<?xml version="1.0"?>
<div class="add">

<b>let </b><font color="Maroon">L</font> be  non <a href="struct_0.html#V3">empty</a> <a href="rlvect_1.html#V3">Abelian</a> <a href="rlvect_1.html#V4">add-associative</a> <a href="rlvect_1.html#V5">right_zeroed</a> <a href="rlvect_1.html#V6">right_complementable</a> <a href="vectsp_1.html#V7">distributive</a>  <a href="vectsp_1.html#L3">doubleLoopStr</a> ;<br/><b>let </b><font color="Maroon">p1</font> be   <a href="polynom3.html#NM1">Polynomial</a> of <font color="Maroon">L</font>, <font color="Maroon">p2</font> be   <a href="polynom3.html#NM1">Polynomial</a> of <font color="Maroon">L</font>;<br/>



<b>reconsider </b><font color="Maroon">p1'</font> = <font color="Maroon">p1</font>, <font color="Maroon">p2'</font> = <font color="Maroon">p2</font> as   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="polynom3.html#K16">Polynom-Ring</a> <font color="Maroon">L</font></span>)</span> <b>by </b><i><a class="ref" href="polynom3.html#D12">POLYNOM3:def 12</a></i>;<br/>
<a NAME="E2:15"/>
<font color="Maroon">p1</font> <a href="polynom3.html#K9">+</a> <font color="Maroon">p2</font> <a href="hidden.html#R1">=</a> <font color="Maroon">p1'</font> <a href="rlvect_1.html#K4">+</a> <font color="Maroon">p2'</font>
 
<b>by </b><i><a class="ref" href="polynom3.html#D12">POLYNOM3:def 12</a></i>;<br/>
<a NAME="E3:15"/><b>then </b><i><font color="Green">E29</font></i>: 
 <a href="polynom3.html#K10">-</a> <span class="p1">(<span class="default"><font color="Maroon">p1</font> <a href="polynom3.html#K9">+</a> <font color="Maroon">p2</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="rlvect_1.html#K5">-</a> <span class="p1">(<span class="default"><font color="Maroon">p1'</font> <a href="rlvect_1.html#K4">+</a> <font color="Maroon">p2'</font></span>)</span>
 
<b>by </b><i/>;<br/>
<a NAME="E4:15"/><i><font color="Green">E30</font></i>: 
(  <a href="polynom3.html#K10">-</a> <font color="Maroon">p1</font> <a href="hidden.html#R1">=</a>  <a href="rlvect_1.html#K5">-</a> <font color="Maroon">p1'</font> &amp;  <a href="polynom3.html#K10">-</a> <font color="Maroon">p2</font> <a href="hidden.html#R1">=</a>  <a href="rlvect_1.html#K5">-</a> <font color="Maroon">p2'</font> )
 
<b>by </b><i/>;<br/>
<a NAME="E5:15"/>
 <a href="rlvect_1.html#K5">-</a> <span class="p1">(<span class="default"><font color="Maroon">p1'</font> <a href="rlvect_1.html#K4">+</a> <font color="Maroon">p2'</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="rlvect_1.html#K5">-</a> <font color="Maroon">p1'</font></span>)</span> <a href="rlvect_1.html#K4">+</a> <span class="p1">(<span class="default"><a href="rlvect_1.html#K5">-</a> <font color="Maroon">p2'</font></span>)</span>
 
<b>by </b><i><a class="ref" href="rlvect_1.html#T45">RLVECT_1:45</a></i>;<br/>
<b>hence </b><a NAME="E6:15"/>
 <a href="polynom3.html#K10">-</a> <span class="p1">(<span class="default"><font color="Maroon">p1</font> <a href="polynom3.html#K9">+</a> <font color="Maroon">p2</font></span>)</span> <a href="funct_2.html#R2">=</a> <span class="p1">(<span class="default"><a href="polynom3.html#K10">-</a> <font color="Maroon">p1</font></span>)</span> <a href="polynom3.html#K9">+</a> <span class="p1">(<span class="default"><a href="polynom3.html#K10">-</a> <font color="Maroon">p2</font></span>)</span>
 <b>by </b><i>, , <a class="ref" href="polynom3.html#D12">POLYNOM3:def 12</a></i>;<br/>


</div>
