
theorem Th10:
  for T be Tree st T = {0,1}* for n be Nat holds 0*n in T-level n
proof
  let T be Tree;
  assume
A1: T = {0,1}*;
  let n be Nat;
  len (0*n) = n & 0*n in T by A1,BINARI_3:4,CARD_1:def 7;
  then 0*n in { w where w is Element of T : len w = n };
  hence thesis by TREES_2:def 6;
end;
