
theorem Th15:
  for T be full Tree for n be non zero Nat holds
  FinSeqLevel(n,T).1 = 0*n
proof
  let T be full Tree;
  let n be non zero Nat;
  T = {0,1}* by Def2;
  then 0*n in T-level n by Th10;
  then
A1: 0*n in dom NumberOnLevel(n,T) by FUNCT_2:def 1;
  1 = NumberOnLevel(n,T).(0*n) by Th13;
  hence thesis by A1,FUNCT_1:32;
end;
