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





<a NAME="E1:20"/><i><font color="Green">E14</font></i>: 
<font color="Maroon">c<sub>2</sub></font> <a href="relat_2.html#R6">is_connected_in</a>  <a href="relat_1.html#K3">field</a> <font color="Maroon">c<sub>2</sub></font>
 
<b>by </b><i><a class="ref" href="relat_2.html#D14">RELAT_2:def 14</a></i>;<br/>
<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="20_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:20_1"/>
( <font color="Maroon">c<sub>3</sub></font> <a href="pboole.html#R6">=</a> <font color="Maroon">c<sub>4</sub></font> or <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> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="20_1_1"><b>suppose </b></a><a NAME="E1:20_1_1"/><i><font color="Green">E15</font></i>: 
<font color="Maroon">c<sub>3</sub></font> <a href="pboole.html#R6">=</a> <font color="Maroon">c<sub>4</sub></font>
 ;<br/><div class="add"><a NAME="E2:20_1_1"/>
 <a href="relat_1.html#K3">field</a> <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a>  <a href="polynom1.html#K14">Bags</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="ref" href="orders_1.html#T97">ORDERS_1:97</a></i>;<br/><a NAME="E3:20_1_1"/><b>then </b><i><font color="Green">E16</font></i>: 
<font color="Maroon">c<sub>2</sub></font> <a href="relat_2.html#R1">is_reflexive_in</a>  <a href="polynom1.html#K14">Bags</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="ref" href="relat_2.html#D9">RELAT_2:def 9</a></i>;<br/><a NAME="E4:20_1_1"/>
( <font color="Maroon">c<sub>3</sub></font> is    <a href="polynom1.html#M1">Element</a> of  <a href="polynom1.html#K14">Bags</a> <font color="Maroon">c<sub>1</sub></font> &amp; <font color="Maroon">c<sub>4</sub></font> is    <a href="polynom1.html#M1">Element</a> of  <a href="polynom1.html#K14">Bags</a> <font color="Maroon">c<sub>1</sub></font> )
 <b>by </b><i><a class="ref" href="polynom1.html#D14">POLYNOM1:def 14</a></i>;<br/><a NAME="E5:20_1_1"/><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>
 <b>by </b><i><a class="txt" href="termord.html#E1:20_1_1"><i><font color="Green">E15</font></i></a>, <a class="txt" href="termord.html#E3:20_1_1"><i><font color="Green">E16</font></i></a>, <a class="ref" href="relat_2.html#D1">RELAT_2:def 1</a></i>;<br/><b>hence </b><a NAME="E6:20_1_1"/>
( <font color="Maroon">c<sub>3</sub></font> <a href="termord.html#R1" target="_self">&lt;=</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>2</sub></font> or <font color="Maroon">c<sub>4</sub></font> <a href="termord.html#R1" target="_self">&lt;=</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>2</sub></font> )
 <b>by </b><i><a class="ref" href="termord.html#D2" target="_self">Def2</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="20_1_2"><b>suppose </b></a><a NAME="E1:20_1_2"/><i><font color="Green">E15</font></i>: 
<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/><div class="add"><b>assume </b><a NAME="E2:20_1_2"/>
not <font color="Maroon">c<sub>3</sub></font> <a href="termord.html#R1" target="_self">&lt;=</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>2</sub></font>
 ;<br/><a NAME="E3:20_1_2"/><b>then </b><i><font color="Green">E16</font></i>: 
not <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>
 <b>by </b><i><a class="ref" href="termord.html#D2" target="_self">Def2</a></i>;<br/><a NAME="E4:20_1_2"/>
( <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K3">field</a> <font color="Maroon">c<sub>2</sub></font> &amp; <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K3">field</a> <font color="Maroon">c<sub>2</sub></font> )
 <b>by </b><i><a class="txt" href="termord.html#E13"><i><font color="Green">Lemma11</font></i></a></i>;<br/><a NAME="E5:20_1_2"/><b>then </b>
<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> <font color="Maroon">c<sub>2</sub></font>
 <b>by </b><i><a class="txt" href="termord.html#E1:20"><i><font color="Green">E14</font></i></a>, <a class="txt" href="termord.html#E1:20_1_2"><i><font color="Green">E15</font></i></a>, <a class="txt" href="termord.html#E3:20_1_2"><i><font color="Green">E16</font></i></a>, <a class="ref" href="relat_2.html#D6">RELAT_2:def 6</a></i>;<br/><b>hence </b><a NAME="E6:20_1_2"/>
<font color="Maroon">c<sub>4</sub></font> <a href="termord.html#R1" target="_self">&lt;=</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>2</sub></font>
 <b>by </b><i><a class="ref" href="termord.html#D2" target="_self">Def2</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div>

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