let T be Tree; :: thesis: ( T = {0 ,1} * implies for n being non empty Element of NAT
for y being Element of n -tuples_on BOOLEAN holds y in T -level n )
assume A1: T = {0 ,1} * ; :: thesis: for n being non empty Element of NAT
for y being Element of n -tuples_on BOOLEAN holds y in T -level n
let n be non empty Element of NAT ; :: thesis: for y being Element of n -tuples_on BOOLEAN holds y in T -level n
let y be Element of n -tuples_on BOOLEAN ; :: thesis: y in T -level n
y in { w where w is Element of T : len w = n } by A1;
hence y in T -level n by TREES_2:def 6; :: thesis: verum