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

<b>let </b><font color="Maroon">n</font> be   <a href="ordinal1.html#NM2">Ordinal</a>;<br/><b>let </b><font color="Maroon">L</font> be  <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="group_1.html#V2">unital</a> <a href="group_1.html#V4">associative</a> <a href="group_1.html#V7">commutative</a> <a href="vectsp_1.html#V7">distributive</a> non <a href="realset2.html#V3">trivial</a>  <a href="vectsp_1.html#L3">doubleLoopStr</a> ;<br/><b>let </b><font color="Maroon">p</font> be   <a href="polynom1.html#NM4">Polynomial</a> of <font color="Maroon">n</font>,<font color="Maroon">L</font>, <font color="Maroon">q</font> be   <a href="polynom1.html#NM4">Polynomial</a> of <font color="Maroon">n</font>,<font color="Maroon">L</font>;<br/>





<b>reconsider </b><font color="Maroon">p'</font> = <font color="Maroon">p</font>, <font color="Maroon">q'</font> = <font color="Maroon">q</font> as   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="polynom1.html#K30">Polynom-Ring</a> <font color="Maroon">n</font>,<font color="Maroon">L</font></span>)</span> <b>by </b><i><a class="ref" href="polynom1.html#D27">POLYNOM1:def 27</a></i>;<br/>
<b>reconsider </b><font color="Maroon">p'</font> = <font color="Maroon">p'</font>, <font color="Maroon">q'</font> = <font color="Maroon">q'</font> as   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="polynom1.html#K30">Polynom-Ring</a> <font color="Maroon">n</font>,<font color="Maroon">L</font></span>)</span> ;<br/>
<a NAME="E3:16"/><i><font color="Green">E23</font></i>: 
 <a href="polynom1.html#K24">-</a> <font color="Maroon">p</font> <a href="hidden.html#R1">=</a>  <a href="rlvect_1.html#K5">-</a> <font color="Maroon">p'</font>
 
<b>by </b><i/>;<br/>
<a NAME="E4:16"/>
 <a href="polynom1.html#K24">-</a> <font color="Maroon">q</font> <a href="hidden.html#R1">=</a>  <a href="rlvect_1.html#K5">-</a> <font color="Maroon">q'</font>
 
<b>by </b><i/>;<br/>
<a NAME="E5:16"/><b>then </b><i><font color="Green">E24</font></i>: 
( <span class="p1">(<span class="default"><a href="rlvect_1.html#K5">-</a> <font color="Maroon">p'</font></span>)</span> <a href="group_1.html#K10">*</a> <font color="Maroon">q'</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="polynom1.html#K24">-</a> <font color="Maroon">p</font></span>)</span> <a href="polynom1.html#K29">*'</a> <font color="Maroon">q</font> &amp; <font color="Maroon">p'</font> <a href="group_1.html#K10">*</a> <span class="p1">(<span class="default"><a href="rlvect_1.html#K5">-</a> <font color="Maroon">q'</font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">p</font> <a href="polynom1.html#K29">*'</a> <span class="p1">(<span class="default"><a href="polynom1.html#K24">-</a> <font color="Maroon">q</font></span>)</span> )
 
<b>by </b><i>, <a class="ref" href="polynom1.html#D27">POLYNOM1:def 27</a></i>;<br/>
<a NAME="E6:16"/><i><font color="Green">E26</font></i>: 
(  <a href="rlvect_1.html#K5">-</a> <span class="p1">(<span class="default"><font color="Maroon">p'</font> <a href="group_1.html#K10">*</a> <font color="Maroon">q'</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">p'</font></span>)</span> <a href="group_1.html#K10">*</a> <font color="Maroon">q'</font> &amp;  <a href="rlvect_1.html#K5">-</a> <span class="p1">(<span class="default"><font color="Maroon">p'</font> <a href="group_1.html#K10">*</a> <font color="Maroon">q'</font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">p'</font> <a href="group_1.html#K10">*</a> <span class="p1">(<span class="default"><a href="rlvect_1.html#K5">-</a> <font color="Maroon">q'</font></span>)</span> )
 
<b>by </b><i><a class="ref" href="vectsp_1.html#T41">VECTSP_1:41</a></i>;<br/>
<a NAME="E7:16"/>
<font color="Maroon">p'</font> <a href="group_1.html#K10">*</a> <font color="Maroon">q'</font> <a href="hidden.html#R1">=</a> <font color="Maroon">p</font> <a href="polynom1.html#K29">*'</a> <font color="Maroon">q</font>
 
<b>by </b><i><a class="ref" href="polynom1.html#D27">POLYNOM1:def 27</a></i>;<br/>
<b>hence </b><a NAME="E8:16"/>
(  <a href="polynom1.html#K24">-</a> <span class="p1">(<span class="default"><font color="Maroon">p</font> <a href="polynom1.html#K29">*'</a> <font color="Maroon">q</font></span>)</span> <a href="funct_2.html#R2">=</a> <span class="p1">(<span class="default"><a href="polynom1.html#K24">-</a> <font color="Maroon">p</font></span>)</span> <a href="polynom1.html#K29">*'</a> <font color="Maroon">q</font> &amp;  <a href="polynom1.html#K24">-</a> <span class="p1">(<span class="default"><font color="Maroon">p</font> <a href="polynom1.html#K29">*'</a> <font color="Maroon">q</font></span>)</span> <a href="funct_2.html#R2">=</a> <font color="Maroon">p</font> <a href="polynom1.html#K29">*'</a> <span class="p1">(<span class="default"><a href="polynom1.html#K24">-</a> <font color="Maroon">q</font></span>)</span> )
 <b>by </b><i>, , </i>;<br/>


</div>
