proposition: Lemma CR_prop2 n: natp n -> CR_next_term f n = \0q \/ CR_next_term f n = (CR_inv3n n).
proof: Proof. move => nN; move /functionsP:fI => [ff sf tf]. have ns: inc n (source f) by ue. move:(CR_prop1 nN) => tq. move:(Vf_target ff ns); rewrite /CR_next_term tf => /set2_P; case => ->. by left; rewrite BQprod_0l. by right;rewrite BQprod_1l. Qed.
imports: mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat)