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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="bagorder.html#V2">admissible</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>, <font color="Maroon">c<sub>4</sub></font>, <font color="Maroon">c<sub>5</sub></font>, <font color="Maroon">c<sub>6</sub></font> be   <a href="polynom1.html#NM1">bag</a> of <font color="Maroon">c<sub>1</sub></font>;<br/>





<b>assume </b><a NAME="E1:6"/><i><font color="Green">E7</font></i>: 
( <font color="Maroon">c<sub>3</sub></font> <a href="termord.html#R1">&lt;=</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>2</sub></font> &amp; <font color="Maroon">c<sub>5</sub></font> <a href="termord.html#R2">&lt;</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>2</sub></font> )
 ;<br/>

<a NAME="E2:6"/><b>then </b>
( <font color="Maroon">c<sub>5</sub></font> <a href="termord.html#R1">&lt;=</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>2</sub></font> &amp; <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>6</sub></font> )
 
<b>by </b><i><a class="ref" href="termord.html#D3">TERMORD:def 3</a></i>;<br/>
<a NAME="E3:6"/><b>then </b>
( <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>2</sub></font> &amp; <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>2</sub></font> )
 
<b>by </b><i><a class="txt" href="groeb_3.html#E1:6"><i><font color="Green">E7</font></i></a>, <a class="ref" href="termord.html#D2">TERMORD:def 2</a></i>;<br/>
<a NAME="E4:6"/><b>then </b>
( <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="polynom1.html#K9">+</a> <font color="Maroon">c<sub>5</sub></font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="polynom1.html#K9">+</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>2</sub></font> &amp; <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="polynom1.html#K9">+</a> <font color="Maroon">c<sub>5</sub></font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="polynom1.html#K9">+</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>2</sub></font> )
 
<b>by </b><i><a class="ref" href="bagorder.html#D7">BAGORDER:def 7</a></i>;<br/>
<a NAME="E5:6"/><b>then </b><i><font color="Green">E8</font></i>: 
( <font color="Maroon">c<sub>3</sub></font> <a href="polynom1.html#K9">+</a> <font color="Maroon">c<sub>5</sub></font> <a href="termord.html#R1">&lt;=</a> <font color="Maroon">c<sub>4</sub></font> <a href="polynom1.html#K9">+</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>2</sub></font> &amp; <font color="Maroon">c<sub>4</sub></font> <a href="polynom1.html#K9">+</a> <font color="Maroon">c<sub>5</sub></font> <a href="termord.html#R1">&lt;=</a> <font color="Maroon">c<sub>4</sub></font> <a href="polynom1.html#K9">+</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>2</sub></font> )
 
<b>by </b><i><a class="ref" href="termord.html#D2">TERMORD:def 2</a></i>;<br/>
<a NAME="E6:6"/><b>then </b><i><font color="Green">E9</font></i>: 
<font color="Maroon">c<sub>3</sub></font> <a href="polynom1.html#K9">+</a> <font color="Maroon">c<sub>5</sub></font> <a href="termord.html#R1">&lt;=</a> <font color="Maroon">c<sub>4</sub></font> <a href="polynom1.html#K9">+</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>2</sub></font>
 
<b>by </b><i><a class="ref" href="termord.html#T8">TERMORD:8</a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="6_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:6_1"/>
<font color="Maroon">c<sub>3</sub></font> <a href="polynom1.html#K9">+</a> <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>4</sub></font> <a href="polynom1.html#K9">+</a> <font color="Maroon">c<sub>6</sub></font>
 ;<br/><a NAME="E2:6_1"/><b>then </b><i><font color="Green">E10</font></i>: 
<font color="Maroon">c<sub>4</sub></font> <a href="polynom1.html#K9">+</a> <font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>4</sub></font> <a href="polynom1.html#K9">+</a> <font color="Maroon">c<sub>5</sub></font>
 <b>by </b><i><a class="txt" href="groeb_3.html#E5:6"><i><font color="Green">E8</font></i></a>, <a class="ref" href="termord.html#T7">TERMORD:7</a></i>;<br/><a NAME="E3:6_1"/>
( <font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="polynom1.html#K9">+</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="polynom1.html#K10">-'</a> <font color="Maroon">c<sub>4</sub></font> &amp; <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="polynom1.html#K9">+</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="polynom1.html#K10">-'</a> <font color="Maroon">c<sub>4</sub></font> )
 <b>by </b><i><a class="ref" href="polynom1.html#T52">POLYNOM1:52</a></i>;<br/><b>hence </b><a NAME="E4:6_1"/>
contradiction
 <b>by </b><i><a class="txt" href="groeb_3.html#E1:6"><i><font color="Green">E7</font></i></a>, <a class="txt" href="groeb_3.html#E2:6_1"><i><font color="Green">E10</font></i></a>, <a class="ref" href="termord.html#D3">TERMORD:def 3</a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E8:6"/>
<font color="Maroon">c<sub>3</sub></font> <a href="polynom1.html#K9">+</a> <font color="Maroon">c<sub>5</sub></font> <a href="termord.html#R2">&lt;</a> <font color="Maroon">c<sub>4</sub></font> <a href="polynom1.html#K9">+</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>2</sub></font>
 <b>by </b><i><a class="txt" href="groeb_3.html#E6:6"><i><font color="Green">E9</font></i></a>, <a class="ref" href="termord.html#D3">TERMORD:def 3</a></i>;<br/>


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