proposition: Lemma ffactnn n : natp n -> n ^_c n = factorial n.
proof: Proof. move: n; apply: Nat_induction; first by rewrite ffactn0 factorial0. move => n nN Hrec; rewrite (ffactnS (NS_succ nN) nN) (cpred_pr2 nN) Hrec. by rewrite cprodC factorial_succ. Qed.
imports: mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat) mathcomp(binomial div)