take
{{}}
; COMPOS_0:def 1 {[0,{},{}],[1,{},{}]} c= [:NAT,(NAT *),({{}} *):]
A1:
{{}} c= {{}} *
by FINSEQ_1:49, ZFMISC_1:31;
A2:
{{}} c= NAT *
by FINSEQ_1:49, ZFMISC_1:31;
{[0,{},{}]} = [:{0},{{}},{{}}:]
by MCART_1:35;
then A3:
{[0,{},{}]} c= [:NAT,(NAT *),({{}} *):]
by A1, A2, MCART_1:73;
{[1,{},{}]} = [:{1},{{}},{{}}:]
by MCART_1:35;
then A4:
{[1,{},{}]} c= [:NAT,(NAT *),({{}} *):]
by A1, A2, MCART_1:73;
{[0,{},{}]} \/ {[1,{},{}]} = {[0,{},{}],[1,0,0]}
by ENUMSET1:1;
hence
{[0,{},{}],[1,{},{}]} c= [:NAT,(NAT *),({{}} *):]
by A3, A4, XBOOLE_1:8; verum