 reserve L for Lattice;
 reserve I,P for non empty ClosedSubset of L;
reserve L for lower-bounded pseudocomplemented Lattice;
reserve L for Stone Lattice;

theorem DivisorsSquare:
  for p being Prime holds NatDivisors (p * p) = {1, p, p*p}
  proof
    let p be Prime;
a1: NatDivisors (p|^2)={p|^k where k is Element of NAT : k <= 2} by NAT_5:19;
    { p|^k where k is Element of NAT : k <= 2 } = {1, p, p * p}
    proof
      thus { p|^k where k is Element of NAT : k <= 2 } c= {1, p, p * p}
      proof
        let x be object;
        assume x in { p|^k where k is Element of NAT : k <= 2 }; then
        consider kk being Element of NAT such that
A2:     x = p |^ kk & kk <= 2;
        kk = 0 or ... or kk = 2 by A2; then
        x = 1 or x = p or x = p * p by A2,NEWTON:81,4;
        hence thesis by ENUMSET1:def 1;
      end;
      let x be object;
      assume x in {1, p, p * p}; then
      x = 1 or x = p or x = p * p by ENUMSET1:def 1; then
      x = p |^ 0 or x = p |^ 1 or x = p |^ 2 by NEWTON:4,81;
      hence thesis;
    end;
    hence thesis by a1,NEWTON:81;
  end;
