proposition: Lemma mul_bin_diag n m : n * 'C(n.-1, m) = m.+1 * 'C(n, m.+1).
proof: Proof. rewrite [RHS]mulnC; elim: n m => [|[|n] IHn] [|m] //=; first by rewrite bin1. by rewrite mulSn [in _ * _]binS mulnDr addnCA !IHn -mulnS -mulnDl -binS. Qed.
imports: HB(structures) mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat seq path) mathcomp(div fintype tuple finfun bigop prime finset)