theorem
  heptatonic_pythagorean_scale(HPS,frequency).8
    = heptatonic_pythagorean_scale_ascending(HPS,frequency).1
  proof
    heptatonic_pythagorean_scale(HPS,frequency).8 = 2 * @frequency &
    heptatonic_pythagorean_scale_ascending(HPS,frequency).1 = 2 * @frequency
      by Th88,Th91;
    hence thesis;
  end;
