(** The falling factorial *)
Definition falling_factorial := nosimpl ffact_rec.
Notation "n ^_ m" := (falling_factorial n m)
(at level 30, right associativity) : nat_scope.

(* Multiply to move left in the Pascal triangle. *)
Lemma mul_bin_left n m : m.+1 * 'C(n, m.+1) = (n - m) * 'C(n, m).