Definition create_token (n:nat) (fac:t) : t*t :=
      match n with
      | O => (fac,bot)
      | S n' =>
         (exist (fun x => canonicalTree x) (mkCanon (create_tok1 n' (proj1_sig fac))) (mkCanon_correct _),
          exist (fun x => canonicalTree x) (mkCanon (create_tok2 n' (proj1_sig fac))) (mkCanon_correct _))
      end.

Lemma tokens_nonfull : forall tok1 n, isToken' tok1 n -> forall tok2 m, isToken' tok2 m -> shareTreeOrd (Leaf true) (union_tree tok1 tok2) -> False.