let T be full Tree; :: thesis: for n being non empty Element of NAT holds (NumberOnLevel n,T) . (0* n) = 1
A1:
T = {0 ,1} *
by Def2;
let n be non empty Element of NAT ; :: thesis: (NumberOnLevel n,T) . (0* n) = 1
A2:
0* n is Element of T
by A1, BINARI_3:5;
A3:
0* n in T -level n
by A1, Th10;
A4:
Rev (0* n) is FinSequence of BOOLEAN
by A2, Lm3;
len (Rev (0* n)) =
len (0* n)
by FINSEQ_5:def 3
.=
n
by FINSEQ_1:def 18
;
then reconsider F = Rev (0* n) as Tuple of n,BOOLEAN by A4, FINSEQ_2:110;
thus (NumberOnLevel n,T) . (0* n) =
(Absval F) + 1
by A3, Def1
.=
0 + 1
by BINARI_3:7, BINARI_3:9
.=
1
; :: thesis: verum