
theorem Th19:
  for T be full Tree for n be non zero Nat holds
  len FinSeqLevel(n,T) = 2 to_power n
proof
  let T be full Tree;
  let n be non zero Nat;
  rng FinSeqLevel(n,T) = dom NumberOnLevel(n,T) by FUNCT_1:33
    .= T-level n by FUNCT_2:def 1;
  then
A1: dom FinSeqLevel(n,T),T-level n are_equipotent by WELLORD2:def 4;
  card Seg len FinSeqLevel(n,T) = card dom FinSeqLevel(n,T) by FINSEQ_1:def 3
    .= card (T-level n) by A1,CARD_1:5
    .= 2 to_power n by Th18;
  hence thesis by FINSEQ_1:57;
end;
