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

<span class="kw">let </span><font color="Maroon" title="c1">T</font> be   <a href="pre_topc.html#NM1" title="PRE_TOPC:NM.1">TopSpace</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c1">T</font> is  <a href="pre_topc.html#V7" title="PRE_TOPC:attr.7">T_1</a>  implies <font color="Maroon" title="c1">T</font> is  <a href="topgen_4.html#V7" title="TOPGEN_4:attr.7">T_1/2</a>  )</span><br/>

<span class="kw">assume </span><a NAME="E1:74"/><span class="lab"><font color="Green" title="E39">A1</font></span>: 
<font color="Maroon" title="c1">T</font> is  <a href="pre_topc.html#V7" title="PRE_TOPC:attr.7">T_1</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c1">T</font> is  <a href="topgen_4.html#V7" title="TOPGEN_4:attr.7">T_1/2</a> </span><br/>

<a NAME="E2:74"/>
for <font color="Olive" title="b1">A</font> being  <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">T</font> holds   <a href="topgen_1.html#K2" title="TOPGEN_1:func.2">Der</a> <font color="Olive" title="b1">A</font> is  <a href="pre_topc.html#V4" title="PRE_TOPC:attr.4">closed</a> 
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="74_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">let </span><font color="Maroon" title="c2">A</font> be   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">T</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide">  <a href="topgen_1.html#K2" title="TOPGEN_1:func.2">Der</a> <font color="Maroon" title="c2">A</font> is  <a href="pre_topc.html#V4" title="PRE_TOPC:attr.4">closed</a> </span><br/>

<a NAME="E1:74_1"/>
 <a href="topgen_1.html#K2" title="TOPGEN_1:func.2">Der</a> <font color="Maroon" title="c2">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="pre_topc.html#K2" title="PRE_TOPC:func.2">Cl</a> <span class="p1">(<span class="default"><a href="topgen_1.html#K2" title="TOPGEN_1:func.2">Der</a> <font color="Maroon" title="c2">A</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:74"><span class="lab"><font color="Green" title="E39">A1</font></span></a>, <a class="ref" href="topgen_1.html#T35" title="TOPGEN_1:th.35">TOPGEN_1:35</a></span>;<br/>
<span class="kw">hence </span><a NAME="E2:74_1"/>
 <a href="topgen_1.html#K2" title="TOPGEN_1:func.2">Der</a> <font color="Maroon" title="c2">A</font> is  <a href="pre_topc.html#V4" title="PRE_TOPC:attr.4">closed</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div>
<span class="kw">hence </span><a NAME="E3:74"/>
<font color="Maroon" title="c1">T</font> is  <a href="topgen_4.html#V7" title="TOPGEN_4:attr.7">T_1/2</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="topgen_4.html#D8" target="_self" title="TOPGEN_4:def.8">Def8</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div>
