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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="group_1.html#V2">unital</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>assume </b><a NAME="E1:36"/><i><font color="Green">E29</font></i>: 
 <a href="hurwitz.html#NK3" target="_self">deg</a> <font color="Maroon">p</font> <a href="hidden.html#R1">=</a> 0
 ;<br/>

<a NAME="E2:36"/><b>then </b><i><font color="Green">E30</font></i>: 
<font color="Maroon">p</font> <a href="funct_2.html#R2">=</a> <span class="p1"><a href="algseq_1.html#K5">&lt;%</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">p</font> <a href="normsp_1.html#K2">.</a> 0</span>)</span></span><a href="algseq_1.html#K5">%&gt;</a></span>
 
<b>by </b><i><a class="ref" href="algseq_1.html#D6">ALGSEQ_1:def 6</a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="36_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:36_1"/>
<font color="Maroon">p</font> is <a href="polynom5.html#V1">with_roots</a>
 ;<br/><b>then consider </b><font color="Maroon">x</font> being   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L</font><b> such that </b><br/><a NAME="E3:36_1"/><i><font color="Green">E31</font></i>: 
<font color="Maroon">x</font> <a href="polynom5.html#R1">is_a_root_of</a> <font color="Maroon">p</font>
 <b>by </b><i><a class="ref" href="polynom5.html#D7">POLYNOM5:def 7</a></i>;<br/> <a href="rlvect_1.html#K1">0.</a> <font color="Maroon">L</font> = 
 <a href="polynom4.html#K2">eval</a> <font color="Maroon">p</font>,<font color="Maroon">x</font>
<b>by </b><i>, <a class="ref" href="polynom5.html#D6">POLYNOM5:def 6</a></i>
<br/>.= 
<font color="Maroon">p</font> <a href="normsp_1.html#K2">.</a> 0
<b>by </b><i>, <a class="ref" href="polynom5.html#T38">POLYNOM5:38</a></i>
;<br/><b>hence </b><a NAME="E5:36_1"/>
contradiction
 <b>by </b><i>, , <a class="ref" href="algseq_1.html#T31">ALGSEQ_1:31</a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E4:36"/>
not <font color="Maroon">p</font> is <a href="polynom5.html#V1">with_roots</a>
 ;<br/>


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