proposition: Lemma fib_mon1 n: 2 <= n -> 3* fib n <= 2 * fib n.+1.
proof: Proof. case: n => [|[|n _]]//; rewrite (fibSS n.+1)mulnDr mulSnr leq_add2l. by rewrite fibSS mul2n - addnn leq_add2l fib_monotone. Qed.
imports: mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat) mathcomp(seq path fintype div bigop binomial) mathcomp(prime finset ssralg ssrnum ssrint)