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

theorem GCDDiv:
  for n being non zero Nat,
      x, y being Nat st x in NatDivisors n & y in NatDivisors n holds
    x gcd y in NatDivisors n
  proof
    let n be non zero Nat;
    let x, y be Nat;
    assume x in NatDivisors n & y in NatDivisors n; then
A0: x divides n & y divides n & x > 0 & y > 0 by MOEBIUS1:39;
    x gcd y divides x by NAT_D:def 5;
    hence thesis by A0,MOEBIUS1:39,NAT_D:4;
  end;
