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(*         *      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)         *)
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Local Open Scope R_scope.
Definition C (n p:nat) : R :=
INR (fact n) / (INR (fact p) * INR (fact (n - p))).

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Lemma binomial :
forall (x y:R) (n:nat),
(x + y) ^ n = sum_f_R0 (fun i:nat => C n i * x ^ i * y ^ (n - i)) n.