proposition: Lemma lucas_gen n: n <= lucas n.
proof: Proof. case:n => //; elim => // n IH. by move: (leq_add IH (lucas_gt0 n)); rewrite addn1 - lucasSS. Qed.
imports: mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat) mathcomp(seq path fintype div bigop binomial) mathcomp(prime finset ssralg ssrnum ssrint)