
theorem
  for a, b be Element of Gauss_INT_Ring, aa, bb be G_INTEG st a = aa & b = bb
  holds aa Divides bb implies a divides b
  proof
    let a, b be Element of Gauss_INT_Ring, aa, bb be G_INTEG such that
A1: a = aa & b = bb;
    assume aa Divides bb; then
    consider cc be G_INTEG such that
A2: bb = aa * cc;
    reconsider c = cc as Element of Gauss_INT_Ring by Th3;
    b = a*c by A1,A2,Th6;
    hence thesis by GCD_1:def 1;
  end;
