(************************************************************************)
(*         *      The Rocq Prover / The Rocq Development Team           *)
(*  v      *         Copyright INRIA, CNRS and contributors             *)
(* <O___,, * (see version control and CREDITS file for authors & dates) *)
(*   \VV/  **************************************************************)
(*    //   *    This file is distributed under the terms of the         *)
(*         *     GNU Lesser General Public License Version 2.1          *)
(*         *     (see LICENSE file for the text of the license)         *)
(************************************************************************)
Local Open Scope R_scope.
Definition C (n p:nat) : R :=
INR (fact n) / (INR (fact p) * INR (fact (n - p))).

Lemma pascal_step2 :
forall n i:nat,
(i <= n)%nat -> C (S n) i = INR (S n) / INR (S n - i) * C n i.