
theorem Th20:
  for S be finite set, s,t be FinSequence of S st
  s is uniformly_distributed & s,t -are_prob_equivalent holds
  t is uniformly_distributed
proof
  let S be finite set, s,t be FinSequence of S;
  assume that
A1: s is uniformly_distributed and
A2: s,t -are_prob_equivalent;
  FDprobSEQ s = FDprobSEQ t by A2,Th8;
  then
  for n be Nat st n in dom FDprobSEQ t holds (FDprobSEQ t).n=1/(card S)
  by A1;
  hence thesis;
end;
