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 Th18:
  a < b & modSeq(m,n).a = 0 implies divSeq(m,n).b = 0
proof
  set fd = divSeq(m,n);
  set fm = modSeq(m,n);
  assume a < b;
  then
A1: a+1 <= b by NAT_1:13;
  assume fm.a = 0;
  then fd.(a+1) = 0 by Lm3;
  hence thesis by A1,Th17;
end;
