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 NAT31:
  for a,b,c,d be Integer holds
    a divides b & c divides d implies a*c divides b*d by NAT_3:1;
