theorem Th32:
  n succ i in HFuncs NAT
proof
  set X=NAT;
  set f=n succ i;
A1: rng f c= NAT by VALUED_0:def 6;
  dom f c= NAT*;
  then f is PartFunc of X*, X by A1,RELSET_1:4;
  then f is Element of PFuncs(X*, X) by PARTFUN1:45;
  hence thesis;
end;
