reserve a,b,c,d for Real;
reserve z,z1,z2 for Complex;

theorem
  |.a.| <= sqrt(a^2+b^2)
proof
  a^2>=0 & a^2+0<= a^2+b^2 by XREAL_1:6,63;
  then sqrt(a^2)<= sqrt(a^2+b^2) by SQUARE_1:26;
  hence thesis by Lm28;
end;
