theorem Th46:
  for B holds {} in B implies B = {{}}
proof
  let B;
  assume A1: {} in B;
  for a st a in B holds a = {}
  proof
    let a;
    assume A3: a in B;
    then reconsider a as FinSequence;
    {}^a in B by A3, FINSEQ_1:34;
    hence thesis by A1, Def16;
  end;
  then for a holds a in B iff a = {} by A1;
  hence thesis by TARSKI:def 1;
end;
