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<b>let </b><font color="Maroon">L</font> be  non <a href="struct_0.html#V3">empty</a> <a href="orders_2.html#V2">reflexive</a> <a href="orders_2.html#V3">transitive</a>  <a href="orders_2.html#L1">RelStr</a> ;<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/>



<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="9_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">z</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>assume </b><a NAME="E1:9_1"/>
<font color="Maroon">z</font> <a href="hidden.html#R2">in</a>  <a href="waybel_8.html#K2" target="_self">compactbelow</a> <font color="Maroon">x</font>
 ;<br/><a NAME="E2:9_1"/><b>then </b>
<font color="Maroon">z</font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <font color="Olive">y</font> where <font color="Olive">y</font> is   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L</font> : ( <font color="Maroon">x</font> <a href="orders_2.html#NR2" target="_self">&gt;=</a> <font color="Olive">y</font> &amp; <font color="Olive">y</font> is <a href="waybel_3.html#V1">compact</a> ) </span>}</span> 
 ;<br/><b>then consider </b><font color="Maroon">z'</font> being   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L</font><b> such that </b><br/><a NAME="E4:9_1"/><i><font color="Green">E31</font></i>: 
( <font color="Maroon">z'</font> <a href="hidden.html#R1">=</a> <font color="Maroon">z</font> &amp; <font color="Maroon">x</font> <a href="orders_2.html#NR2" target="_self">&gt;=</a> <font color="Maroon">z'</font> &amp; <font color="Maroon">z'</font> is <a href="waybel_3.html#V1">compact</a> )
 ;<br/><a NAME="E5:9_1"/>
<font color="Maroon">z'</font> <a href="waybel_3.html#NR2" target="_self">&lt;&lt;</a> <font color="Maroon">z'</font>
 <b>by </b><i>, <a class="ref" href="waybel_3.html#D2">WAYBEL_3:def 2</a></i>;<br/><a NAME="E6:9_1"/><b>then </b>
<font color="Maroon">z'</font> <a href="waybel_3.html#NR2" target="_self">&lt;&lt;</a> <font color="Maroon">x</font>
 <b>by </b><i>, <a class="ref" href="waybel_3.html#T2">WAYBEL_3:2</a></i>;<br/><b>hence </b><a NAME="E7:9_1"/>
<font color="Maroon">z</font> <a href="hidden.html#R2">in</a>  <a href="waybel_3.html#K1">waybelow</a> <font color="Maroon">x</font>
 <b>by </b><i>, <a class="ref" href="waybel_3.html#T7">WAYBEL_3:7</a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E2:9"/>
 <a href="waybel_8.html#K2" target="_self">compactbelow</a> <font color="Maroon">x</font> <a href="tarski.html#R1">c=</a>  <a href="waybel_3.html#K1">waybelow</a> <font color="Maroon">x</font>
 <b>by </b><i><a class="ref" href="tarski.html#D3">TARSKI:def 3</a></i>;<br/>


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