proposition: Lemma ffact_fact n m : m <= n -> n ^_ m * (n - m)`! = n`!.
proof: Proof. by elim: n m => [|n IHn] [|m] //= le_m_n; rewrite ?mul1n // -mulnA IHn. Qed.
imports: HB(structures) mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat seq path) mathcomp(div fintype tuple finfun bigop prime finset)