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<b>let </b><font color="Maroon">L</font> be  non <a href="vectsp_1.html#V10">degenerated</a> <a href="vectsp_2.html#NM1">comRing</a>;<br/><b>let </b><font color="Maroon">r</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L</font>;<br/><b>let </b><font color="Maroon">p</font> be   <a href="polynom3.html#NM1">Polynomial</a> of <font color="Maroon">L</font>, <font color="Maroon">q</font> be   <a href="polynom3.html#NM1">Polynomial</a> of <font color="Maroon">L</font>;<br/>





<b>assume </b><a NAME="E1:69"/>
<font color="Maroon">p</font> <a href="funct_2.html#R2">=</a> <span class="p1"><a href="polynom5.html#K4">&lt;%</a><span class="default"><span class="p2">(<span class="default"><a href="rlvect_1.html#K5">-</a> <font color="Maroon">r</font></span>)</span>,<span class="p2">(<span class="default"><a href="group_1.html#K2">1.</a> <font color="Maroon">L</font></span>)</span></span><a href="polynom5.html#K4">%&gt;</a></span> <a href="polynom3.html#K15">*'</a> <font color="Maroon">q</font>
 ;<br/>

<b>then </b> <a href="polynom4.html#K2">eval</a> <font color="Maroon">p</font>,<font color="Maroon">r</font> = 
<span class="p1">(<span class="default"><a href="polynom4.html#K2">eval</a> <span class="p2"><a href="polynom5.html#K4">&lt;%</a><span class="default"><span class="p3">(<span class="default"><a href="rlvect_1.html#K5">-</a> <font color="Maroon">r</font></span>)</span>,<span class="p3">(<span class="default"><a href="group_1.html#K2">1.</a> <font color="Maroon">L</font></span>)</span></span><a href="polynom5.html#K4">%&gt;</a></span>,<font color="Maroon">r</font></span>)</span> <a href="group_1.html#K10">*</a> <span class="p1">(<span class="default"><a href="polynom4.html#K2">eval</a> <font color="Maroon">q</font>,<font color="Maroon">r</font></span>)</span>
<b>by </b><i><a class="ref" href="polynom4.html#T27">POLYNOM4:27</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="rlvect_1.html#K5">-</a> <font color="Maroon">r</font></span>)</span> <a href="rlvect_1.html#K4">+</a> <font color="Maroon">r</font></span>)</span> <a href="group_1.html#K10">*</a> <span class="p1">(<span class="default"><a href="polynom4.html#K2">eval</a> <font color="Maroon">q</font>,<font color="Maroon">r</font></span>)</span>
<b>by </b><i><a class="ref" href="polynom5.html#T48">POLYNOM5:48</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="rlvect_1.html#K1">0.</a> <font color="Maroon">L</font></span>)</span> <a href="group_1.html#K10">*</a> <span class="p1">(<span class="default"><a href="polynom4.html#K2">eval</a> <font color="Maroon">q</font>,<font color="Maroon">r</font></span>)</span>
<b>by </b><i><a class="ref" href="rlvect_1.html#D10">RLVECT_1:def 10</a></i>
<br/>.= 
 <a href="rlvect_1.html#K1">0.</a> <font color="Maroon">L</font>
<b>by </b><i><a class="ref" href="vectsp_1.html#T39">VECTSP_1:39</a></i>
;<br/>
<b>hence </b><a NAME="E3:69"/>
<font color="Maroon">r</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#D6">POLYNOM5:def 6</a></i>;<br/>


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