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<b>set </b><font color="Maroon">L</font> =  <a href="orders_2.html#G1">RelStr</a>(# <span class="p1">(<span class="default"><a href="polynom1.html#K14">Bags</a> <font color="Maroon">n</font></span>)</span>,<font color="Maroon">T</font> #);<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="37_1_1_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">x</font> be   <a href="struct_0.html#NM1">Element</a> of <a href="orders_2.html#G1">RelStr</a>(# <span class="p1">(<span class="default"><a href="polynom1.html#K14">Bags</a> <font color="Maroon">n</font></span>)</span>,<font color="Maroon">T</font> #), <font color="Maroon">y</font> be   <a href="struct_0.html#NM1">Element</a> of <a href="orders_2.html#G1">RelStr</a>(# <span class="p1">(<span class="default"><a href="polynom1.html#K14">Bags</a> <font color="Maroon">n</font></span>)</span>,<font color="Maroon">T</font> #);<br/><a NAME="E1:37_1_1_1"/><i><font color="Green">E23</font></i>: 
<font color="Maroon">T</font> <a href="relat_2.html#R6">is_connected_in</a>  <a href="relat_1.html#K3">field</a> <font color="Maroon">T</font>
 <b>by </b><i><a class="ref" href="relat_2.html#D14">RELAT_2:def 14</a></i>;<br/><b>reconsider </b><font color="Maroon">x'</font> = <font color="Maroon">x</font> as   <a href="polynom1.html#NM1">bag</a> of <font color="Maroon">n</font> <b>by </b><i><a class="ref" href="polynom1.html#D14">POLYNOM1:def 14</a></i>;<br/><a NAME="E3:37_1_1_1"/>
<font color="Maroon">x'</font> <a href="termord.html#R1">&lt;=</a> <font color="Maroon">x'</font>,<font color="Maroon">T</font>
 <b>by </b><i><a class="ref" href="termord.html#T6">TERMORD:6</a></i>;<br/><a NAME="E4:37_1_1_1"/><b>then </b>
<span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">x'</font>,<font color="Maroon">x'</font></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R2">in</a> <font color="Maroon">T</font>
 <b>by </b><i><a class="ref" href="termord.html#D2">TERMORD:def 2</a></i>;<br/><a NAME="E5:37_1_1_1"/><b>then </b><i><font color="Green">E24</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K3">field</a> <font color="Maroon">T</font>
 <b>by </b><i><a class="ref" href="relat_1.html#T30">RELAT_1:30</a></i>;<br/><b>reconsider </b><font color="Maroon">y'</font> = <font color="Maroon">y</font> as   <a href="polynom1.html#NM1">bag</a> of <font color="Maroon">n</font> <b>by </b><i><a class="ref" href="polynom1.html#D14">POLYNOM1:def 14</a></i>;<br/><a NAME="E7:37_1_1_1"/>
<font color="Maroon">y'</font> <a href="termord.html#R1">&lt;=</a> <font color="Maroon">y'</font>,<font color="Maroon">T</font>
 <b>by </b><i><a class="ref" href="termord.html#T6">TERMORD:6</a></i>;<br/><a NAME="E8:37_1_1_1"/><b>then </b>
<span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">y'</font>,<font color="Maroon">y'</font></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R2">in</a> <font color="Maroon">T</font>
 <b>by </b><i><a class="ref" href="termord.html#D2">TERMORD:def 2</a></i>;<br/><a NAME="E9:37_1_1_1"/><b>then </b><i><font color="Green">E26</font></i>: 
<font color="Maroon">y</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K3">field</a> <font color="Maroon">T</font>
 <b>by </b><i><a class="ref" href="relat_1.html#T30">RELAT_1:30</a></i>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="37_1_1_1_1"><b>now </b></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="37_1_1_1_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:37_1_1_1_1_1"/>
( <font color="Maroon">x</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">y</font> or <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">y</font> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="37_1_1_1_1_1_1"><b>case </b></a><a NAME="E1:37_1_1_1_1_1_1"/>
<font color="Maroon">x</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">y</font>
 ;<br/><div class="add"><a NAME="E2:37_1_1_1_1_1_1"/><b>then </b>
( <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">y</font></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R2">in</a> the <a href="orders_2.html#U1">InternalRel</a> of <a href="orders_2.html#G1">RelStr</a>(# <span class="p1">(<span class="default"><a href="polynom1.html#K14">Bags</a> <font color="Maroon">n</font></span>)</span>,<font color="Maroon">T</font> #) or <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">y</font>,<font color="Maroon">x</font></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R2">in</a> the <a href="orders_2.html#U1">InternalRel</a> of <a href="orders_2.html#G1">RelStr</a>(# <span class="p1">(<span class="default"><a href="polynom1.html#K14">Bags</a> <font color="Maroon">n</font></span>)</span>,<font color="Maroon">T</font> #) )
 <b>by </b><i>, , <a class="txt" href="polyred.html#E2"><i><font color="Green">Lemma32</font></i></a>, <a class="ref" href="relat_2.html#D6">RELAT_2:def 6</a></i>;<br/><b>hence </b><a NAME="E3:37_1_1_1_1_1_1"/>
( <font color="Maroon">x</font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">y</font> or <font color="Maroon">y</font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">x</font> )
 <b>by </b><i><a class="ref" href="orders_2.html#D9">ORDERS_2:def 9</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="37_1_1_1_1_1_2"><b>case </b></a><a NAME="E1:37_1_1_1_1_1_2"/>
<font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">y</font>
 ;<br/><div class="add"><a NAME="E2:37_1_1_1_1_1_2"/><b>then </b>
<font color="Maroon">x'</font> <a href="termord.html#R1">&lt;=</a> <font color="Maroon">y'</font>,<font color="Maroon">T</font>
 <b>by </b><i><a class="ref" href="termord.html#T6">TERMORD:6</a></i>;<br/><a NAME="E3:37_1_1_1_1_1_2"/><b>then </b>
<span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">x'</font>,<font color="Maroon">y'</font></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R2">in</a> the <a href="orders_2.html#U1">InternalRel</a> of <a href="orders_2.html#G1">RelStr</a>(# <span class="p1">(<span class="default"><a href="polynom1.html#K14">Bags</a> <font color="Maroon">n</font></span>)</span>,<font color="Maroon">T</font> #)
 <b>by </b><i><a class="ref" href="termord.html#D2">TERMORD:def 2</a></i>;<br/><b>hence </b><a NAME="E4:37_1_1_1_1_1_2"/>
( <font color="Maroon">x</font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">y</font> or <font color="Maroon">y</font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">x</font> )
 <b>by </b><i><a class="ref" href="orders_2.html#D9">ORDERS_2:def 9</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div><b>hence </b><a NAME="E11:37_1_1_1"/>
( <font color="Maroon">x</font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">y</font> or <font color="Maroon">y</font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">x</font> )
 ;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E2:37_1_1"/>
 <a href="orders_2.html#G1">RelStr</a>(# <span class="p1">(<span class="default"><a href="polynom1.html#K14">Bags</a> <font color="Maroon">n</font></span>)</span>,<font color="Maroon">T</font> #) is <a href="waybel_0.html#V16">connected</a>
 <b>by </b><i><a class="ref" href="waybel_0.html#D29">WAYBEL_0:def 29</a></i>;<br/>


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