proposition: Lemma Zeckv_bound2 n l : path ggen n l -> Zeck_val (n::l) < fib (n.+3).
proof: Proof. elim: l n => [n _ | a l Hrec /= n/andP []]. by rewrite Zeckv_cons Zeckv_nil addn0 fib_smonotone_bis. rewrite - ltnS => /fib_monotone la /Hrec lb. by rewrite fibSS Zeckv_cons ltn_add2l (leq_trans lb la). Qed.
imports: mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat) mathcomp(seq path fintype div bigop binomial) mathcomp(prime finset ssralg ssrnum ssrint)