let i be Element of NAT ; :: thesis: for f1 being NAT * -defined to-naturals homogeneous len-total unary Function
for f2 being non empty NAT * -defined to-naturals homogeneous Function holds (primrec (f1,f2,2)) . <*i,0*> = f1 . <*i*>
let f1 be NAT * -defined to-naturals homogeneous len-total unary Function; :: thesis: for f2 being non empty NAT * -defined to-naturals homogeneous Function holds (primrec (f1,f2,2)) . <*i,0*> = f1 . <*i*>
let f2 be non empty NAT * -defined to-naturals homogeneous Function; :: thesis: (primrec (f1,f2,2)) . <*i,0*> = f1 . <*i*>
arity f1 = 1 by Def25;
then reconsider p = <*i,0*> as Element of ((arity f1) + 1) -tuples_on NAT by FINSEQ_2:121;
len p = 2 by FINSEQ_1:61;
then A1: 2 in dom p by FINSEQ_3:27;
p +* (2,0) = p by Th3;
hence (primrec (f1,f2,2)) . <*i,0*> = f1 . (Del (p,2)) by A1, Th64
.= f1 . <*i*> by WSIERP_1:26 ;
:: thesis: verum