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<b>let </b><font color="Maroon">L</font> be  <a href="yellow_0.html#V1">lower-bounded</a> <a href="waybel_0.html#NM7">sup-Semilattice</a>;<br/><b>let </b><font color="Maroon">AR</font> be  <a href="waybel_4.html#V1" target="_self">auxiliary(i)</a> <a href="alg_1.html#NM1">Relation</a> of <font color="Maroon">L</font>;<br/><b>let </b><font color="Maroon">x</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L</font>;<br/>





<b>assume </b><a NAME="E1:43"/><i><font color="Green">E31</font></i>: 
<font color="Maroon">AR</font> <a href="hidden.html#R1">=</a> the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">L</font>
 ;<br/>

<b>thus </b><a NAME="E2:43"/>
<font color="Maroon">AR</font> <a href="waybel_4.html#K5" target="_self">-below</a> <font color="Maroon">x</font> <a href="tarski.html#R1">c=</a>  <a href="waybel_0.html#K5">downarrow</a> <font color="Maroon">x</font>
 <b>by </b><i/>; <i><font color="Red">:: according to </font></i><a class="ref" href="xboole_0.html#D10">XBOOLE_0:def 10</a><br/>

<b>thus </b><a NAME="E3:43"/>
 <a href="waybel_0.html#K5">downarrow</a> <font color="Maroon">x</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">AR</font> <a href="waybel_4.html#K5" target="_self">-below</a> <font color="Maroon">x</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="43_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">a</font> be    <a href="hidden.html#M1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3">TARSKI:def 3</a><br/>

<b>assume </b><a NAME="E1:43_1"/>
<font color="Maroon">a</font> <a href="hidden.html#R2">in</a>  <a href="waybel_0.html#K5">downarrow</a> <font color="Maroon">x</font>
 ;<br/>

<a NAME="E2:43_1"/><b>then </b>
<span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">a</font>,<font color="Maroon">x</font></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R2">in</a> <font color="Maroon">AR</font>
 
<b>by </b><i>, <a class="ref" href="waybel_4.html#D2" target="_self">Def2</a></i>;<br/>
<b>hence </b><a NAME="E3:43_1"/>
<font color="Maroon">a</font> <a href="hidden.html#R2">in</a> <font color="Maroon">AR</font> <a href="waybel_4.html#K5" target="_self">-below</a> <font color="Maroon">x</font>
 <b>by </b><i/>;<br/>


</div><b>end;</b></div>


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