
theorem Th19:
  for S be finite set, s be FinSequence of S st
  s is uniformly_distributed holds FDprobSEQ (s) is constant
proof
  let S be finite set, s be FinSequence of S;
  assume
A1: s is uniformly_distributed;
  let a,b be object;
  assume that
A2: a in dom FDprobSEQ(s) and
A3: b in dom FDprobSEQ(s);
  reconsider na=a,nb=b as Nat by A2,A3;
  (FDprobSEQ s).na = 1/card S by A1,A2
    .= (FDprobSEQ s).nb by A1,A3;
  hence thesis;
end;
