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





<b>thus </b><a NAME="E1:27"/>
( <font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">A</font> <a href="fintopo2.html#K9" target="_self">^Fob</a>  implies 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">x</font> holds <br/><font color="Olive">W</font> <a href="xboole_0.html#NR5" target="_self">meets</a> <font color="Maroon">A</font> )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="27_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:27_1"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">A</font> <a href="fintopo2.html#K9" target="_self">^Fob</a> 
 ;<br/>

<a NAME="E2:27_1"/><b>then </b>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <font color="Olive">y</font> where <font color="Olive">y</font> is   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">FMT</font> : 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">y</font> holds <br/><font color="Olive">W</font> <a href="xboole_0.html#NR5" target="_self">meets</a> <font color="Maroon">A</font> </span>}</span> 
 
;<br/>
<a NAME="E3:27_1"/><b>then </b>
 ex <font color="Olive">y</font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">FMT</font> st <br/>( <font color="Olive">y</font> <a href="hidden.html#R1">=</a> <font color="Maroon">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">y</font> holds <br/><font color="Olive">W</font> <a href="xboole_0.html#NR5" target="_self">meets</a> <font color="Maroon">A</font> ) )
 
;<br/>
<b>hence </b><a NAME="E4:27_1"/>
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">x</font> holds <br/><font color="Olive">W</font> <a href="xboole_0.html#NR5" target="_self">meets</a> <font color="Maroon">A</font>
 ;<br/>


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

<b>assume </b><a NAME="E2:27"/>
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">x</font> holds <br/><font color="Olive">W</font> <a href="xboole_0.html#NR5" target="_self">meets</a> <font color="Maroon">A</font>
 ;<br/>

<a NAME="E3:27"/><b>then </b>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <font color="Olive">y</font> where <font color="Olive">y</font> is   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">FMT</font> : 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">y</font> holds <br/><font color="Olive">W</font> <a href="xboole_0.html#NR5" target="_self">meets</a> <font color="Maroon">A</font> </span>}</span> 
 
;<br/>
<b>hence </b><a NAME="E4:27"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">A</font> <a href="fintopo2.html#K9" target="_self">^Fob</a> 
 ;<br/>


</div>
