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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="rlvect_1.html#L1">LoopStr</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/>



<i><font color="Green">E29</font></i>:  <a href="algseq_1.html#K3">len</a> <font color="Maroon">p</font> = 
 <a href="algseq_1.html#K3">len</a> <span class="p1">(<span class="default"><a href="polynom3.html#K10">-</a> <font color="Maroon">p</font></span>)</span>
<b>by </b><i><a class="ref" href="polynom4.html#T11">POLYNOM4:11</a></i>
<br/>.= 
 <a href="algseq_1.html#K3">len</a> <span class="p1">(<span class="default"><a href="polynom3.html#K10">-</a> <span class="p2">(<span class="default"><a href="polynom3.html#K10">-</a> <font color="Maroon">p</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="polynom4.html#T11">POLYNOM4:11</a></i>
;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="12_2"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">x</font> be    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/><b>assume </b><a NAME="E1:12_2"/>
<font color="Maroon">x</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a>  <a href="algseq_1.html#K3">len</a> <font color="Maroon">p</font>
 ;<br/><b>thus </b><span class="p1">(<span class="default"><a href="polynom3.html#K10">-</a> <span class="p2">(<span class="default"><a href="polynom3.html#K10">-</a> <font color="Maroon">p</font></span>)</span></span>)</span> <a href="normsp_1.html#K2">.</a> <font color="Maroon">x</font> = 
 <a href="rlvect_1.html#K5">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="polynom3.html#K10">-</a> <font color="Maroon">p</font></span>)</span> <a href="normsp_1.html#K2">.</a> <font color="Maroon">x</font></span>)</span>
<b>by </b><i><a class="ref" href="polynom3.html#D7">POLYNOM3:def 7</a></i>
<br/>.= 
 <a href="rlvect_1.html#K5">-</a> <span class="p1">(<span class="default"><a href="rlvect_1.html#K5">-</a> <span class="p2">(<span class="default"><font color="Maroon">p</font> <a href="normsp_1.html#K2">.</a> <font color="Maroon">x</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="polynom3.html#D7">POLYNOM3:def 7</a></i>
<br/>.= 
<font color="Maroon">p</font> <a href="normsp_1.html#K2">.</a> <font color="Maroon">x</font>
<b>by </b><i><a class="ref" href="rlvect_1.html#T30">RLVECT_1:30</a></i>
;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E3:12"/>
 <a href="polynom3.html#K10">-</a> <span class="p1">(<span class="default"><a href="polynom3.html#K10">-</a> <font color="Maroon">p</font></span>)</span> <a href="funct_2.html#R2">=</a> <font color="Maroon">p</font>
 <b>by </b><i>, <a class="ref" href="algseq_1.html#T28">ALGSEQ_1:28</a></i>;<br/>


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