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<b>let </b><font color="Maroon" title="c1">L</font> be    <a href="orders_2.html#L1" title="ORDERS_2:struct.1">RelStr</a> ;<br/><b>let </b><font color="Maroon" title="c2">C</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/><b>let </b><font color="Maroon" title="c3">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>assume </b><a NAME="E1:41"/><i><font color="Green" title="E17">A1</font></i>: 
<font color="Maroon" title="c3">R</font> <a href="waybel35.html#R1" title="WAYBEL35:pred.1">satisfies_SIC_on</a> <font color="Maroon" title="c2">C</font>
 ;<br/>

<b>let </b><font color="Maroon" title="c4">x</font>, <font color="Maroon" title="c5">z</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><a NAME="E2:41"/>
( <font color="Maroon" title="c4">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">C</font> &amp; <font color="Maroon" title="c5">z</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">C</font> &amp; <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">z</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="c3">R</font> &amp; <font color="Maroon" title="c4">x</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c5">z</font> )
 ;<br/>

<b>then consider </b><font color="Maroon" title="c6">y</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">L</font><b> such that </b><br/><a NAME="E4:41"/><i><font color="Green" title="E18">A2</font></i>: 
<font color="Maroon" title="c6">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">C</font>
 <b>and </b><br/><a NAME="E5:41"/><i><font color="Green" title="E19">A3</font></i>: 
<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="c6">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="c3">R</font>
 <b>and </b><br/><a NAME="E6:41"/><i><font color="Green" title="E20">A4</font></i>: 
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c6">y</font>,<font color="Maroon" title="c5">z</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="c3">R</font>
 <b>and </b><br/><a NAME="E7:41"/><i><font color="Green" title="E21">A5</font></i>: 
<font color="Maroon" title="c4">x</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c6">y</font>
 <b>by </b><i><a class="txt" href="waybel35.html#E1:41"><i><font color="Green" title="E17">A1</font></i></a>, <a class="ref" href="waybel35.html#D6" target="_self" title="WAYBEL35:def.6">Def6</a></i>;<br/>
<b>take </b>
<font color="Maroon" title="c6">y</font>
;<br/>

<b>thus </b><a NAME="E8:41"/>
( <font color="Maroon" title="c6">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">C</font> &amp; <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="c6">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="c3">R</font> &amp; <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c6">y</font>,<font color="Maroon" title="c5">z</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="c3">R</font> )
 <b>by </b><i><a class="txt" href="waybel35.html#E4:41"><i><font color="Green" title="E18">A2</font></i></a>, <a class="txt" href="waybel35.html#E5:41"><i><font color="Green" title="E19">A3</font></i></a>, <a class="txt" href="waybel35.html#E6:41"><i><font color="Green" title="E20">A4</font></i></a></i>;<br/>

<a NAME="E9:41"/>
<font color="Maroon" title="c4">x</font> <a href="orders_2.html#R1" title="ORDERS_2:pred.1">&lt;=</a> <font color="Maroon" title="c6">y</font>
 
<b>by </b><i><a class="txt" href="waybel35.html#E5:41"><i><font color="Green" title="E19">A3</font></i></a>, <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="E10:41"/>
<font color="Maroon" title="c4">x</font> <a href="orders_2.html#R2" title="ORDERS_2:pred.2">&lt;</a> <font color="Maroon" title="c6">y</font>
 <b>by </b><i><a class="txt" href="waybel35.html#E7:41"><i><font color="Green" title="E21">A5</font></i></a>, <a class="ref" href="orders_2.html#D10" title="ORDERS_2:def.10">ORDERS_2:def 10</a></i>;<br/>


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