
theorem SquareNotDiv:
  for k being Nat st k > 1 holds
    not (k*k) divides k
  proof
    let k be Nat;
    assume
A1: k > 1;
    assume
A2: (k*k) divides k;
    k divides (k * k); then
    k * k = k by A2,NAT_D:5; then
    k * (k - 1) = 0; then
    k = 0 or (k - 1) = 0;
    hence thesis by A1;
  end;
