reserve n, k, r, m, i, j for Nat;

theorem Th34:
  tau_bar = (- tau) to_power (-1)
proof
A1: 1 - sqrt 5 <> 0 by SQUARE_1:20,27;
  (- tau) to_power (-1) = ((- 1 - sqrt 5) / 2) #Z (-1) by FIB_NUM:def 1
,POWER:def 2
    .= 1 / ((- 1 - sqrt 5) / 2) #Z 1 by PREPOWER:41
    .= 1 / ((- 1 - sqrt 5) / 2) by PREPOWER:35
    .= 2 / (-(1 + sqrt 5)) by XCMPLX_1:57
    .= -2 / (1 + sqrt 5) by XCMPLX_1:188
    .= (-2) / (1 + sqrt 5) by XCMPLX_1:187
    .= ((-2) * (1 - sqrt 5)) / ((1 + sqrt 5) * (1 - sqrt 5)) by A1,XCMPLX_1:91
    .= ((-2) * (1 - sqrt 5)) / (1 ^2 - (sqrt 5) ^2)
    .= ((-2) * (1 - sqrt 5)) / (1 - 5) by SQUARE_1:def 2
    .= tau_bar by FIB_NUM:def 2;
  hence thesis;
end;
