As you all know I am working on the ECE text book. I have finished now the first three chapters: introduction, mathematical foundations and geometrical identities of Cartan geometry. I worked out the proofs of the Cartan-Bianchi and Cartan-Evans identity. The latter is the Hodge dual of the Cartan-Bianchi identity which is the usual Bianchi identity including torsion. I have spent some time to work out computational examples. So the validity of both identities is shown by Maxima code examples. The code is usable for any tetrad matrix and fully general. Myron would have been delighted about this. I ask you for some patience, until the proofreading is finished. Then we will have a little mathematical textbook for studying Cartan geometry. Of course this is not yet ECE theory. The axioms of ECE theory, ECE2 and electrodynamics will follow. Then a reader can get a fuller grasp of ECE.