
theorem Th5:
  |.tau_bar.| < 1
  proof
    sqrt 5 < sqrt (3 ^2) by SQUARE_1:27; then
    sqrt 5 < 3 by SQUARE_1:def 2; then
    sqrt 5 - 1 < 2 + 1 - 1 by XREAL_1:9; then
    - (sqrt 5 - 1) > -2 by XREAL_1:24; then
    (1 - sqrt 5) / 2 > (-2) / 2 by XREAL_1:74; then
A1: |.tau_bar.| < |.-1 .| + |.0 .| by FIB_NUM:def 2,MEASURE6:37;
    |.-1 .| = - -1 by ABSVALUE:def 1; then
    |.tau_bar.| < 1 + 0 by A1;
    hence thesis;
  end;
