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<b>let </b><font color="Maroon" title="c1">L</font> be  non <a href="struct_0.html#V3" title="STRUCT_0:attr.3">empty</a> <a href="orders_2.html#V2" title="ORDERS_2:attr.2">reflexive</a> <a href="orders_2.html#V3" title="ORDERS_2:attr.3">transitive</a>  <a href="orders_2.html#L1" title="ORDERS_2:struct.1">RelStr</a> ;<br/><b>let </b><font color="Maroon" title="c2">x</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">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" title="c3">z</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/><b>assume </b><a NAME="E1:9_1"/>
<font color="Maroon" title="c3">z</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="waybel_8.html#K2" title="WAYBEL_8:func.2">compactbelow</a> <font color="Maroon" title="c2">x</font>
 ;<br/><a NAME="E2:9_1"/><b>then </b>
<font color="Maroon" title="c3">z</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">{<span class="default"> <font color="Olive" title="b1">y</font> where <font color="Olive" title="b1">y</font> is   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">L</font> : ( <font color="Maroon" title="c2">x</font> <a href="orders_2.html#NR2" title="ORDERS_2:NR.2">&gt;=</a> <font color="Olive" title="b1">y</font> &amp; <font color="Olive" title="b1">y</font> is <a href="waybel_3.html#V1" title="WAYBEL_3:attr.1">compact</a> ) </span>}</span> 
 ;<br/><b>then consider </b><font color="Maroon" title="c4">z'</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="E4:9_1"/><i><font color="Green" title="E5">A1</font></i>: 
( <font color="Maroon" title="c4">z'</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">z</font> &amp; <font color="Maroon" title="c2">x</font> <a href="orders_2.html#NR2" title="ORDERS_2:NR.2">&gt;=</a> <font color="Maroon" title="c4">z'</font> &amp; <font color="Maroon" title="c4">z'</font> is <a href="waybel_3.html#V1" title="WAYBEL_3:attr.1">compact</a> )
 ;<br/><a NAME="E5:9_1"/>
<font color="Maroon" title="c4">z'</font> <a href="waybel_3.html#NR2" title="WAYBEL_3:NR.2">&lt;&lt;</a> <font color="Maroon" title="c4">z'</font>
 <b>by </b><i><a class="txt" href="waybel_8.html#E4:9_1"><i><font color="Green" title="E5">A1</font></i></a>, <a class="ref" href="waybel_3.html#D2" title="WAYBEL_3:def.2">WAYBEL_3:def 2</a></i>;<br/><a NAME="E6:9_1"/><b>then </b>
<font color="Maroon" title="c4">z'</font> <a href="waybel_3.html#NR2" title="WAYBEL_3:NR.2">&lt;&lt;</a> <font color="Maroon" title="c2">x</font>
 <b>by </b><i><a class="txt" href="waybel_8.html#E4:9_1"><i><font color="Green" title="E5">A1</font></i></a>, <a class="ref" href="waybel_3.html#T2" title="WAYBEL_3:th.2">WAYBEL_3:2</a></i>;<br/><b>hence </b><a NAME="E7:9_1"/>
<font color="Maroon" title="c3">z</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="waybel_3.html#K1" title="WAYBEL_3:func.1">waybelow</a> <font color="Maroon" title="c2">x</font>
 <b>by </b><i><a class="txt" href="waybel_8.html#E4:9_1"><i><font color="Green" title="E5">A1</font></i></a>, <a class="ref" href="waybel_3.html#T7" title="WAYBEL_3:th.7">WAYBEL_3:7</a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E2:9"/>
 <a href="waybel_8.html#K2" title="WAYBEL_8:func.2">compactbelow</a> <font color="Maroon" title="c2">x</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="waybel_3.html#K1" title="WAYBEL_3:func.1">waybelow</a> <font color="Maroon" title="c2">x</font>
 <b>by </b><i><a class="ref" href="tarski.html#D3" title="TARSKI:def.3">TARSKI:def 3</a></i>;<br/>


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