proposition: Lemma lucas_ge_2fib n: 2 <= n -> (fib n).*2 <= lucas n.
proof: Proof. case:n => [|[| n]] //_; rewrite lucas_fib // -addnn (fibSS n.+1). rewrite {2} fibSS addnA 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)