
theorem Hartr 7 = <*1/7,1/42,1/105,1/140,1/105,1/42,1/7*>
  proof
    reconsider f = Hartr 7 as 7-element complex-valued FinSequence;
    reconsider g = RHartr 7 as 7-element complex-valued FinSequence;
    A1: g.1 = 7 & g.2 = 42 & g.3 = 105 & g.4 = 140 & g.5 = 105 & g.6 = 42 &
      g.7 = 7 by RH7;
    len f = 7 & len g = 7 by CARD_1:def 7; then
    dom f = Seg 7 & dom g = Seg 7 by FINSEQ_1:def 3; then
    1 in dom f & 2 in dom f & 3 in dom f & 4 in dom f & 5 in dom f &
      6 in dom f & 7 in dom f; then
    f.1 = (g.1)" & f.2 = (g.2)" & f.3 = (g.3)" & f.4 = (g.4)" & f.5 = (g.5)" &
      f.6 = (g.6)" & f.7 = (g.7)" by VALUED_1:def 7;
    hence thesis by A1;
  end;
