reserve a,b,c,d,x,j,k,l,m,n,o,xi,xj for Nat,
  p,q,t,z,u,v for Integer,
  a1,b1,c1,d1 for Complex;

theorem NATD29:
  for a,b be Integer holds
    |.a*b.| = (a gcd b)*(a lcm b)
  proof
    let a,b be Integer;
    |.a*b.| = |.a.|*|.b.| by COMPLEX1:65
    .= (|.a.|gcd |.b.|)*(|.a.| lcm |.b.|) by NAT_D:29
    .= (a gcd b)*(|.a.| lcm |.b.|) by INT_2:34
    .= (a gcd b)*(a lcm b) by INT_2:33;
    hence thesis;
  end;
