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

<b>let </b><font color="Maroon">c<sub>1</sub></font> be  non <a href="struct_0.html#V3">empty</a> <a href="tdlat_3.html#V2">anti-discrete</a> <a href="pre_topc.html#NM1">TopSpace</a>;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font> be  non <a href="xboole_0.html#V1">empty</a> <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">c<sub>1</sub></font>;<br/>



<div><b>hereby </b>
<div class="add"><b>assume </b><a NAME="E1:85_1"/><i><font color="Green">E34</font></i>: 
<font color="Maroon">c<sub>2</sub></font> is <a href="tex_2.html#V3" target="_self">discrete</a>
 ;<br/><b>consider </b><font color="Maroon">c<sub>3</sub></font> being    <a href="hidden.html#M1">set</a> <b> such that </b><br/><a NAME="E3:85_1"/><i><font color="Green">E35</font></i>: 
<font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>2</sub></font>
 <b>by </b><i><a class="ref" href="xboole_0.html#D1">XBOOLE_0:def 1</a></i>;<br/><b>reconsider </b><font color="Maroon">c<sub>4</sub></font> = <font color="Maroon">c<sub>3</sub></font> as   <a href="pre_topc.html#NM2">Point</a> of <font color="Maroon">c<sub>1</sub></font> <b>by </b><i><a class="txt" href="tex_2.html#E3:85_1"><i><font color="Green">E35</font></i></a></i>;<br/><b>consider </b><font color="Maroon">c<sub>5</sub></font> being   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">c<sub>1</sub></font><b> such that </b><br/><a NAME="E6:85_1"/><i><font color="Green">E36</font></i>: 
<font color="Maroon">c<sub>5</sub></font> is <a href="pre_topc.html#V3">open</a>
 <b>and </b><br/><a NAME="E7:85_1"/><i><font color="Green">E37</font></i>: 
<font color="Maroon">c<sub>2</sub></font> <a href="subset_1.html#K9">/\</a> <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>4</sub></font></span><a href="domain_1.html#K6">}</a></span>
 <b>by </b><i><a class="txt" href="tex_2.html#E1:85_1"><i><font color="Green">E34</font></i></a>, <a class="txt" href="tex_2.html#E3:85_1"><i><font color="Green">E35</font></i></a>, <a class="ref" href="tex_2.html#T32" target="_self">Th32</a></i>;<br/><a NAME="E8:85_1"/>
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a> 
 <b>by </b><i><a class="txt" href="tex_2.html#E7:85_1"><i><font color="Green">E37</font></i></a></i>;<br/><a NAME="E9:85_1"/><b>then </b><i><font color="Green">E38</font></i>: 
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="tex_2.html#E6:85_1"><i><font color="Green">E36</font></i></a>, <a class="ref" href="tdlat_3.html#T20">TDLAT_3:20</a></i>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="85_1_1"><b>now </b></a><div class="add"><b>take </b><font color="Maroon">c<sub>6</sub></font> = <font color="Maroon">c<sub>4</sub></font>;<br/><b>thus </b><a NAME="E1:85_1_1"/>
<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>6</sub></font></span><a href="domain_1.html#K6">}</a></span>
 <b>by </b><i><a class="txt" href="tex_2.html#E7:85_1"><i><font color="Green">E37</font></i></a>, <a class="txt" href="tex_2.html#E9:85_1"><i><font color="Green">E38</font></i></a>, <a class="ref" href="xboole_1.html#T28">XBOOLE_1:28</a></i>;<br/></div><b>end;</b></div><b>hence </b><a NAME="E11:85_1"/>
<font color="Maroon">c<sub>2</sub></font> is <a href="realset1.html#V1">trivial</a>
 ;<br/></div>
<b>end;</b></div>

<div><b>hereby </b>
<div class="add"><b>assume </b><a NAME="E1:85_2"/>
<font color="Maroon">c<sub>2</sub></font> is <a href="realset1.html#V1">trivial</a>
 ;<br/><b>then consider </b><font color="Maroon">c<sub>3</sub></font> being    <a href="struct_0.html#M1">Element</a> of <font color="Maroon">c<sub>2</sub></font><b> such that </b><br/><a NAME="E3:85_2"/><i><font color="Green">E34</font></i>: 
<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">c<sub>3</sub></font></span><a href="domain_1.html#K6">}</a></span>
 <b>by </b><i><a class="ref" href="tex_2.html#D1" target="_self">Def1</a></i>;<br/><b>thus </b><a NAME="E4:85_2"/>
<font color="Maroon">c<sub>2</sub></font> is <a href="tex_2.html#V3" target="_self">discrete</a>
 <b>by </b><i><a class="txt" href="tex_2.html#E3:85_2"><i><font color="Green">E34</font></i></a>, <a class="ref" href="tex_2.html#T36" target="_self">Th36</a></i>;<br/></div>
<b>end;</b></div>


</div>
