 reserve n,i for Nat;
 reserve p for Prime;

theorem LCMDiv:
  for n being non zero Nat,
      x, y being Nat st x in NatDivisors n & y in NatDivisors n holds
    x lcm y in NatDivisors n
  proof
    let n be non zero Nat;
    let x, y be Nat;
    assume
a0: x in NatDivisors n & y in NatDivisors n; then
    x divides n & y divides n & x > 0 & y > 0 by MOEBIUS1:39; then
    x lcm y divides n by NAT_D:def 4;
    hence thesis by a0,MOEBIUS1:39;
  end;
