(* ::Package:: *)

(************************************************************************)
(* This file was generated automatically by the Mathematica front end.  *)
(* It contains Initialization cells from a Notebook file, which         *)
(* typically will have the same name as this file except ending in      *)
(* ".nb" instead of ".m".                                               *)
(*                                                                      *)
(* This file is intended to be loaded into the Mathematica kernel using *)
(* the package loading commands Get or Needs.  Doing so is equivalent   *)
(* to using the Evaluate Initialization Cells menu command in the front *)
(* end.                                                                 *)
(*                                                                      *)
(* DO NOT EDIT THIS FILE.  This entire file is regenerated              *)
(* automatically each time the parent Notebook file is saved in the     *)
(* Mathematica front end.  Any changes you make to this file will be    *)
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(************************************************************************)



Off[General::spell1];
Needs["Graphics`Colors`"];

(* To do our induction proof we need to force 
Mma to expand some forms a particular way. 
These expansions are of course completely obvious 
but unfortuneately they are not in Mma's standard 
bag of tricks.*)
 
Unprotect[Times,Sin,Expand];
n_*(n_-1)!:=n!
Expand[a_*Sin[(n_+1)*x_]]:=Expand[
			a*Cos[n*x]*Sin[x] + a*Cos[x]*Sin[n*x]]
Protect[Times,Sin,Expand];



