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 create_token_correct : forall fac fac' tok x n, create_token n fac = (fac',tok) -> isTokenFactory fac x -> isTokenFactory fac' (n+x) /\ isToken tok n /\ join fac' tok fac.