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<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="vectsp_2.html#V2">domRing-like</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>;<br/><b>let </b><font color="Maroon">a</font> be  <a href="rlvect_1.html#V8">non-zero</a> <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L</font>;<br/>







<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="33_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">u</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>assume </b><a NAME="E1:33_1"/><i><font color="Green">E23</font></i>: 
<font color="Maroon">u</font> <a href="hidden.html#R2">in</a>  <a href="polynom1.html#K12">Support</a> <font color="Maroon">p</font>
 ;<br/><b>then reconsider </b><font color="Maroon">u'</font> = <font color="Maroon">u</font> as    <a href="polynom1.html#M1">Element</a> of  <a href="polynom1.html#K14">Bags</a> <font color="Maroon">n</font> ;<br/><a NAME="E3:33_1"/><i><font color="Green">E24</font></i>: 
<font color="Maroon">p</font> <a href="polynom1.html#K15">.</a> <font color="Maroon">u'</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="rlvect_1.html#K1">0.</a> <font color="Maroon">L</font>
 <b>by </b><i>, <a class="ref" href="polynom1.html#D9">POLYNOM1:def 9</a></i>;<br/><a NAME="E4:33_1"/><i><font color="Green">E26</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">a</font> <a href="polynom7.html#K5">*</a> <font color="Maroon">p</font></span>)</span> <a href="polynom1.html#K15">.</a> <font color="Maroon">u'</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a</font> <a href="group_1.html#K1">*</a> <span class="p1">(<span class="default"><font color="Maroon">p</font> <a href="polynom1.html#K15">.</a> <font color="Maroon">u'</font></span>)</span>
 <b>by </b><i><a class="ref" href="polynom7.html#D10">POLYNOM7:def 10</a></i>;<br/><a NAME="E5:33_1"/>
<font color="Maroon">a</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="rlvect_1.html#K1">0.</a> <font color="Maroon">L</font>
 <b>by </b><i><a class="ref" href="rlvect_1.html#D13">RLVECT_1:def 13</a></i>;<br/><a NAME="E6:33_1"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon">a</font> <a href="polynom7.html#K5">*</a> <font color="Maroon">p</font></span>)</span> <a href="polynom1.html#K15">.</a> <font color="Maroon">u'</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="rlvect_1.html#K1">0.</a> <font color="Maroon">L</font>
 <b>by </b><i><a class="txt" href="polyred.html#E1"><i><font color="Green">Lemma29</font></i></a>, , <a class="ref" href="vectsp_2.html#D5">VECTSP_2:def 5</a></i>;<br/><b>hence </b><a NAME="E7:33_1"/>
<font color="Maroon">u</font> <a href="hidden.html#R2">in</a>  <a href="polynom1.html#K12">Support</a> <span class="p1">(<span class="default"><font color="Maroon">a</font> <a href="polynom7.html#K5">*</a> <font color="Maroon">p</font></span>)</span>
 <b>by </b><i><a class="ref" href="polynom1.html#D9">POLYNOM1:def 9</a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E2:33"/>
 <a href="polynom1.html#K12">Support</a> <font color="Maroon">p</font> <a href="tarski.html#R1">c=</a>  <a href="polynom1.html#K12">Support</a> <span class="p1">(<span class="default"><font color="Maroon">a</font> <a href="polynom7.html#K5">*</a> <font color="Maroon">p</font></span>)</span>
 <b>by </b><i><a class="ref" href="tarski.html#D3">TARSKI:def 3</a></i>;<br/>


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