proposition: Lemma lucas_monotoneE m n: lucas m <= lucas n = [|| m== n, 0< m < n, (m==1) && (n== 0)| (m == 0) && (2<= n )].
proof: Proof. by rewrite leq_eqVlt lucas_injective_bis lucas_smonotoneE. Qed.
imports: mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat) mathcomp(seq path fintype div bigop binomial) mathcomp(prime finset ssralg ssrnum ssrint)