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<div class="add">

<b>let </b><font color="Maroon" title="c1">FMT</font> be  non <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>  <a href="fintopo2.html#L1" title="FINTOPO2:struct.1">FMT_Space_Str</a> ;<br/><b>let </b><font color="Maroon" title="c2">x</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">FMT</font>;<br/><b>let </b><font color="Maroon" title="c3">A</font> be   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">FMT</font>;<br/>





<b>thus </b><a NAME="E1:25"/>
( <font color="Maroon" title="c2">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">A</font> <a href="fintopo2.html#K8" title="FINTOPO2:func.8">^Fodelta</a>  implies for <font color="Olive" title="b1">W</font> being  <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">FMT</font>  st <font color="Olive" title="b1">W</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="fintopo2.html#K6" title="FINTOPO2:func.6">U_FMT</a> <font color="Maroon" title="c2">x</font> holds <br/>( <font color="Olive" title="b1">W</font> <a href="xboole_0.html#NR5" title="XBOOLE_0:NR.5">meets</a> <font color="Maroon" title="c3">A</font> &amp; <font color="Olive" title="b1">W</font> <a href="xboole_0.html#NR5" title="XBOOLE_0:NR.5">meets</a> <font color="Maroon" title="c3">A</font> <a href="subset_1.html#K3" title="SUBSET_1:func.3">`</a>  ) )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="25_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:25_1"/>
<font color="Maroon" title="c2">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">A</font> <a href="fintopo2.html#K8" title="FINTOPO2:func.8">^Fodelta</a> 
 ;<br/>

<a NAME="E2:25_1"/><b>then </b>
 ex <font color="Olive" title="b1">y</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">FMT</font> st <br/>( <font color="Olive" title="b1">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">x</font> &amp; ( for <font color="Olive" title="b2">W</font> being  <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">FMT</font>  st <font color="Olive" title="b2">W</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="fintopo2.html#K6" title="FINTOPO2:func.6">U_FMT</a> <font color="Olive" title="b1">y</font> holds <br/>( <font color="Olive" title="b2">W</font> <a href="xboole_0.html#NR5" title="XBOOLE_0:NR.5">meets</a> <font color="Maroon" title="c3">A</font> &amp; <font color="Olive" title="b2">W</font> <a href="xboole_0.html#NR5" title="XBOOLE_0:NR.5">meets</a> <font color="Maroon" title="c3">A</font> <a href="subset_1.html#K3" title="SUBSET_1:func.3">`</a>  ) ) )
 
;<br/>
<b>hence </b><a NAME="E3:25_1"/>
for <font color="Olive" title="b1">W</font> being  <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">FMT</font>  st <font color="Olive" title="b1">W</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="fintopo2.html#K6" title="FINTOPO2:func.6">U_FMT</a> <font color="Maroon" title="c2">x</font> holds <br/>( <font color="Olive" title="b1">W</font> <a href="xboole_0.html#NR5" title="XBOOLE_0:NR.5">meets</a> <font color="Maroon" title="c3">A</font> &amp; <font color="Olive" title="b1">W</font> <a href="xboole_0.html#NR5" title="XBOOLE_0:NR.5">meets</a> <font color="Maroon" title="c3">A</font> <a href="subset_1.html#K3" title="SUBSET_1:func.3">`</a>  )
 ;<br/>


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

<b>assume </b><a NAME="E2:25"/>
for <font color="Olive" title="b1">W</font> being  <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">FMT</font>  st <font color="Olive" title="b1">W</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="fintopo2.html#K6" title="FINTOPO2:func.6">U_FMT</a> <font color="Maroon" title="c2">x</font> holds <br/>( <font color="Olive" title="b1">W</font> <a href="xboole_0.html#NR5" title="XBOOLE_0:NR.5">meets</a> <font color="Maroon" title="c3">A</font> &amp; <font color="Olive" title="b1">W</font> <a href="xboole_0.html#NR5" title="XBOOLE_0:NR.5">meets</a> <font color="Maroon" title="c3">A</font> <a href="subset_1.html#K3" title="SUBSET_1:func.3">`</a>  )
 ;<br/>

<b>hence </b><a NAME="E3:25"/>
<font color="Maroon" title="c2">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">A</font> <a href="fintopo2.html#K8" title="FINTOPO2:func.8">^Fodelta</a> 
 ;<br/>


</div>
