
theorem Hartr 4 = <*1/4,1/12,1/12,1/4*>
  proof
    reconsider f = Hartr 4 as 4-element complex-valued FinSequence;
    reconsider g = RHartr 4 as 4-element complex-valued FinSequence;
    A1: g.1 = 4 & g.2 = 12 & g.3 = 12 & g.4 = 4 by RH4;
    len f = 4 & len g = 4 by CARD_1:def 7; then
    dom f = Seg 4 & dom g = Seg 4 by FINSEQ_1:def 3; then
    1 in dom f & 2 in dom f & 3 in dom f & 4 in dom f; then
    f.1 = (g.1)" & f.2 = (g.2)" & f.3 = (g.3)" & f.4 = (g.4)"
      by VALUED_1:def 7;
    hence thesis by A1;
  end;
