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<b>let </b><font color="Maroon">c<sub>1</sub></font> be   <a href="ordinal1.html#NM2">Ordinal</a>;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font> be  <a href="relat_2.html#V6">connected</a> <a href="bagorder.html#NM1">TermOrder</a> of <font color="Maroon">c<sub>1</sub></font>;<br/><b>let </b><font color="Maroon">c<sub>3</sub></font> be  non <a href="realset2.html#V3">trivial</a>  <a href="struct_0.html#L2">ZeroStr</a> ;<br/><b>let </b><font color="Maroon">c<sub>4</sub></font> be   <a href="polynom1.html#NM4">Polynomial</a> of <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>3</sub></font>;<br/>







<b>assume </b><a NAME="E1:37"/><i><font color="Green">E26</font></i>: 
 <a href="termord.html#K4" target="_self">HC</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a>  <a href="rlvect_1.html#K1">0.</a> <font color="Maroon">c<sub>3</sub></font>
 ;<br/>

<a NAME="E2:37"/><b>then </b><i><font color="Green">E27</font></i>: 
<font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a>  <a href="polynom1.html#K26">0_</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>3</sub></font>
 
<b>by </b><i><a class="txt" href="termord.html#E31"><i><font color="Green">Lemma22</font></i></a></i>;<br/>
<a NAME="E3:37"/><b>then </b>
 <a href="polynom1.html#K12">Support</a> <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a> 
 
<b>by </b><i><a class="ref" href="polynom7.html#T1">POLYNOM7:1</a></i>;<br/>
<a NAME="E4:37"/><b>then </b><i><font color="Green">E28</font></i>: 
 <a href="termord.html#K3" target="_self">HT</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>2</sub></font> <a href="pboole.html#R6">=</a>  <a href="polynom1.html#K16">EmptyBag</a> <font color="Maroon">c<sub>1</sub></font>
 
<b>by </b><i><a class="ref" href="termord.html#D6" target="_self">Def6</a></i>;<br/>
<a NAME="E5:37"/><b>then </b>
 <a href="termord.html#K5" target="_self">HM</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a>  <a href="polynom7.html#K1">Monom</a> <span class="p1">(<span class="default"><a href="rlvect_1.html#K1">0.</a> <font color="Maroon">c<sub>3</sub></font></span>)</span>,<span class="p1">(<span class="default"><a href="polynom1.html#K16">EmptyBag</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>
 
<b>by </b><i><a class="txt" href="termord.html#E1:37"><i><font color="Green">E26</font></i></a></i>;<br/>
<a NAME="E6:37"/><b>then </b><i><font color="Green">E29</font></i>: 
 <a href="polynom7.html#K2">term</a> <span class="p1">(<span class="default"><a href="termord.html#K5" target="_self">HM</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="pboole.html#R6">=</a>  <a href="polynom1.html#K16">EmptyBag</a> <font color="Maroon">c<sub>1</sub></font>
 
<b>by </b><i><a class="ref" href="polynom7.html#T8">POLYNOM7:8</a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="37_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:37_1"/>
 <a href="polynom1.html#K12">Support</a> <span class="p1">(<span class="default"><a href="termord.html#K5" target="_self">HM</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a> 
 ;<br/><a NAME="E2:37_1"/><b>then </b>
 <a href="polynom1.html#K12">Support</a> <span class="p1">(<span class="default"><a href="termord.html#K5" target="_self">HM</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2">(<span class="default"><a href="polynom7.html#K2">term</a> <span class="p3">(<span class="default"><a href="termord.html#K5" target="_self">HM</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span><a href="tarski.html#K1">}</a></span>
 <b>by </b><i><a class="ref" href="polynom7.html#T7">POLYNOM7:7</a></i>;<br/><a NAME="E3:37_1"/><b>then </b>
 <a href="polynom7.html#K2">term</a> <span class="p1">(<span class="default"><a href="termord.html#K5" target="_self">HM</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="hidden.html#R2">in</a>  <a href="polynom1.html#K12">Support</a> <span class="p1">(<span class="default"><a href="termord.html#K5" target="_self">HM</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span>
 <b>by </b><i><a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/><a NAME="E4:37_1"/><b>then </b>
<span class="p1">(<span class="default"><a href="termord.html#K5" target="_self">HM</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="polynom1.html#K15">.</a> <span class="p1">(<span class="default"><a href="polynom1.html#K16">EmptyBag</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="rlvect_1.html#K1">0.</a> <font color="Maroon">c<sub>3</sub></font>
 <b>by </b><i><a class="txt" href="termord.html#E6:37"><i><font color="Green">E29</font></i></a>, <a class="ref" href="polynom1.html#D9">POLYNOM1:def 9</a></i>;<br/><a NAME="E5:37_1"/><b>then </b>
<font color="Maroon">c<sub>4</sub></font> <a href="polynom1.html#K15">.</a> <span class="p1">(<span class="default"><a href="termord.html#K3" target="_self">HT</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="rlvect_1.html#K1">0.</a> <font color="Maroon">c<sub>3</sub></font>
 <b>by </b><i><a class="txt" href="termord.html#E4:37"><i><font color="Green">E28</font></i></a>, <a class="txt" href="termord.html#E32"><i><font color="Green">Lemma23</font></i></a></i>;<br/><b>hence </b><a NAME="E6:37_1"/>
contradiction
 <b>by </b><i><a class="txt" href="termord.html#E2:37"><i><font color="Green">E27</font></i></a>, <a class="ref" href="polynom1.html#T81">POLYNOM1:81</a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E8:37"/>
 <a href="polynom1.html#K12">Support</a> <span class="p1">(<span class="default"><a href="termord.html#K5" target="_self">HM</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a> 
 ;<br/>


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