theorem
  for a,b being Real st a^2 + b^2 = 1 holds |[-b,a,0]| is non zero
  proof
    let a,b be Real;
    assume
A1: a^2 + b^2 = 1;
    assume |[-b,a,0]| is zero;
    then -b = 0 & a = 0 by EUCLID_5:4,FINSEQ_1:78;
    hence contradiction by A1;
  end;
