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

<b>let </b><font color="Maroon">T</font> be   <a href="pre_topc.html#NM1">TopSpace</a>;<br/><b>let </b><font color="Maroon">A</font> be   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">T</font>;<br/>



<b>thus </b><a NAME="E1:47"/>
( <font color="Maroon">A</font> is <a href="tops_1.html#V4">condensed</a> implies (  <a href="tops_1.html#K1">Int</a> <font color="Maroon">A</font> is <a href="tops_1.html#V6">regular_open</a> &amp;  <a href="pre_topc.html#K4">Cl</a> <font color="Maroon">A</font> is <a href="tops_1.html#V5">regular_closed</a> &amp;  <a href="isomichi.html#K1" target="_self">Border</a> <font color="Maroon">A</font> is <a href="xboole_0.html#V1">empty</a> ) )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="47_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:47_1"/>
<font color="Maroon">A</font> is <a href="tops_1.html#V4">condensed</a>
 ;<br/>

<a NAME="E2:47_1"/><b>then </b>
( <font color="Maroon">A</font> is <a href="isomichi.html#V1" target="_self">supercondensed</a> &amp; <font color="Maroon">A</font> is <a href="isomichi.html#V2" target="_self">subcondensed</a> )
 
<b>by </b><i/>;<br/>
<b>hence </b><a NAME="E3:47_1"/>
(  <a href="tops_1.html#K1">Int</a> <font color="Maroon">A</font> is <a href="tops_1.html#V6">regular_open</a> &amp;  <a href="pre_topc.html#K4">Cl</a> <font color="Maroon">A</font> is <a href="tops_1.html#V5">regular_closed</a> &amp;  <a href="isomichi.html#K1" target="_self">Border</a> <font color="Maroon">A</font> is <a href="xboole_0.html#V1">empty</a> )
 <b>by </b><i>, </i>;<br/>


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

<b>assume </b><a NAME="E2:47"/>
(  <a href="tops_1.html#K1">Int</a> <font color="Maroon">A</font> is <a href="tops_1.html#V6">regular_open</a> &amp;  <a href="pre_topc.html#K4">Cl</a> <font color="Maroon">A</font> is <a href="tops_1.html#V5">regular_closed</a> &amp;  <a href="isomichi.html#K1" target="_self">Border</a> <font color="Maroon">A</font> is <a href="xboole_0.html#V1">empty</a> )
 ;<br/>

<a NAME="E3:47"/><b>then </b>
( <font color="Maroon">A</font> is <a href="isomichi.html#V1" target="_self">supercondensed</a> &amp; <font color="Maroon">A</font> is <a href="isomichi.html#V2" target="_self">subcondensed</a> )
 
<b>by </b><i>, </i>;<br/>
<b>hence </b><a NAME="E4:47"/>
<font color="Maroon">A</font> is <a href="tops_1.html#V4">condensed</a>
 <b>by </b><i/>;<br/>


</div>
