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

<b>thus </b><a NAME="E1:32_1_1"/>
( <font color="Maroon">A</font> is <a href="tops_3.html#V1" target="_self">everywhere_dense</a> implies  <a href="pre_topc.html#K4">Cl</a> <span class="p1">(<span class="default"><a href="tops_1.html#K1">Int</a> <font color="Maroon">A</font></span>)</span> <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">X</font> )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="32_1_1_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:32_1_1_1"/>
<font color="Maroon">A</font> is <a href="tops_3.html#V1" target="_self">everywhere_dense</a>
 ;<br/>

<a NAME="E2:32_1_1_1"/><b>then </b>
 <a href="pre_topc.html#K4">Cl</a> <span class="p1">(<span class="default"><a href="tops_1.html#K1">Int</a> <font color="Maroon">A</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="pre_topc.html#K2">[#]</a> <font color="Maroon">X</font>
 
<b>by </b><i><a class="ref" href="tops_3.html#D1" target="_self">Def1</a></i>;<br/>
<b>hence </b><a NAME="E3:32_1_1_1"/>
 <a href="pre_topc.html#K4">Cl</a> <span class="p1">(<span class="default"><a href="tops_1.html#K1">Int</a> <font color="Maroon">A</font></span>)</span> <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">X</font>
 ;<br/>


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

<b>assume </b><a NAME="E2:32_1_1"/>
 <a href="pre_topc.html#K4">Cl</a> <span class="p1">(<span class="default"><a href="tops_1.html#K1">Int</a> <font color="Maroon">A</font></span>)</span> <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">X</font>
 ;<br/>

<a NAME="E3:32_1_1"/><b>then </b>
 <a href="pre_topc.html#K4">Cl</a> <span class="p1">(<span class="default"><a href="tops_1.html#K1">Int</a> <font color="Maroon">A</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="pre_topc.html#K2">[#]</a> <font color="Maroon">X</font>
 
;<br/>
<b>hence </b><a NAME="E4:32_1_1"/>
<font color="Maroon">A</font> is <a href="tops_3.html#V1" target="_self">everywhere_dense</a>
 <b>by </b><i><a class="ref" href="tops_3.html#D1" target="_self">Def1</a></i>;<br/>


</div>
