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<b>let </b><font color="Maroon" title="c1">L</font> be  non <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a> <a href="orders_2.html#V3" title="ORDERS_2:attr.3">reflexive</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>, <font color="Maroon" title="c3">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>thus </b><a NAME="E1:7"/>
( <font color="Maroon" title="c3">y</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> implies ( <font color="Maroon" title="c2">x</font> <a href="orders_2.html#NR2" title="ORDERS_2:NR.2">&gt;=</a> <font color="Maroon" title="c3">y</font> &amp; <font color="Maroon" title="c3">y</font> is <a href="waybel_3.html#V1" title="WAYBEL_3:attr.1">compact</a> ) )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="7_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:7_1"/>
<font color="Maroon" title="c3">y</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/>

<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="E3:7_1"/><i><font color="Green" title="E3">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">y</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/>
<b>thus </b><a NAME="E4:7_1"/>
( <font color="Maroon" title="c2">x</font> <a href="orders_2.html#NR2" title="ORDERS_2:NR.2">&gt;=</a> <font color="Maroon" title="c3">y</font> &amp; <font color="Maroon" title="c3">y</font> is <a href="waybel_3.html#V1" title="WAYBEL_3:attr.1">compact</a> )
 <b>by </b><i><a class="txt" href="waybel_8.html#E3:7_1"><i><font color="Green" title="E3">A1</font></i></a></i>;<br/>


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

<b>assume </b><a NAME="E2:7"/>
( <font color="Maroon" title="c2">x</font> <a href="orders_2.html#NR2" title="ORDERS_2:NR.2">&gt;=</a> <font color="Maroon" title="c3">y</font> &amp; <font color="Maroon" title="c3">y</font> is <a href="waybel_3.html#V1" title="WAYBEL_3:attr.1">compact</a> )
 ;<br/>

<b>hence </b><a NAME="E3:7"/>
<font color="Maroon" title="c3">y</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/>


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