
theorem Th16:
  for S be non empty finite set,
  D be EqSampleSpaces of S,
  s be Element of D holds
  freqSEQ(s) = (len s) (#) FDprobSEQ(s)
  proof
    let S be non empty finite set,
    D be EqSampleSpaces of S, s be Element of D;
    dom freqSEQ(s) = Seg card S by DIST_1:def 9;then
    A1: dom freqSEQ(s) = dom FDprobSEQ(s) by DIST_1:def 3;
    for n be object st n in dom freqSEQ(s)
    holds (freqSEQ(s)).n=(len s) * (FDprobSEQ(s)).n by DIST_1:def 9;
    hence thesis by A1,VALUED_1:def 5;
  end;
