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

<b>let </b><font color="Maroon">FMT</font> be  non <a href="struct_0.html#V3">empty</a>  <a href="fintopo2.html#L1" target="_self">FMT_Space_Str</a> ;<br/>

<b>thus </b><a NAME="E1:41"/>
( ( for <font color="Olive">x</font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">FMT</font><br/> for <font color="Olive">V1</font>, <font color="Olive">V2</font> being  <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">FMT</font>  st <font color="Olive">V1</font> <a href="hidden.html#R2">in</a>  <a href="fintopo2.html#K6" target="_self">U_FMT</a> <font color="Olive">x</font> &amp; <font color="Olive">V2</font> <a href="hidden.html#R2">in</a>  <a href="fintopo2.html#K6" target="_self">U_FMT</a> <font color="Olive">x</font> holds <br/> ex <font color="Olive">W</font> being  <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">FMT</font> st <br/>( <font color="Olive">W</font> <a href="hidden.html#R2">in</a>  <a href="fintopo2.html#K6" target="_self">U_FMT</a> <font color="Olive">x</font> &amp; <font color="Olive">W</font> <a href="tarski.html#R1">c=</a> <font color="Olive">V1</font> <a href="subset_1.html#K9">/\</a> <font color="Olive">V2</font> ) ) implies for <font color="Olive">A</font>, <font color="Olive">B</font> being  <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">FMT</font> holds  <span class="p1">(<span class="default"><font color="Olive">A</font> <a href="fintopo2.html#K10" target="_self">^Foi</a> </span>)</span> <a href="subset_1.html#K9">/\</a> <span class="p1">(<span class="default"><font color="Olive">B</font> <a href="fintopo2.html#K10" target="_self">^Foi</a> </span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Olive">A</font> <a href="subset_1.html#K9">/\</a> <font color="Olive">B</font></span>)</span> <a href="fintopo2.html#K10" target="_self">^Foi</a>  )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="41_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:41_1"/><i><font color="Green">E19</font></i>: 
for <font color="Olive">x</font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">FMT</font><br/> for <font color="Olive">V1</font>, <font color="Olive">V2</font> being  <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">FMT</font>  st <font color="Olive">V1</font> <a href="hidden.html#R2">in</a>  <a href="fintopo2.html#K6" target="_self">U_FMT</a> <font color="Olive">x</font> &amp; <font color="Olive">V2</font> <a href="hidden.html#R2">in</a>  <a href="fintopo2.html#K6" target="_self">U_FMT</a> <font color="Olive">x</font> holds <br/> ex <font color="Olive">W</font> being  <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">FMT</font> st <br/>( <font color="Olive">W</font> <a href="hidden.html#R2">in</a>  <a href="fintopo2.html#K6" target="_self">U_FMT</a> <font color="Olive">x</font> &amp; <font color="Olive">W</font> <a href="tarski.html#R1">c=</a> <font color="Olive">V1</font> <a href="subset_1.html#K9">/\</a> <font color="Olive">V2</font> )
 ;<br/>

<b>let </b><font color="Maroon">A</font> be   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">FMT</font>, <font color="Maroon">B</font> be   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">FMT</font>;<br/>

<b>thus </b><a NAME="E2:41_1"/>
<span class="p1">(<span class="default"><font color="Maroon">A</font> <a href="fintopo2.html#K10" target="_self">^Foi</a> </span>)</span> <a href="subset_1.html#K9">/\</a> <span class="p1">(<span class="default"><font color="Maroon">B</font> <a href="fintopo2.html#K10" target="_self">^Foi</a> </span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">A</font> <a href="subset_1.html#K9">/\</a> <font color="Maroon">B</font></span>)</span> <a href="fintopo2.html#K10" target="_self">^Foi</a> 
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="41_1_1"><b>proof </b></a><div class="add">

<a NAME="E1:41_1_1"/>
for <font color="Olive">x</font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">FMT</font> holds <br/> ( <font color="Olive">x</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><font color="Maroon">A</font> <a href="fintopo2.html#K10" target="_self">^Foi</a> </span>)</span> <a href="subset_1.html#K9">/\</a> <span class="p1">(<span class="default"><font color="Maroon">B</font> <a href="fintopo2.html#K10" target="_self">^Foi</a> </span>)</span> iff <font color="Olive">x</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><font color="Maroon">A</font> <a href="subset_1.html#K9">/\</a> <font color="Maroon">B</font></span>)</span> <a href="fintopo2.html#K10" target="_self">^Foi</a>  )
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="41_1_1_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">x</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">FMT</font>;<br/>

<a NAME="E1:41_1_1_1"/><i><font color="Green">E21</font></i>: 
( <font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><font color="Maroon">A</font> <a href="fintopo2.html#K10" target="_self">^Foi</a> </span>)</span> <a href="subset_1.html#K9">/\</a> <span class="p1">(<span class="default"><font color="Maroon">B</font> <a href="fintopo2.html#K10" target="_self">^Foi</a> </span>)</span> implies <font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><font color="Maroon">A</font> <a href="subset_1.html#K9">/\</a> <font color="Maroon">B</font></span>)</span> <a href="fintopo2.html#K10" target="_self">^Foi</a>  )
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="41_1_1_1_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:41_1_1_1_1"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><font color="Maroon">A</font> <a href="fintopo2.html#K10" target="_self">^Foi</a> </span>)</span> <a href="subset_1.html#K9">/\</a> <span class="p1">(<span class="default"><font color="Maroon">B</font> <a href="fintopo2.html#K10" target="_self">^Foi</a> </span>)</span>
 ;<br/>

<a NAME="E2:41_1_1_1_1"/><b>then </b>
( <font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">A</font> <a href="fintopo2.html#K10" target="_self">^Foi</a>  &amp; <font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">B</font> <a href="fintopo2.html#K10" target="_self">^Foi</a>  )
 
<b>by </b><i><a class="ref" href="xboole_0.html#D3">XBOOLE_0:def 3</a></i>;<br/>
<a NAME="E3:41_1_1_1_1"/><b>then </b>
(  ex <font color="Olive">W1</font> being  <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">FMT</font> st <br/>( <font color="Olive">W1</font> <a href="hidden.html#R2">in</a>  <a href="fintopo2.html#K6" target="_self">U_FMT</a> <font color="Maroon">x</font> &amp; <font color="Olive">W1</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">A</font> ) &amp;  ex <font color="Olive">W2</font> being  <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">FMT</font> st <br/>( <font color="Olive">W2</font> <a href="hidden.html#R2">in</a>  <a href="fintopo2.html#K6" target="_self">U_FMT</a> <font color="Maroon">x</font> &amp; <font color="Olive">W2</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">B</font> ) )
 
<b>by </b><i/>;<br/>
<b>then consider </b><font color="Maroon">W1</font> being   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">FMT</font>, <font color="Maroon">W2</font> being   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">FMT</font><b> such that </b><br/><a NAME="E5:41_1_1_1_1"/><i><font color="Green">E23</font></i>: 
( <font color="Maroon">W1</font> <a href="hidden.html#R2">in</a>  <a href="fintopo2.html#K6" target="_self">U_FMT</a> <font color="Maroon">x</font> &amp; <font color="Maroon">W2</font> <a href="hidden.html#R2">in</a>  <a href="fintopo2.html#K6" target="_self">U_FMT</a> <font color="Maroon">x</font> )
 <b>and </b><br/><a NAME="E6:41_1_1_1_1"/><i><font color="Green">E33</font></i>: 
( <font color="Maroon">W1</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">A</font> &amp; <font color="Maroon">W2</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">B</font> )
 ;<br/>
<b>consider </b><font color="Maroon">W</font> being   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">FMT</font><b> such that </b><br/><a NAME="E8:41_1_1_1_1"/><i><font color="Green">E35</font></i>: 
<font color="Maroon">W</font> <a href="hidden.html#R2">in</a>  <a href="fintopo2.html#K6" target="_self">U_FMT</a> <font color="Maroon">x</font>
 <b>and </b><br/><a NAME="E9:41_1_1_1_1"/><i><font color="Green">E36</font></i>: 
<font color="Maroon">W</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">W1</font> <a href="subset_1.html#K9">/\</a> <font color="Maroon">W2</font>
 <b>by </b><i>, <a class="txt" href="fintopo2.html#E1:41_1"><i><font color="Green">E19</font></i></a></i>;<br/>
<a NAME="E10:41_1_1_1_1"/>
( <font color="Maroon">W1</font> <a href="subset_1.html#K9">/\</a> <font color="Maroon">W2</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">W1</font> &amp; <font color="Maroon">W1</font> <a href="subset_1.html#K9">/\</a> <font color="Maroon">W2</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">W2</font> )
 
<b>by </b><i><a class="ref" href="xboole_1.html#T17">XBOOLE_1:17</a></i>;<br/>
<a NAME="E11:41_1_1_1_1"/><b>then </b>
( <font color="Maroon">W</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">W1</font> &amp; <font color="Maroon">W</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">W2</font> )
 
<b>by </b><i>, <a class="ref" href="xboole_1.html#T1">XBOOLE_1:1</a></i>;<br/>
<a NAME="E12:41_1_1_1_1"/><b>then </b>
( <font color="Maroon">W</font> <a href="hidden.html#R2">in</a>  <a href="fintopo2.html#K6" target="_self">U_FMT</a> <font color="Maroon">x</font> &amp; <font color="Maroon">W</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">A</font> &amp; <font color="Maroon">W</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">B</font> )
 
<b>by </b><i>, <a class="txt" href="fintopo2.html#E1:41_1_1_1"><i><font color="Green">E21</font></i></a>, <a class="ref" href="xboole_1.html#T1">XBOOLE_1:1</a></i>;<br/>
<a NAME="E13:41_1_1_1_1"/><b>then </b>
( <font color="Maroon">W</font> <a href="hidden.html#R2">in</a>  <a href="fintopo2.html#K6" target="_self">U_FMT</a> <font color="Maroon">x</font> &amp; <font color="Maroon">W</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">A</font> <a href="subset_1.html#K9">/\</a> <font color="Maroon">B</font> )
 
<b>by </b><i><a class="ref" href="xboole_1.html#T19">XBOOLE_1:19</a></i>;<br/>
<b>hence </b><a NAME="E14:41_1_1_1_1"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><font color="Maroon">A</font> <a href="subset_1.html#K9">/\</a> <font color="Maroon">B</font></span>)</span> <a href="fintopo2.html#K10" target="_self">^Foi</a> 
 ;<br/>


</div><b>end;</b></div>
<a NAME="E2:41_1_1_1"/>
( <font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><font color="Maroon">A</font> <a href="subset_1.html#K9">/\</a> <font color="Maroon">B</font></span>)</span> <a href="fintopo2.html#K10" target="_self">^Foi</a>  implies <font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><font color="Maroon">A</font> <a href="fintopo2.html#K10" target="_self">^Foi</a> </span>)</span> <a href="subset_1.html#K9">/\</a> <span class="p1">(<span class="default"><font color="Maroon">B</font> <a href="fintopo2.html#K10" target="_self">^Foi</a> </span>)</span> )
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="41_1_1_1_2"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:41_1_1_1_2"/><i><font color="Green">E37</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><font color="Maroon">A</font> <a href="subset_1.html#K9">/\</a> <font color="Maroon">B</font></span>)</span> <a href="fintopo2.html#K10" target="_self">^Foi</a> 
 ;<br/>

<a NAME="E2:41_1_1_1_2"/>
<span class="p1">(<span class="default"><font color="Maroon">A</font> <a href="subset_1.html#K9">/\</a> <font color="Maroon">B</font></span>)</span> <a href="fintopo2.html#K10" target="_self">^Foi</a>  <a href="tarski.html#R1">c=</a> <span class="p1">(<span class="default"><font color="Maroon">A</font> <a href="fintopo2.html#K10" target="_self">^Foi</a> </span>)</span> <a href="subset_1.html#K9">/\</a> <span class="p1">(<span class="default"><font color="Maroon">B</font> <a href="fintopo2.html#K10" target="_self">^Foi</a> </span>)</span>
 
<b>by </b><i/>;<br/>
<b>hence </b><a NAME="E3:41_1_1_1_2"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><font color="Maroon">A</font> <a href="fintopo2.html#K10" target="_self">^Foi</a> </span>)</span> <a href="subset_1.html#K9">/\</a> <span class="p1">(<span class="default"><font color="Maroon">B</font> <a href="fintopo2.html#K10" target="_self">^Foi</a> </span>)</span>
 <b>by </b><i><a class="txt" href="fintopo2.html#E1:41_1"><i><font color="Green">E19</font></i></a></i>;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E3:41_1_1_1"/>
( <font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><font color="Maroon">A</font> <a href="fintopo2.html#K10" target="_self">^Foi</a> </span>)</span> <a href="subset_1.html#K9">/\</a> <span class="p1">(<span class="default"><font color="Maroon">B</font> <a href="fintopo2.html#K10" target="_self">^Foi</a> </span>)</span> iff <font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><font color="Maroon">A</font> <a href="subset_1.html#K9">/\</a> <font color="Maroon">B</font></span>)</span> <a href="fintopo2.html#K10" target="_self">^Foi</a>  )
 <b>by </b><i/>;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E2:41_1_1"/>
<span class="p1">(<span class="default"><font color="Maroon">A</font> <a href="fintopo2.html#K10" target="_self">^Foi</a> </span>)</span> <a href="subset_1.html#K9">/\</a> <span class="p1">(<span class="default"><font color="Maroon">B</font> <a href="fintopo2.html#K10" target="_self">^Foi</a> </span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">A</font> <a href="subset_1.html#K9">/\</a> <font color="Maroon">B</font></span>)</span> <a href="fintopo2.html#K10" target="_self">^Foi</a> 
 <b>by </b><i><a class="ref" href="subset_1.html#T8">SUBSET_1:8</a></i>;<br/>


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

<b>thus </b><a NAME="E3:41_1"/>
verum
 ;<br/>


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

<b>thus </b><a NAME="E2:41"/>
( ( for <font color="Olive">A</font>, <font color="Olive">B</font> being  <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">FMT</font> holds  <span class="p1">(<span class="default"><font color="Olive">A</font> <a href="fintopo2.html#K10" target="_self">^Foi</a> </span>)</span> <a href="subset_1.html#K9">/\</a> <span class="p1">(<span class="default"><font color="Olive">B</font> <a href="fintopo2.html#K10" target="_self">^Foi</a> </span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Olive">A</font> <a href="subset_1.html#K9">/\</a> <font color="Olive">B</font></span>)</span> <a href="fintopo2.html#K10" target="_self">^Foi</a>  ) implies for <font color="Olive">x</font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">FMT</font><br/> for <font color="Olive">V1</font>, <font color="Olive">V2</font> being  <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">FMT</font>  st <font color="Olive">V1</font> <a href="hidden.html#R2">in</a>  <a href="fintopo2.html#K6" target="_self">U_FMT</a> <font color="Olive">x</font> &amp; <font color="Olive">V2</font> <a href="hidden.html#R2">in</a>  <a href="fintopo2.html#K6" target="_self">U_FMT</a> <font color="Olive">x</font> holds <br/> ex <font color="Olive">W</font> being  <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">FMT</font> st <br/>( <font color="Olive">W</font> <a href="hidden.html#R2">in</a>  <a href="fintopo2.html#K6" target="_self">U_FMT</a> <font color="Olive">x</font> &amp; <font color="Olive">W</font> <a href="tarski.html#R1">c=</a> <font color="Olive">V1</font> <a href="subset_1.html#K9">/\</a> <font color="Olive">V2</font> ) )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="41_2"><b>proof </b></a><div class="add">

<a NAME="E1:41_2"/>
(  ex <font color="Olive">x</font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">FMT</font> ex <font color="Olive">V1</font>, <font color="Olive">V2</font> being  <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">FMT</font> st <br/>( <font color="Olive">V1</font> <a href="hidden.html#R2">in</a>  <a href="fintopo2.html#K6" target="_self">U_FMT</a> <font color="Olive">x</font> &amp; <font color="Olive">V2</font> <a href="hidden.html#R2">in</a>  <a href="fintopo2.html#K6" target="_self">U_FMT</a> <font color="Olive">x</font> &amp; ( for <font color="Olive">W</font> being  <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">FMT</font>  st <font color="Olive">W</font> <a href="hidden.html#R2">in</a>  <a href="fintopo2.html#K6" target="_self">U_FMT</a> <font color="Olive">x</font> holds <br/> not <font color="Olive">W</font> <a href="tarski.html#R1">c=</a> <font color="Olive">V1</font> <a href="subset_1.html#K9">/\</a> <font color="Olive">V2</font> ) ) implies  ex <font color="Olive">A</font>, <font color="Olive">B</font> being  <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">FMT</font> st <span class="p1">(<span class="default"><font color="Olive">A</font> <a href="fintopo2.html#K10" target="_self">^Foi</a> </span>)</span> <a href="subset_1.html#K9">/\</a> <span class="p1">(<span class="default"><font color="Olive">B</font> <a href="fintopo2.html#K10" target="_self">^Foi</a> </span>)</span> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <span class="p1">(<span class="default"><font color="Olive">A</font> <a href="subset_1.html#K9">/\</a> <font color="Olive">B</font></span>)</span> <a href="fintopo2.html#K10" target="_self">^Foi</a>  )
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="41_2_1"><b>proof </b></a><div class="add">

<b>given </b><font color="Maroon">x0</font> being   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">FMT</font>, <font color="Maroon">V1</font> being   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">FMT</font>, <font color="Maroon">V2</font> being   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">FMT</font><b> such that </b><a NAME="E1:41_2_1"/><i><font color="Green">E38</font></i>: 
( <font color="Maroon">V1</font> <a href="hidden.html#R2">in</a>  <a href="fintopo2.html#K6" target="_self">U_FMT</a> <font color="Maroon">x0</font> &amp; <font color="Maroon">V2</font> <a href="hidden.html#R2">in</a>  <a href="fintopo2.html#K6" target="_self">U_FMT</a> <font color="Maroon">x0</font> )
 <b>and </b><br/><a NAME="E2:41_2_1"/><i><font color="Green">E43</font></i>: 
for <font color="Olive">W</font> being  <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">FMT</font>  st <font color="Olive">W</font> <a href="hidden.html#R2">in</a>  <a href="fintopo2.html#K6" target="_self">U_FMT</a> <font color="Maroon">x0</font> holds <br/> not <font color="Olive">W</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">V1</font> <a href="subset_1.html#K9">/\</a> <font color="Maroon">V2</font>
 ;<br/>

<a NAME="E3:41_2_1"/>
( <font color="Maroon">x0</font> <a href="hidden.html#R2">in</a> <font color="Maroon">V1</font> <a href="fintopo2.html#K10" target="_self">^Foi</a>  &amp; <font color="Maroon">x0</font> <a href="hidden.html#R2">in</a> <font color="Maroon">V2</font> <a href="fintopo2.html#K10" target="_self">^Foi</a>  )
 
<b>by </b><i/>;<br/>
<a NAME="E4:41_2_1"/><b>then </b><i><font color="Green">E54</font></i>: 
( <font color="Maroon">x0</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><font color="Maroon">V1</font> <a href="fintopo2.html#K10" target="_self">^Foi</a> </span>)</span> <a href="subset_1.html#K9">/\</a> <span class="p1">(<span class="default"><font color="Maroon">V2</font> <a href="fintopo2.html#K10" target="_self">^Foi</a> </span>)</span> &amp; not <font color="Maroon">x0</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><font color="Maroon">V1</font> <a href="subset_1.html#K9">/\</a> <font color="Maroon">V2</font></span>)</span> <a href="fintopo2.html#K10" target="_self">^Foi</a>  )
 
<b>by </b><i>, , <a class="ref" href="xboole_0.html#D3">XBOOLE_0:def 3</a></i>;<br/>
<b>take </b>
<font color="Maroon">V1</font>
;<br/>

<b>take </b>
<font color="Maroon">V2</font>
;<br/>

<b>thus </b><a NAME="E5:41_2_1"/>
<span class="p1">(<span class="default"><font color="Maroon">V1</font> <a href="fintopo2.html#K10" target="_self">^Foi</a> </span>)</span> <a href="subset_1.html#K9">/\</a> <span class="p1">(<span class="default"><font color="Maroon">V2</font> <a href="fintopo2.html#K10" target="_self">^Foi</a> </span>)</span> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <span class="p1">(<span class="default"><font color="Maroon">V1</font> <a href="subset_1.html#K9">/\</a> <font color="Maroon">V2</font></span>)</span> <a href="fintopo2.html#K10" target="_self">^Foi</a> 
 <b>by </b><i/>;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E2:41_2"/>
( ( for <font color="Olive">A</font>, <font color="Olive">B</font> being  <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">FMT</font> holds  <span class="p1">(<span class="default"><font color="Olive">A</font> <a href="fintopo2.html#K10" target="_self">^Foi</a> </span>)</span> <a href="subset_1.html#K9">/\</a> <span class="p1">(<span class="default"><font color="Olive">B</font> <a href="fintopo2.html#K10" target="_self">^Foi</a> </span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Olive">A</font> <a href="subset_1.html#K9">/\</a> <font color="Olive">B</font></span>)</span> <a href="fintopo2.html#K10" target="_self">^Foi</a>  ) implies for <font color="Olive">x</font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">FMT</font><br/> for <font color="Olive">V1</font>, <font color="Olive">V2</font> being  <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">FMT</font>  st <font color="Olive">V1</font> <a href="hidden.html#R2">in</a>  <a href="fintopo2.html#K6" target="_self">U_FMT</a> <font color="Olive">x</font> &amp; <font color="Olive">V2</font> <a href="hidden.html#R2">in</a>  <a href="fintopo2.html#K6" target="_self">U_FMT</a> <font color="Olive">x</font> holds <br/> ex <font color="Olive">W</font> being  <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">FMT</font> st <br/>( <font color="Olive">W</font> <a href="hidden.html#R2">in</a>  <a href="fintopo2.html#K6" target="_self">U_FMT</a> <font color="Olive">x</font> &amp; <font color="Olive">W</font> <a href="tarski.html#R1">c=</a> <font color="Olive">V1</font> <a href="subset_1.html#K9">/\</a> <font color="Olive">V2</font> ) )
 ;<br/>


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


</div>
