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 Th19:
  n <> 0 implies m = divSeq(m,n).0 * n + modSeq(m,n).0
proof
  set fd = divSeq(m,n);
  set fm = modSeq(m,n);
  assume
A1: n <> 0;
  fd.0 = m div n & fm.0 = m mod n by Def1,Def2;
  hence thesis by A1,NAT_D:2;
end;
