proposition: Lemma lucas_mon1 n: 3 <= n -> 3* lucas n <= 2 * lucas n.+1.
proof: Proof. case: n => [|[|n ]]//;rewrite (lucasSS n.+1) mulnDr mulSnr leq_add2l !ltnS => h. rewrite lucasSS mul2n - addnn leq_add2l lucas_monotone ?h //=. Qed.
imports: mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat) mathcomp(seq path fintype div bigop binomial) mathcomp(prime finset ssralg ssrnum ssrint)