
theorem Th16:
  for T be full Tree for n be non zero Nat for y be
  Element of n-tuples_on BOOLEAN
  st y = 0*n holds FinSeqLevel(n,T).(2 to_power n) = 'not' y
proof
  let T be full Tree;
  let n be non zero Nat;
  let y be Element of n-tuples_on BOOLEAN;
  reconsider ny = 'not' y as
  Element of n-tuples_on BOOLEAN by FINSEQ_2:131;
  T = {0,1}* by Def2;
  then ny in T-level n by Th11;
  then
A1: 'not' y in dom NumberOnLevel(n,T) by FUNCT_2:def 1;
  assume y = 0*n;
  then 2 to_power n = NumberOnLevel(n,T).'not' y by Th14;
  hence thesis by A1,FUNCT_1:32;
end;
