<?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>thus </b><a NAME="E1:37"/>
( <font color="Maroon">T</font> <a href="compts_1.html#NR3" target="_self">is_T3</a>  implies for <font color="Olive">A</font> being <a href="pre_topc.html#V3">open</a> <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">T</font><br/> for <font color="Olive">p</font> being  <a href="pre_topc.html#NM2">Point</a> of <font color="Maroon">T</font>  st <font color="Olive">p</font> <a href="hidden.html#R2">in</a> <font color="Olive">A</font> holds <br/> ex <font color="Olive">B</font> being <a href="pre_topc.html#V3">open</a> <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">T</font> st <br/>( <font color="Olive">p</font> <a href="hidden.html#R2">in</a> <font color="Olive">B</font> &amp;  <a href="pre_topc.html#K4">Cl</a> <font color="Olive">B</font> <a href="tarski.html#R1">c=</a> <font color="Olive">A</font> ) )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="37_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:37_1"/><i><font color="Green">E23</font></i>: 
<font color="Maroon">T</font> <a href="compts_1.html#NR3" target="_self">is_T3</a> 
 ;<br/>

<b>thus </b><a NAME="E2:37_1"/>
for <font color="Olive">A</font> being <a href="pre_topc.html#V3">open</a> <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">T</font><br/> for <font color="Olive">p</font> being  <a href="pre_topc.html#NM2">Point</a> of <font color="Maroon">T</font>  st <font color="Olive">p</font> <a href="hidden.html#R2">in</a> <font color="Olive">A</font> holds <br/> ex <font color="Olive">B</font> being <a href="pre_topc.html#V3">open</a> <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">T</font> st <br/>( <font color="Olive">p</font> <a href="hidden.html#R2">in</a> <font color="Olive">B</font> &amp;  <a href="pre_topc.html#K4">Cl</a> <font color="Olive">B</font> <a href="tarski.html#R1">c=</a> <font color="Olive">A</font> )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="37_1_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">A</font> be  <a href="pre_topc.html#V3">open</a> <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">T</font>;<br/><b>let </b><font color="Maroon">p</font> be   <a href="pre_topc.html#NM2">Point</a> of <font color="Maroon">T</font>;<br/>



<b>assume </b><a NAME="E1:37_1_1"/><i><font color="Green">E29</font></i>: 
<font color="Maroon">p</font> <a href="hidden.html#R2">in</a> <font color="Maroon">A</font>
 ;<br/>

<a NAME="E2:37_1_1"/><b>then </b><i><font color="Green">E31</font></i>: 
<font color="Maroon">p</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><font color="Maroon">A</font> <a href="subset_1.html#K3">`</a> </span>)</span> <a href="subset_1.html#K3">`</a> 
 
;<br/>
<b>thus </b><a NAME="E3:37_1_1"/>
 ex <font color="Olive">B</font> being <a href="pre_topc.html#V3">open</a> <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">T</font> st <br/>( <font color="Maroon">p</font> <a href="hidden.html#R2">in</a> <font color="Olive">B</font> &amp;  <a href="pre_topc.html#K4">Cl</a> <font color="Olive">B</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">A</font> )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="37_1_1_1"><b>proof </b></a><div class="add">

<b>reconsider </b><font color="Maroon">P</font> = <font color="Maroon">A</font> <a href="subset_1.html#K3">`</a>  as   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">T</font> ;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="37_1_1_1_1"><b>now </b></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="37_1_1_1_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:37_1_1_1_1_1"/>
( <font color="Maroon">P</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a>  or <font color="Maroon">P</font> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a>  )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="37_1_1_1_1_1_1"><b>case </b></a><a NAME="E1:37_1_1_1_1_1_1"/>
<font color="Maroon">P</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a> 
 ;<br/><div class="add"><b>then consider </b><font color="Maroon">W</font> being   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">T</font>, <font color="Maroon">V</font> being   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">T</font><b> such that </b><br/><a NAME="E3:37_1_1_1_1_1_1"/><i><font color="Green">E32</font></i>: 
( <font color="Maroon">W</font> is <a href="pre_topc.html#V3">open</a> &amp; <font color="Maroon">V</font> is <a href="pre_topc.html#V3">open</a> &amp; <font color="Maroon">p</font> <a href="hidden.html#R2">in</a> <font color="Maroon">W</font> &amp; <font color="Maroon">P</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">V</font> &amp; <font color="Maroon">W</font> <a href="xboole_0.html#R1">misses</a> <font color="Maroon">V</font> )
 <b>by </b><i><a class="txt" href="urysohn1.html#E1:37_1"><i><font color="Green">E23</font></i></a>, <a class="ref" href="urysohn1.html#D3" target="_self">Def3</a>, <a class="ref" href="compts_1.html#D5">COMPTS_1:def 5</a></i>;<br/><b>take </b><font color="Maroon">W</font> = <font color="Maroon">W</font>;<br/><a NAME="E4:37_1_1_1_1_1_1"/>
 <a href="pre_topc.html#K4">Cl</a> <font color="Maroon">W</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">A</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="37_1_1_1_1_1_1_1"><b>proof </b></a><div class="add">

<a NAME="E1:37_1_1_1_1_1_1_1"/>
<font color="Maroon">W</font> <a href="subset_1.html#K9">/\</a> <font color="Maroon">V</font> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a> 
 
<b>by </b><i>, <a class="ref" href="xboole_0.html#D7">XBOOLE_0:def 7</a></i>;<br/>
<a NAME="E2:37_1_1_1_1_1_1_1"/><b>then </b>
<font color="Maroon">V</font> <a href="subset_1.html#K9">/\</a> <span class="p1">(<span class="default"><a href="pre_topc.html#K4">Cl</a> <font color="Maroon">W</font></span>)</span> <a href="tarski.html#R1">c=</a>  <a href="pre_topc.html#K4">Cl</a> <span class="p1">(<span class="default"><a href="pre_topc.html#K1">{}</a> <font color="Maroon">T</font></span>)</span>
 
<b>by </b><i>, <a class="ref" href="tops_1.html#T40">TOPS_1:40</a></i>;<br/>
<a NAME="E3:37_1_1_1_1_1_1_1"/><b>then </b>
<font color="Maroon">V</font> <a href="subset_1.html#K9">/\</a> <span class="p1">(<span class="default"><a href="pre_topc.html#K4">Cl</a> <font color="Maroon">W</font></span>)</span> <a href="tarski.html#R1">c=</a>  <a href="xboole_0.html#K1">{}</a> 
 
<b>by </b><i><a class="ref" href="pre_topc.html#T52">PRE_TOPC:52</a></i>;<br/>
<a NAME="E4:37_1_1_1_1_1_1_1"/><b>then </b>
<font color="Maroon">V</font> <a href="subset_1.html#K9">/\</a> <span class="p1">(<span class="default"><a href="pre_topc.html#K4">Cl</a> <font color="Maroon">W</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a> 
 
<b>by </b><i><a class="ref" href="xboole_1.html#T3">XBOOLE_1:3</a></i>;<br/>
<a NAME="E5:37_1_1_1_1_1_1_1"/><b>then </b>
<font color="Maroon">V</font> <a href="xboole_0.html#R1">misses</a>  <a href="pre_topc.html#K4">Cl</a> <font color="Maroon">W</font>
 
<b>by </b><i><a class="ref" href="xboole_0.html#D7">XBOOLE_0:def 7</a></i>;<br/>
<a NAME="E6:37_1_1_1_1_1_1_1"/><b>then </b><i><font color="Green">E39</font></i>: 
<font color="Maroon">P</font> <a href="xboole_0.html#R1">misses</a>  <a href="pre_topc.html#K4">Cl</a> <font color="Maroon">W</font>
 
<b>by </b><i>, <a class="ref" href="xboole_1.html#T63">XBOOLE_1:63</a></i>;<br/>
<a NAME="E7:37_1_1_1_1_1_1_1"/>
<span class="p1">(<span class="default"><font color="Maroon">A</font> <a href="subset_1.html#K3">`</a> </span>)</span> <a href="subset_1.html#K3">`</a>  <a href="hidden.html#R1">=</a> <font color="Maroon">A</font>
 
;<br/>
<b>hence </b><a NAME="E8:37_1_1_1_1_1_1_1"/>
 <a href="pre_topc.html#K4">Cl</a> <font color="Maroon">W</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">A</font>
 <b>by </b><i>, <a class="ref" href="subset_1.html#T43">SUBSET_1:43</a></i>;<br/>


</div><b>end;</b></div><b>hence </b><a NAME="E5:37_1_1_1_1_1_1"/>
 ex <font color="Olive">B</font> being <a href="pre_topc.html#V3">open</a> <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">T</font> st <br/>( <font color="Maroon">p</font> <a href="hidden.html#R2">in</a> <font color="Olive">B</font> &amp;  <a href="pre_topc.html#K4">Cl</a> <font color="Olive">B</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">A</font> )
 <b>by </b><i/>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="37_1_1_1_1_1_2"><b>case </b></a><a NAME="E1:37_1_1_1_1_1_2"/>
<font color="Maroon">P</font> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a> 
 ;<br/><div class="add"><a NAME="E2:37_1_1_1_1_1_2"/><b>then </b>
<span class="p1">(<span class="default"><a href="pre_topc.html#K2">[#]</a> <font color="Maroon">T</font></span>)</span> <a href="subset_1.html#K7">\</a> <font color="Maroon">A</font> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a> 
 ;<br/><a NAME="E3:37_1_1_1_1_1_2"/><b>then </b><i><font color="Green">E40</font></i>: 
<font color="Maroon">A</font> <a href="hidden.html#R1">=</a>  <a href="pre_topc.html#K2">[#]</a> <font color="Maroon">T</font>
 <b>by </b><i><a class="ref" href="pre_topc.html#T23">PRE_TOPC:23</a></i>;<br/><b>take </b><font color="Maroon">A</font> = <font color="Maroon">A</font>;<br/><a NAME="E4:37_1_1_1_1_1_2"/>
 <a href="pre_topc.html#K4">Cl</a> <font color="Maroon">A</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">A</font>
 <b>by </b><i/>;<br/><b>hence </b><a NAME="E5:37_1_1_1_1_1_2"/>
 ex <font color="Olive">B</font> being <a href="pre_topc.html#V3">open</a> <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">T</font> st <br/>( <font color="Maroon">p</font> <a href="hidden.html#R2">in</a> <font color="Olive">B</font> &amp;  <a href="pre_topc.html#K4">Cl</a> <font color="Olive">B</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">A</font> )
 <b>by </b><i/>;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div>
<b>hence </b><a NAME="E3:37_1_1_1"/>
 ex <font color="Olive">B</font> being <a href="pre_topc.html#V3">open</a> <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">T</font> st <br/>( <font color="Maroon">p</font> <a href="hidden.html#R2">in</a> <font color="Olive">B</font> &amp;  <a href="pre_topc.html#K4">Cl</a> <font color="Olive">B</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">A</font> )
 ;<br/>


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


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


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

<b>assume </b><a NAME="E2:37"/><i><font color="Green">E41</font></i>: 
for <font color="Olive">A</font> being <a href="pre_topc.html#V3">open</a> <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">T</font><br/> for <font color="Olive">p</font> being  <a href="pre_topc.html#NM2">Point</a> of <font color="Maroon">T</font>  st <font color="Olive">p</font> <a href="hidden.html#R2">in</a> <font color="Olive">A</font> holds <br/> ex <font color="Olive">B</font> being <a href="pre_topc.html#V3">open</a> <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">T</font> st <br/>( <font color="Olive">p</font> <a href="hidden.html#R2">in</a> <font color="Olive">B</font> &amp;  <a href="pre_topc.html#K4">Cl</a> <font color="Olive">B</font> <a href="tarski.html#R1">c=</a> <font color="Olive">A</font> )
 ;<br/>

<b>thus </b><a NAME="E3:37"/>
<font color="Maroon">T</font> <a href="compts_1.html#NR3" target="_self">is_T3</a> 
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="37_2"><b>proof </b></a><div class="add">

<a NAME="E1:37_2"/>
for <font color="Olive">p</font> being  <a href="pre_topc.html#NM2">Point</a> of <font color="Maroon">T</font><br/> for <font color="Olive">P</font> being  <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">T</font>  st <font color="Olive">P</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a>  &amp; <font color="Olive">P</font> is <a href="pre_topc.html#V4">closed</a> &amp; <font color="Olive">p</font> <a href="hidden.html#R2">in</a> <font color="Olive">P</font> <a href="subset_1.html#K3">`</a>  holds <br/> ex <font color="Olive">W</font>, <font color="Olive">V</font> being  <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">T</font> st <br/>( <font color="Olive">W</font> is <a href="pre_topc.html#V3">open</a> &amp; <font color="Olive">V</font> is <a href="pre_topc.html#V3">open</a> &amp; <font color="Olive">p</font> <a href="hidden.html#R2">in</a> <font color="Olive">W</font> &amp; <font color="Olive">P</font> <a href="tarski.html#R1">c=</a> <font color="Olive">V</font> &amp; <font color="Olive">W</font> <a href="xboole_0.html#R1">misses</a> <font color="Olive">V</font> )
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="37_2_1"><b>proof </b></a><div class="add">

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



<b>assume </b><a NAME="E1:37_2_1"/><i><font color="Green">E42</font></i>: 
( <font color="Maroon">P</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a>  &amp; <font color="Maroon">P</font> is <a href="pre_topc.html#V4">closed</a> &amp; <font color="Maroon">p</font> <a href="hidden.html#R2">in</a> <font color="Maroon">P</font> <a href="subset_1.html#K3">`</a>  )
 ;<br/>

<b>thus </b><a NAME="E2:37_2_1"/>
 ex <font color="Olive">W</font>, <font color="Olive">V</font> being  <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">T</font> st <br/>( <font color="Olive">W</font> is <a href="pre_topc.html#V3">open</a> &amp; <font color="Olive">V</font> is <a href="pre_topc.html#V3">open</a> &amp; <font color="Maroon">p</font> <a href="hidden.html#R2">in</a> <font color="Olive">W</font> &amp; <font color="Maroon">P</font> <a href="tarski.html#R1">c=</a> <font color="Olive">V</font> &amp; <font color="Olive">W</font> <a href="xboole_0.html#R1">misses</a> <font color="Olive">V</font> )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="37_2_1_1"><b>proof </b></a><div class="add">

<b>consider </b><font color="Maroon">A</font> being   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">T</font><b> such that </b><br/><a NAME="E2:37_2_1_1"/><i><font color="Green">E50</font></i>: 
<font color="Maroon">A</font> <a href="hidden.html#R1">=</a> <font color="Maroon">P</font> <a href="subset_1.html#K3">`</a> 
 ;<br/>
<a NAME="E3:37_2_1_1"/><i><font color="Green">E51</font></i>: 
<font color="Maroon">A</font> is <a href="pre_topc.html#V3">open</a>
 
<b>by </b><i>, <a class="ref" href="urysohn1.html#D3" target="_self">Def3</a>, <a class="ref" href="tops_1.html#T29">TOPS_1:29</a></i>;<br/>
<a NAME="E4:37_2_1_1"/><i><font color="Green">E52</font></i>: 
<font color="Maroon">A</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="pre_topc.html#K2">[#]</a> <font color="Maroon">T</font></span>)</span> <a href="subset_1.html#K7">\</a> <font color="Maroon">P</font>
 
<b>by </b><i><a class="ref" href="urysohn1.html#D3" target="_self">Def3</a></i>;<br/>
<a NAME="E5:37_2_1_1"/>
( <font color="Maroon">p</font> <a href="hidden.html#R2">in</a>  <a href="pre_topc.html#K2">[#]</a> <font color="Maroon">T</font> &amp; not <font color="Maroon">p</font> <a href="hidden.html#R2">in</a> <font color="Maroon">P</font> )
 
<b>by </b><i>, <a class="ref" href="xboole_0.html#D4">XBOOLE_0:def 4</a></i>;<br/>
<a NAME="E6:37_2_1_1"/><b>then </b>
<font color="Maroon">p</font> <a href="hidden.html#R2">in</a> <font color="Maroon">A</font>
 
<b>by </b><i>, <a class="ref" href="xboole_0.html#D4">XBOOLE_0:def 4</a></i>;<br/>
<b>then consider </b><font color="Maroon">B</font> being  <a href="pre_topc.html#V3">open</a> <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">T</font><b> such that </b><br/><a NAME="E8:37_2_1_1"/><i><font color="Green">E53</font></i>: 
( <font color="Maroon">p</font> <a href="hidden.html#R2">in</a> <font color="Maroon">B</font> &amp;  <a href="pre_topc.html#K4">Cl</a> <font color="Maroon">B</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">A</font> )
 <b>by </b><i>, </i>;<br/>
<b>consider </b><font color="Maroon">C</font> being   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">T</font><b> such that </b><br/><a NAME="E10:37_2_1_1"/><i><font color="Green">E54</font></i>: 
<font color="Maroon">C</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="pre_topc.html#K2">[#]</a> <font color="Maroon">T</font></span>)</span> <a href="subset_1.html#K7">\</a> <span class="p1">(<span class="default"><a href="pre_topc.html#K4">Cl</a> <font color="Maroon">B</font></span>)</span>
 ;<br/>
<b>reconsider </b><font color="Maroon">B</font> = <font color="Maroon">B</font>, <font color="Maroon">C</font> = <font color="Maroon">C</font> as   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">T</font> ;<br/>
<a NAME="E12:37_2_1_1"/><i><font color="Green">E55</font></i>: 
<span class="p1">(<span class="default"><a href="pre_topc.html#K4">Cl</a> <font color="Maroon">B</font></span>)</span> <a href="subset_1.html#K3">`</a>  is <a href="pre_topc.html#V3">open</a>
 
;<br/>
<b>take </b>
<font color="Maroon">B</font>
;<br/>

<b>take </b>
<font color="Maroon">C</font>
;<br/>

<a NAME="E13:37_2_1_1"/>
( <font color="Maroon">p</font> <a href="hidden.html#R2">in</a> <font color="Maroon">B</font> &amp; <font color="Maroon">P</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">C</font> &amp; <font color="Maroon">B</font> <a href="xboole_0.html#R1">misses</a> <font color="Maroon">C</font> )
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="37_2_1_1_1"><b>proof </b></a><div class="add">

<b>thus </b><a NAME="E1:37_2_1_1_1"/>
<font color="Maroon">p</font> <a href="hidden.html#R2">in</a> <font color="Maroon">B</font>
 <b>by </b><i/>;<br/>

<a NAME="E2:37_2_1_1_1"/>
<span class="p1">(<span class="default"><font color="Maroon">P</font> <a href="subset_1.html#K3">`</a> </span>)</span> <a href="subset_1.html#K3">`</a>  <a href="hidden.html#R1">=</a> <font color="Maroon">P</font>
 
;<br/>
<a NAME="E3:37_2_1_1_1"/><b>then </b><i><font color="Green">E69</font></i>: 
<font color="Maroon">P</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="pre_topc.html#K2">[#]</a> <font color="Maroon">T</font></span>)</span> <a href="subset_1.html#K7">\</a> <font color="Maroon">A</font>
 
<b>by </b><i><a class="ref" href="urysohn1.html#D3" target="_self">Def3</a></i>;<br/>
<a NAME="E4:37_2_1_1_1"/>
( <font color="Maroon">B</font> <a href="tarski.html#R1">c=</a>  <a href="pre_topc.html#K4">Cl</a> <font color="Maroon">B</font> &amp;  <a href="pre_topc.html#K4">Cl</a> <font color="Maroon">B</font> <a href="xboole_0.html#R1">misses</a> <font color="Maroon">C</font> )
 
<b>by </b><i>, <a class="ref" href="pre_topc.html#T48">PRE_TOPC:48</a>, <a class="ref" href="xboole_1.html#T79">XBOOLE_1:79</a></i>;<br/>
<b>hence </b><a NAME="E5:37_2_1_1_1"/>
( <font color="Maroon">P</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">C</font> &amp; <font color="Maroon">B</font> <a href="xboole_0.html#R1">misses</a> <font color="Maroon">C</font> )
 <b>by </b><i>, , , <a class="ref" href="xboole_1.html#T34">XBOOLE_1:34</a>, <a class="ref" href="xboole_1.html#T63">XBOOLE_1:63</a></i>;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E14:37_2_1_1"/>
( <font color="Maroon">B</font> is <a href="pre_topc.html#V3">open</a> &amp; <font color="Maroon">C</font> is <a href="pre_topc.html#V3">open</a> &amp; <font color="Maroon">p</font> <a href="hidden.html#R2">in</a> <font color="Maroon">B</font> &amp; <font color="Maroon">P</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">C</font> &amp; <font color="Maroon">B</font> <a href="xboole_0.html#R1">misses</a> <font color="Maroon">C</font> )
 <b>by </b><i>, </i>;<br/>


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


</div><b>end;</b></div>
<b>hence </b><a NAME="E2:37_2"/>
<font color="Maroon">T</font> <a href="compts_1.html#NR3" target="_self">is_T3</a> 
 <b>by </b><i><a class="ref" href="compts_1.html#D5">COMPTS_1:def 5</a></i>;<br/>


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


</div>
