proposition: Lemma bin_of_nato n: bin_of_nat ((n.+1).*2.+1) = Npos (xI (pos_of_nat' n)).
proof: Proof. by rewrite /bin_of_nat doubleS -{1} addnn; elim: {1 3}n. Qed.
imports: mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat) mathcomp(seq choice fintype order bigop ssralg) mathcomp(div ssrnum ssrint rat prime path binomial) mathcomp(tuple finset) gaia(fibm)