take
{{}}
; :: according to COMPOS_0:def 1 :: thesis: {[0,{},{}]} 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;

hence {[0,{},{}]} c= [:NAT,(NAT *),({{}} *):] by A1, A2, MCART_1:73; :: thesis: verum

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;

hence {[0,{},{}]} c= [:NAT,(NAT *),({{}} *):] by A1, A2, MCART_1:73; :: thesis: verum