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<b>defpred </b><font color="Maroon">S<sub>1</sub></font>[   <a href="hidden.html#M1">set</a> ] <b>means </b> ex <font color="Olive">y</font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L</font> st <br/>( <font color="Olive">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a<sub>1</sub></font> &amp; <font color="Olive">y</font> is <a href="waybel_3.html#V1">compact</a> );<br/>
<b>consider </b><font color="Maroon">X</font> being   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">L</font><b> such that </b><br/><a NAME="E2:1_1_1"/><i><font color="Green">E31</font></i>: 
for <font color="Olive">x</font> being   <a href="hidden.html#M1">set</a>  holds <br/> ( <font color="Olive">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">X</font> iff ( <font color="Olive">x</font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">L</font> &amp; <font color="Maroon">S<sub>1</sub></font>[<font color="Olive">x</font>] ) )
 <b>from </b><i><a class="ref" href="subset_1.html#S1">SUBSET_1:sch 1</a>();<br/></i>
<b>reconsider </b><font color="Maroon">S</font> =  <a href="orders_2.html#G1">RelStr</a>(# <font color="Maroon">X</font>,<span class="p1">(<span class="default">the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">L</font> <a href="toler_1.html#K1">|_2</a> <font color="Maroon">X</font></span>)</span> #) as  <a href="orders_2.html#V1">strict</a> <a href="yellow_0.html#V4">full</a>  <a href="yellow_0.html#M1">SubRelStr</a> of <font color="Maroon">L</font> <b>by </b><i><a class="ref" href="yellow_0.html#T57">YELLOW_0:57</a></i>;<br/>
<b>take </b>
<font color="Maroon">S</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>thus </b><a NAME="E4:1_1_1"/>
( <font color="Maroon">x</font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">S</font> implies <font color="Maroon">x</font> is <a href="waybel_3.html#V1">compact</a> )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="1_1_1_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:1_1_1_1"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">S</font>
 ;<br/>

<b>then consider </b><font color="Maroon">y</font> being   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L</font><b> such that </b><br/><a NAME="E3:1_1_1_1"/><i><font color="Green">E33</font></i>: 
( <font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">x</font> &amp; <font color="Maroon">y</font> is <a href="waybel_3.html#V1">compact</a> )
 <b>by </b><i/>;<br/>
<b>thus </b><a NAME="E4:1_1_1_1"/>
<font color="Maroon">x</font> is <a href="waybel_3.html#V1">compact</a>
 <b>by </b><i/>;<br/>


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

<b>thus </b><a NAME="E5:1_1_1"/>
( <font color="Maroon">x</font> is <a href="waybel_3.html#V1">compact</a> implies <font color="Maroon">x</font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">S</font> )
 <b>by </b><i/>;<br/>


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