dom (p +* (i,k)) = dom p by FUNCT_7:32;
then len (p +* (i,k)) = len p by FINSEQ_3:31
.= n by FINSEQ_1:def 18 ;
hence p +* (i,k) is Element of n -tuples_on NAT by FINSEQ_2:110; :: thesis: verum