proposition: Lemma bin_fact2n_d n : 0<n -> 'C(n.*2, n.-1) <= 'C(n.*2, n).
proof: Proof. move => /bin_fact2n_b ea. have h: 0 < (n`! * n.+1`!) by rewrite muln_gt0 !fact_gt0. by rewrite -(leq_pmul2r h) ea bin_fact2n_c leq_mul2l leqnSn orbT. Qed.
imports: mathcomp(ssreflect ssrfun ssrbool eqtype) mathcomp(ssrnat seq path div) mathcomp(fintype tuple finfun bigop finset binomial)