<?xml version="1.0"?>
<div class="add">

<b>let </b><font color="Maroon" title="c2">S</font> be   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">X</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c2">S</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> implies <font color="Maroon" title="c2">S</font> is <a href="compact1.html#V2" title="COMPACT1:attr.2">relatively-compact</a> )</span><br/>

<b>assume </b><a NAME="E1:3_1_1"/><i><font color="Green" title="E3">Z</font></i>: 
<font color="Maroon" title="c2">S</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c2">S</font> is <a href="compact1.html#V2" title="COMPACT1:attr.2">relatively-compact</a></span><br/>

<a NAME="E2:3_1_1"/><b>then </b>
 <a href="pre_topc.html#K2" title="PRE_TOPC:func.2">Cl</a> <font color="Maroon" title="c2">S</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">S</font>
 
<b>by </b><i><a class="ref" href="pre_topc.html#T52" title="PRE_TOPC:th.52">PRE_TOPC:52</a></i>;<br/>
<b>hence </b><a NAME="E3:3_1_1"/>
<font color="Maroon" title="c2">S</font> is <a href="compact1.html#V2" title="COMPACT1:attr.2">relatively-compact</a>
 <b>by </b><i><a class="ref" href="compact1.html#D2" target="_self" title="COMPACT1:def.2">Def2</a>, <a class="txt" href="#E1:3_1_1"><i><font color="Green" title="E3">Z</font></i></a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div>
