proposition: Lemma Sba_j_snum x: 0 < x <1 -> (snumden (Sba_j x) < snumden x)%N.
proof: Proof. move => H; have h1:= (Sba_j_pos H); move/andP:H => [ha hb]. by rewrite (snumden_inv h1) Sba_mjK (snumden_inv ha) Sba_m_snum // invf_gt1. 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)