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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">O</font> be  <a href="relat_2.html#V6">connected</a> <a href="bagorder.html#NM1">TermOrder</a> of <font color="Maroon">n</font>;<br/><b>let </b><font color="Maroon">L</font> be  <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> non <a href="realset2.html#V3">trivial</a>  <a href="rlvect_1.html#L1">LoopStr</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/>







<div><i><font color="Green">E32</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="59_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="E1:59_1"/>
<font color="Maroon">u</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="polynom1.html#K12">Support</a> <font color="Maroon">p</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2">(<span class="default"><a href="termord.html#K3" target="_self">HT</a> <font color="Maroon">p</font>,<font color="Maroon">O</font></span>)</span></span><a href="tarski.html#K1">}</a></span>
 ;<br/><a NAME="E2:59_1"/><b>then </b><i><font color="Green">E33</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> &amp; not <font color="Maroon">u</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2">(<span class="default"><a href="termord.html#K3" target="_self">HT</a> <font color="Maroon">p</font>,<font color="Maroon">O</font></span>)</span></span><a href="tarski.html#K1">}</a></span> )
 <b>by </b><i><a class="ref" href="xboole_0.html#D4">XBOOLE_0:def 4</a></i>;<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/><b>reconsider </b><font color="Maroon">u'</font> = <font color="Maroon">u'</font> as   <a href="polynom1.html#NM1">bag</a> of <font color="Maroon">n</font> ;<br/><a NAME="E5:59_1"/>
<font color="Maroon">u'</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="termord.html#K3" target="_self">HT</a> <font color="Maroon">p</font>,<font color="Maroon">O</font>
 <b>by </b><i>, <a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/><b>hence </b><a NAME="E6:59_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"><a href="termord.html#K6" target="_self">Red</a> <font color="Maroon">p</font>,<font color="Maroon">O</font></span>)</span>
 <b>by </b><i>, </i>;<br/></div><b>end;</b></div>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="59_2"><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="E1:59_2"/><i><font color="Green">E35</font></i>: 
<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"><a href="termord.html#K6" target="_self">Red</a> <font color="Maroon">p</font>,<font color="Maroon">O</font></span>)</span>
 ;<br/><a NAME="E2:59_2"/><b>then </b><i><font color="Green">E37</font></i>: 
<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">p</font> <a href="polynom1.html#K25">-</a> <span class="p2">(<span class="default"><a href="termord.html#K5" target="_self">HM</a> <font color="Maroon">p</font>,<font color="Maroon">O</font></span>)</span></span>)</span>
 ;<br/><b>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> <b>by </b><i/>;<br/><b>reconsider </b><font color="Maroon">u'</font> = <font color="Maroon">u'</font> as   <a href="polynom1.html#NM1">bag</a> of <font color="Maroon">n</font> ;<br/><a NAME="E5:59_2"/><i><font color="Green">E39</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">p</font> <a href="polynom1.html#K25">-</a> <span class="p2">(<span class="default"><a href="termord.html#K5" target="_self">HM</a> <font color="Maroon">p</font>,<font color="Maroon">O</font></span>)</span></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="ref" href="polynom1.html#D9">POLYNOM1:def 9</a></i>;<br/><i><font color="Green">E44</font></i>: <span class="p1">(<span class="default"><font color="Maroon">p</font> <a href="polynom1.html#K22">+</a> <span class="p2">(<span class="default"><a href="polynom1.html#K24">-</a> <span class="p3">(<span class="default"><a href="termord.html#K5" target="_self">HM</a> <font color="Maroon">p</font>,<font color="Maroon">O</font></span>)</span></span>)</span></span>)</span> <a href="polynom1.html#K15">.</a> <font color="Maroon">u'</font> = 
<span class="p1">(<span class="default"><font color="Maroon">p</font> <a href="polynom1.html#K15">.</a> <font color="Maroon">u'</font></span>)</span> <a href="rlvect_1.html#K2">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="polynom1.html#K24">-</a> <span class="p3">(<span class="default"><a href="termord.html#K5" target="_self">HM</a> <font color="Maroon">p</font>,<font color="Maroon">O</font></span>)</span></span>)</span> <a href="polynom1.html#K15">.</a> <font color="Maroon">u'</font></span>)</span>
<b>by </b><i><a class="ref" href="polynom1.html#D21">POLYNOM1:def 21</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">p</font> <a href="polynom1.html#K15">.</a> <font color="Maroon">u'</font></span>)</span> <a href="rlvect_1.html#K2">+</a> <span class="p1">(<span class="default"><a href="rlvect_1.html#K5">-</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="termord.html#K5" target="_self">HM</a> <font color="Maroon">p</font>,<font color="Maroon">O</font></span>)</span> <a href="polynom1.html#K15">.</a> <font color="Maroon">u'</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="polynom1.html#D22">POLYNOM1:def 22</a></i>
;<br/><a NAME="E7:59_2"/><i><font color="Green">E45</font></i>: 
not <font color="Maroon">u'</font> <a href="pboole.html#R6">=</a>  <a href="termord.html#K3" target="_self">HT</a> <font color="Maroon">p</font>,<font color="Maroon">O</font>
 <b>by </b><i>, </i>;<br/><b>then </b><span class="p1">(<span class="default"><font color="Maroon">p</font> <a href="polynom1.html#K22">+</a> <span class="p2">(<span class="default"><a href="polynom1.html#K24">-</a> <span class="p3">(<span class="default"><a href="termord.html#K5" target="_self">HM</a> <font color="Maroon">p</font>,<font color="Maroon">O</font></span>)</span></span>)</span></span>)</span> <a href="polynom1.html#K15">.</a> <font color="Maroon">u'</font> = 
<span class="p1">(<span class="default"><font color="Maroon">p</font> <a href="polynom1.html#K15">.</a> <font color="Maroon">u'</font></span>)</span> <a href="rlvect_1.html#K2">+</a> <span class="p1">(<span class="default"><a href="rlvect_1.html#K5">-</a> <span class="p2">(<span class="default"><a href="rlvect_1.html#K1">0.</a> <font color="Maroon">L</font></span>)</span></span>)</span>
<b>by </b><i>, </i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">p</font> <a href="polynom1.html#K15">.</a> <font color="Maroon">u'</font></span>)</span> <a href="rlvect_1.html#K2">+</a> <span class="p1">(<span class="default"><a href="rlvect_1.html#K1">0.</a> <font color="Maroon">L</font></span>)</span>
<b>by </b><i><a class="ref" href="rlvect_1.html#T25">RLVECT_1:25</a></i>
<br/>.= 
<font color="Maroon">p</font> <a href="polynom1.html#K15">.</a> <font color="Maroon">u'</font>
<b>by </b><i><a class="ref" href="rlvect_1.html#T10">RLVECT_1:10</a></i>
;<br/><a NAME="E9:59_2"/><b>then </b>
<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#D23">POLYNOM1:def 23</a></i>;<br/><a NAME="E10:59_2"/><b>then </b><i><font color="Green">E47</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>
 <b>by </b><i><a class="ref" href="polynom1.html#D9">POLYNOM1:def 9</a></i>;<br/><a NAME="E11:59_2"/>
not <font color="Maroon">u'</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2">(<span class="default"><a href="termord.html#K3" target="_self">HT</a> <font color="Maroon">p</font>,<font color="Maroon">O</font></span>)</span></span><a href="tarski.html#K1">}</a></span>
 <b>by </b><i><a class="txt" href="termord.html#E6:59_2"><i><font color="Green">E44</font></i></a>, <a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/><b>hence </b><a NAME="E12:59_2"/>
<font color="Maroon">u</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="polynom1.html#K12">Support</a> <font color="Maroon">p</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2">(<span class="default"><a href="termord.html#K3" target="_self">HT</a> <font color="Maroon">p</font>,<font color="Maroon">O</font></span>)</span></span><a href="tarski.html#K1">}</a></span>
 <b>by </b><i><a class="txt" href="termord.html#E7:59_2"><i><font color="Green">E45</font></i></a>, <a class="ref" href="xboole_0.html#D4">XBOOLE_0:def 4</a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E3:59"/>
 <a href="polynom1.html#K12">Support</a> <span class="p1">(<span class="default"><a href="termord.html#K6" target="_self">Red</a> <font color="Maroon">p</font>,<font color="Maroon">O</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="polynom1.html#K12">Support</a> <font color="Maroon">p</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2">(<span class="default"><a href="termord.html#K3" target="_self">HT</a> <font color="Maroon">p</font>,<font color="Maroon">O</font></span>)</span></span><a href="tarski.html#K1">}</a></span>
 <b>by </b><i>, <a class="ref" href="tarski.html#T2">TARSKI:2</a></i>;<br/>


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