
theorem DivNonZero:
  for n,a being non zero Nat st a divides n holds
    n div a <> 0
  proof
    let n,a be non zero Nat;
    assume
A0: a divides n;
    assume n div a = 0; then
    n < a by NAT_2:12;
    hence thesis by NAT_D:7,A0;
  end;
