reserve i, j, k, c, m, n for Nat,
  a, x, y, z, X, Y for set,
  D, E for non empty set,
  R for Relation,
  f, g for Function,
  p, q for FinSequence;

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;
