
theorem
  for a, b be Element of Gauss_INT_Ring, aa, bb be G_INTEG st a = aa & b = bb
  holds a divides b implies aa Divides bb
  proof
    let a, b be Element of Gauss_INT_Ring, aa, bb be G_INTEG such that
    A1: a = aa & b = bb;
    assume a divides b;
    then consider c be Element of Gauss_INT_Ring such that
    A2: b = a * c by GCD_1:def 1;
    reconsider cc = c as G_INTEG by Th2;
    bb = aa*cc by A1,A2,Th6;
    hence thesis;
  end;
