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<b>let </b><font color="Maroon">L</font> be  non <a href="struct_0.html#V3">empty</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">p</font> be   <a href="polynom3.html#NM1">Polynomial</a> of <font color="Maroon">L</font>;<br/><b>let </b><font color="Maroon">f</font> be   <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>;<br/>





<b>assume </b><a NAME="E1:14"/><i><font color="Green">E29</font></i>: 
<font color="Maroon">f</font> <a href="hidden.html#R1">=</a> <font color="Maroon">p</font>
 ;<br/>

<b>reconsider </b><font color="Maroon">x</font> =  <a href="polynom3.html#K10">-</a> <font color="Maroon">p</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/>
<b>reconsider </b><font color="Maroon">x</font> = <font color="Maroon">x</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> ;<br/>
<font color="Maroon">f</font> <a href="rlvect_1.html#K2">+</a> <font color="Maroon">x</font> = 
<font color="Maroon">p</font> <a href="polynom3.html#K11">-</a> <font color="Maroon">p</font>
<b>by </b><i>, <a class="ref" href="polynom3.html#D12">POLYNOM3:def 12</a></i>
<br/>.= 
 <a href="polynom3.html#K12">0_.</a> <font color="Maroon">L</font>
<b>by </b><i><a class="ref" href="polynom3.html#T30">POLYNOM3:30</a></i>
<br/>.= 
 <a href="rlvect_1.html#K1">0.</a> <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="E5:14"/><b>then </b>
<font color="Maroon">f</font> <a href="hidden.html#R1">=</a>  <a href="rlvect_1.html#K5">-</a> <font color="Maroon">x</font>
 
<b>by </b><i><a class="ref" href="rlvect_1.html#T19">RLVECT_1:19</a></i>;<br/>
<b>hence </b><a NAME="E6:14"/>
 <a href="rlvect_1.html#K5">-</a> <font color="Maroon">f</font> <a href="hidden.html#R1">=</a>  <a href="polynom3.html#K10">-</a> <font color="Maroon">p</font>
 <b>by </b><i><a class="ref" href="rlvect_1.html#T30">RLVECT_1:30</a></i>;<br/>


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