
theorem Th5:
  for S be finite set, s,t be FinSequence of S holds
  s,t -are_prob_equivalent iff t in Finseq-EQclass(s)
proof
  let S be finite set, s,t be FinSequence of S;
  now
    assume t in Finseq-EQclass(s);
    then ex t0 be FinSequence of S st t=t0 & s,t0 -are_prob_equivalent;
    hence s,t -are_prob_equivalent;
  end;
  hence thesis;
end;
