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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  <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">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="E1:57"/>
 <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="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">c<sub>4</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span>
 ;<br/>

<a NAME="E2:57"/><b>then </b>
<span class="p1">(<span class="default"><a href="termord.html#K6" target="_self">Red</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="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="ref" href="polynom1.html#D9">POLYNOM1:def 9</a></i>;<br/>
<a NAME="E3:57"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></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">c<sub>4</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <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>
 
;<br/>
<a NAME="E4:57"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></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">c<sub>4</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span></span>)</span> <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="ref" href="polynom1.html#D23">POLYNOM1:def 23</a></i>;<br/>
<a NAME="E5:57"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="polynom1.html#K15">.</a> <span class="p2">(<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></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">c<sub>4</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="polynom1.html#K15">.</a> <span class="p2">(<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></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="ref" href="polynom1.html#D21">POLYNOM1:def 21</a></i>;<br/>
<a NAME="E6:57"/><b>then </b><i><font color="Green">E37</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="polynom1.html#K15">.</a> <span class="p2">(<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></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">c<sub>4</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="polynom1.html#K15">.</a> <span class="p3">(<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></span>)</span></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="ref" href="polynom1.html#D22">POLYNOM1:def 22</a></i>;<br/>
<a NAME="E7:57"/>
<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="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#R1">=</a> <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>
 
<b>by </b><i><a class="txt" href="termord.html#E32"><i><font color="Green">Lemma23</font></i></a></i>;<br/>
<b>hence </b><a NAME="E8:57"/>
contradiction
 <b>by </b><i><a class="txt" href="termord.html#E6:57"><i><font color="Green">E37</font></i></a>, <a class="ref" href="rlvect_1.html#D10">RLVECT_1:def 10</a></i>;<br/>


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