
theorem
  FPower(1_F_Complex,2) = id(COMPLEX)(#)id(COMPLEX)
proof
  the carrier of F_Complex = COMPLEX by COMPLFLD:def 1;
  then reconsider
  f=id(COMPLEX)(#)id(COMPLEX) as Function of F_Complex,F_Complex;
  now
    let x be Element of F_Complex;
    reconsider x1=x as Element of COMPLEX by COMPLFLD:def 1;
    id(COMPLEX)/.x1 = x1 & dom (id(COMPLEX)(#)id(COMPLEX)) = COMPLEX by
FUNCT_2:def 1;
    hence f.x = x*x by VALUED_1:def 4
      .= (power F_Complex).(x,2) by GROUP_1:51
      .= 1_F_Complex*power(x,2);
  end;
  hence thesis by Def12;
end;
