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<b>let </b><font color="Maroon" title="c1">L</font> be  <a href="orders_2.html#V5" title="ORDERS_2:attr.5">antisymmetric</a>  <a href="orders_2.html#L1" title="ORDERS_2:struct.1">RelStr</a> ;<br/><b>let </b><font color="Maroon" title="c2">R</font> be  <a href="waybel_4.html#V1" title="WAYBEL_4:attr.1">auxiliary(i)</a> <a href="alg_1.html#NM1" title="ALG_1:NM.1">Relation</a> of <font color="Maroon" title="c1">L</font>;<br/><b>let </b><font color="Maroon" title="c3">C</font> be    <a href="waybel35.html#M1" title="WAYBEL35:mode.1">strict_chain</a> of <font color="Maroon" title="c2">R</font>;<br/><b>let </b><font color="Maroon" title="c4">x</font>, <font color="Maroon" title="c5">y</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">L</font>;<br/>







<b>assume </b><b>that </b><br/><a NAME="E1:22"/><i><font color="Green" title="E8">A1</font></i>: 
( <font color="Maroon" title="c4">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">C</font> &amp; <font color="Maroon" title="c5">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">C</font> )
 <b>and </b><br/><a NAME="E2:22"/><i><font color="Green" title="E9">A2</font></i>: 
<font color="Maroon" title="c4">x</font> <a href="orders_2.html#R2" title="ORDERS_2:pred.2">&lt;</a> <font color="Maroon" title="c5">y</font>
 ;<br/>

<a NAME="E3:22"/>
( <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c4">x</font>,<font color="Maroon" title="c5">y</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">R</font> or <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c5">y</font>,<font color="Maroon" title="c4">x</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">R</font> )
 
<b>by </b><i><a class="txt" href="waybel35.html#E1:22"><i><font color="Green" title="E8">A1</font></i></a>, <a class="txt" href="waybel35.html#E2:22"><i><font color="Green" title="E9">A2</font></i></a>, <a class="ref" href="waybel35.html#D3" target="_self" title="WAYBEL35:def.3">Def3</a></i>;<br/>
<a NAME="E4:22"/><b>then </b>
( <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c4">x</font>,<font color="Maroon" title="c5">y</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">R</font> or <font color="Maroon" title="c5">y</font> <a href="orders_2.html#R1" title="ORDERS_2:pred.1">&lt;=</a> <font color="Maroon" title="c4">x</font> )
 
<b>by </b><i><a class="ref" href="waybel_4.html#D4" title="WAYBEL_4:def.4">WAYBEL_4:def 4</a></i>;<br/>
<b>hence </b><a NAME="E5:22"/>
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c4">x</font>,<font color="Maroon" title="c5">y</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">R</font>
 <b>by </b><i><a class="txt" href="waybel35.html#E2:22"><i><font color="Green" title="E9">A2</font></i></a>, <a class="ref" href="orders_2.html#T30" title="ORDERS_2:th.30">ORDERS_2:30</a></i>;<br/>


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