
theorem
  for a be light positive Real holds  (1/(1+a)) + (1/(1-a)) > 2
  proof
    let a be light positive Real;
    A1: 1 - a*a < 1 - 0 by XREAL_1:10;
    A2: (1*(1-a))/((1-a)*(1+a)) = 1/(1+a) & (1*(1+a))/((1+a)*(1-a)) = 1/(1-a)
      by XCMPLX_1:91;
    ((1-a)+(1+a))/((1-a)*(1+a)) > ((1-a)+(1+a))/1 by A1,XREAL_1:76;
    hence thesis by A2;
  end;
