
theorem Th10:
  for S be finite set, s be FinSequence of S holds
  (GenProbSEQ (S)).(Finseq-EQclass(s)) = FDprobSEQ (s)
proof
  let S be finite set, s be FinSequence of S;
  Finseq-EQclass(s) is Element of distribution_family(S) by Def6;
  then consider u be FinSequence of S such that
A1: u in Finseq-EQclass(s) and
A2: (GenProbSEQ (S)).(Finseq-EQclass(s)) =FDprobSEQ (u) by Def7;
  s,u -are_prob_equivalent by A1,Th5;
  hence thesis by A2,Th8;
end;
