
theorem Th37:
  for r being positive Real
  for u being Element of TOP-REAL 2 st u in circle(0,0,r)
  holds u is non zero
  proof
    let r be positive Real;
    let u be Element of TOP-REAL 2;
    assume
A1: u in circle(0,0,r);
    assume u is zero;
    then r^2 = 0 by A1,BKMODEL1:14,EUCLID:54,Lem01;
    hence contradiction;
  end;
