proposition: Lemma Stern_bij1_lt1 x : 0 < x < 1 -> Stern_bij1 x = xO (Stern_bij1 (Sba_j x)).
proof: Proof. move => xp1; rewrite -(Stern_bij_recE (Sba_j_pos xp1) (Sba_j_snum xp1)). by rewrite /Stern_bij1 /= xp1. 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)