proposition: Lemma like_fibE F: like_fib F -> forall n, F n.+1 = (F 0) * (fib n) + (F 1) * (fib n.+1).
proof: Proof. move => H; apply:like_fib_eq => //=. - by apply: like_fib_add; apply: like_fib_mul. - by rewrite muln0 muln1. - by rewrite H !muln1 addnC. Qed.
imports: mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat) mathcomp(seq path fintype div bigop binomial) mathcomp(prime finset ssralg ssrnum ssrint)