
theorem
  for T be full Tree for n be non zero Nat holds
    rng FinSeqLevel(n,T) = T-level n
proof
  let T be full Tree;
  let n be non zero Nat;
  reconsider Tln = T-level n as finite set;
  T = {0,1}* by Def2;
  then T-level n is non empty by Th10;
  then reconsider
  p = FinSeqLevel(n,T) as Function of dom FinSeqLevel(n,T), T-level
  n by FINSEQ_2:26;
  reconsider dp = dom p as finite set;
  card dp = card Seg (2 to_power n) by Th20
    .= 2 to_power n by FINSEQ_1:57
    .= card Tln by Th18; then
  p is onto by FINSEQ_4:63;
  hence thesis by FUNCT_2:def 3;
end;
