reserve a, b, k, n, m for Nat,
  i for Integer,
  r for Real,
  p for Rational,
  c for Complex,
  x for object,
  f for Function;

theorem Th9:
  f is sequence of INT iff f is Integer_Sequence
proof
  hereby
    assume f is sequence of INT;
    then reconsider g = f as sequence of INT;
    dom g = NAT & for x st x in NAT holds g.x is integer by FUNCT_2:def 1;
    hence f is Integer_Sequence by Th8;
  end;
  assume f is Integer_Sequence;
  then dom f = NAT & rng f c= INT by FUNCT_2:def 1,RELAT_1:def 19;
  hence thesis by FUNCT_2:2;
end;
