A1:
g in PrimRec
by Def19;
A2:
arity f = 0
by Def24;
f is Element of PrimRec
by Def19;
then dom f =
0 -tuples_on NAT
by A2, Th25
.=
{(<*> NAT )}
by FINSEQ_2:112
;
then A3:
{} in dom f
by TARSKI:def 1;
A4:
f in PrimRec
by Def19;
A5:
1 <= 0 + 1
;
arity g = 0 + 2
by Def26;
hence
primrec f,g,1 in PrimRec
by A5, A2, A4, A1, Th77; COMPUT_1:def 19 primrec f,g,1 is unary
reconsider ii = <*0 *> as Element of 1 -tuples_on NAT by FINSEQ_2:151;
dom <*0 *> = {1}
by FINSEQ_1:4, FINSEQ_1:55;
then A6:
1 in dom <*0 *>
by TARSKI:def 1;
Del <*0 *>,1 = {}
by WSIERP_1:26;
then
ii +* 1,0 in dom (primrec f,g,1)
by A5, A2, A3, A6, Lm6;
then A7:
<*0 *> in dom (primrec f,g,1)
by FUNCT_7:97;
len <*0 *> = 1
by FINSEQ_1:56;
hence
arity (primrec f,g,1) = 1
by A7, MARGREL1:def 26; COMPUT_1:def 25 verum