reserve X,Y,z,s for set, L,L1,L2,A,B for List of X, x for Element of X,
  O,O1,O2,O3 for Operation of X, a,b,y for Element of X, n,m for Nat;

theorem
  n <> 0 & L1 c= L2 implies L1 WHEREeq(O,n) c= L2 WHERE O
  proof
    assume
A1: n <> 0 & L1 c= L2;
    let z be object; assume z in L1 WHEREeq(O,n); then
    consider x such that
A2: z = x & card(x.O) = n & x in L1;
    x.O <> {} by A1,A2;
    hence thesis by A1,A2,Th3;
  end;
