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<b>set </b><font color="Maroon">c<sub>2</sub></font> =  <a href="bagorder.html#NK4" target="_self">LexOrder</a> <font color="Maroon">c<sub>1</sub></font>;<br/>
<b>take </b>
 <a href="bagorder.html#NK4" target="_self">LexOrder</a> <font color="Maroon">c<sub>1</sub></font>
;<br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="11_1_1_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">c<sub>3</sub></font>, <font color="Maroon">c<sub>4</sub></font> be    <a href="hidden.html#M1">set</a> ;<br/><b>assume </b><a NAME="E1:11_1_1_1"/>
( <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K3">field</a> <span class="p1">(<span class="default"><a href="bagorder.html#NK4" target="_self">LexOrder</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> &amp; <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K3">field</a> <span class="p1">(<span class="default"><a href="bagorder.html#NK4" target="_self">LexOrder</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> &amp; <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>4</sub></font> )
 ;<br/><b>then reconsider </b><font color="Maroon">c<sub>5</sub></font> = <font color="Maroon">c<sub>3</sub></font>, <font color="Maroon">c<sub>6</sub></font> = <font color="Maroon">c<sub>4</sub></font> as   <a href="polynom1.html#NM1">bag</a> of <font color="Maroon">c<sub>1</sub></font> <b>by </b><i><a class="txt" href="termord.html#E6"><i><font color="Green">Lemma4</font></i></a></i>;<br/><a NAME="E3:11_1_1_1"/>
( <font color="Maroon">c<sub>5</sub></font> <a href="polynom1.html#R2">&lt;='</a> <font color="Maroon">c<sub>6</sub></font> or <font color="Maroon">c<sub>6</sub></font> <a href="polynom1.html#R2">&lt;='</a> <font color="Maroon">c<sub>5</sub></font> )
 <b>by </b><i><a class="ref" href="polynom1.html#T49">POLYNOM1:49</a></i>;<br/><b>hence </b><a NAME="E4:11_1_1_1"/>
( <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>  <a href="bagorder.html#NK4" target="_self">LexOrder</a> <font color="Maroon">c<sub>1</sub></font> or <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>3</sub></font></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R2">in</a>  <a href="bagorder.html#NK4" target="_self">LexOrder</a> <font color="Maroon">c<sub>1</sub></font> )
 <b>by </b><i><a class="ref" href="polynom1.html#D16">POLYNOM1:def 16</a></i>;<br/></div><b>end;</b></div>
<a NAME="E2:11_1_1"/><b>then </b>
 <a href="bagorder.html#NK4" target="_self">LexOrder</a> <font color="Maroon">c<sub>1</sub></font> <a href="relat_2.html#R6">is_connected_in</a>  <a href="relat_1.html#K3">field</a> <span class="p1">(<span class="default"><a href="bagorder.html#NK4" target="_self">LexOrder</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>
 
<b>by </b><i><a class="ref" href="relat_2.html#D6">RELAT_2:def 6</a></i>;<br/>
<b>hence </b><a NAME="E3:11_1_1"/>
(  <a href="bagorder.html#NK4" target="_self">LexOrder</a> <font color="Maroon">c<sub>1</sub></font> is <a href="bagorder.html#V2">admissible</a> &amp;  <a href="bagorder.html#NK4" target="_self">LexOrder</a> <font color="Maroon">c<sub>1</sub></font> is <a href="relat_2.html#V6">connected</a> )
 <b>by </b><i><a class="ref" href="relat_2.html#D14">RELAT_2:def 14</a></i>;<br/>


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