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

<b>let </b><font color="Maroon">c<sub>1</sub></font> be   <a href="pre_topc.html#NM1">TopSpace</a>;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font> be   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">c<sub>1</sub></font>;<br/>



<b>thus </b><a NAME="E1:17"/>
( <font color="Maroon">c<sub>2</sub></font> is <a href="tops_1.html#V4">condensed</a> implies (  <a href="tops_1.html#K1">Int</a> <span class="p1">(<span class="default"><a href="pre_topc.html#K4">Cl</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>2</sub></font> &amp; <font color="Maroon">c<sub>2</sub></font> <a href="tarski.html#R1">c=</a>  <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">c<sub>2</sub></font></span>)</span> ) )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="17_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:17_1"/>
<font color="Maroon">c<sub>2</sub></font> is <a href="tops_1.html#V4">condensed</a>
 ;<br/>

<a NAME="E2:17_1"/><b>then </b>
( <font color="Maroon">c<sub>2</sub></font> is <a href="isomichi.html#V1" target="_self">supercondensed</a> &amp; <font color="Maroon">c<sub>2</sub></font> is <a href="isomichi.html#V2" target="_self">subcondensed</a> )
 
<b>by </b><i><a class="ref" href="isomichi.html#T5" target="_self">Th5</a></i>;<br/>
<b>hence </b><a NAME="E3:17_1"/>
(  <a href="tops_1.html#K1">Int</a> <span class="p1">(<span class="default"><a href="pre_topc.html#K4">Cl</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>2</sub></font> &amp; <font color="Maroon">c<sub>2</sub></font> <a href="tarski.html#R1">c=</a>  <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">c<sub>2</sub></font></span>)</span> )
 <b>by </b><i><a class="ref" href="isomichi.html#T8" target="_self">Th8</a>, <a class="ref" href="isomichi.html#T9" target="_self">Th9</a></i>;<br/>


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

<b>assume </b><a NAME="E2:17"/>
(  <a href="tops_1.html#K1">Int</a> <span class="p1">(<span class="default"><a href="pre_topc.html#K4">Cl</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>2</sub></font> &amp; <font color="Maroon">c<sub>2</sub></font> <a href="tarski.html#R1">c=</a>  <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">c<sub>2</sub></font></span>)</span> )
 ;<br/>

<a NAME="E3:17"/><b>then </b>
( <font color="Maroon">c<sub>2</sub></font> is <a href="isomichi.html#V1" target="_self">supercondensed</a> &amp; <font color="Maroon">c<sub>2</sub></font> is <a href="isomichi.html#V2" target="_self">subcondensed</a> )
 
<b>by </b><i><a class="ref" href="isomichi.html#T8" target="_self">Th8</a>, <a class="ref" href="isomichi.html#T9" target="_self">Th9</a></i>;<br/>
<b>hence </b><a NAME="E4:17"/>
<font color="Maroon">c<sub>2</sub></font> is <a href="tops_1.html#V4">condensed</a>
 <b>by </b><i><a class="ref" href="isomichi.html#T5" target="_self">Th5</a></i>;<br/>


</div>
