reserve i, j, k, l, m, n, t for Nat;

theorem Th12:
  k > 0 & n div k = 0 implies n < k
proof
  assume that
A1: k > 0 and
A2: n div k = 0;
  ex t be Nat st n = k * (n div k) + t & t < k by A1,NAT_D:def 1;
  hence thesis by A2;
end;
