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 mergeToken : forall tok1 n1 tok2 n2 tok', isToken tok1 n1 -> isToken tok2 n2 -> join tok1 tok2 tok' -> isToken tok' (n1+n2).