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<b>let </b><font color="Maroon">S</font> be  non <a href="struct_0.html#V3">empty</a> <a href="pre_topc.html#NM1">TopSpace</a>, <font color="Maroon">T</font> be  non <a href="struct_0.html#V3">empty</a> <a href="pre_topc.html#NM1">TopSpace</a>;<br/>

<b>assume </b><b>that </b><br/><a NAME="E1:56"/><i><font color="Green">E42</font></i>: 
 <a href="pre_topc.html#G1">TopStruct</a>(# the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">S</font>,the <a href="pre_topc.html#U1">topology</a> of <font color="Maroon">S</font> #) <a href="hidden.html#R1">=</a>  <a href="pre_topc.html#G1">TopStruct</a>(# the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">T</font>,the <a href="pre_topc.html#U1">topology</a> of <font color="Maroon">T</font> #)
 <b>and </b><br/><a NAME="E2:56"/><i><font color="Green">E43</font></i>: 
for <font color="Olive">D</font> being non <a href="xboole_0.html#V1">empty</a> <a href="waybel_0.html#V1">directed</a> <a href="struct_0.html#NM2">Subset</a> of <span class="p1">(<span class="default"><a href="waybel25.html#K1" target="_self">Omega</a> <font color="Maroon">S</font></span>)</span> holds <br/> (  <a href="yellow_0.html#R1">ex_sup_of</a> <font color="Olive">D</font>, <a href="waybel25.html#K1" target="_self">Omega</a> <font color="Maroon">S</font> &amp; ( for <font color="Olive">V</font> being <a href="pre_topc.html#V3">open</a> <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">S</font>  st  <a href="yellow_0.html#NK3" target="_self">sup</a> <font color="Olive">D</font> <a href="hidden.html#R2">in</a> <font color="Olive">V</font> holds <br/><font color="Olive">D</font> <a href="xboole_0.html#NR5" target="_self">meets</a> <font color="Olive">V</font> ) )
 ; <i><font color="Red">:: according to </font></i><a class="ref" href="waybel25.html#D4" target="_self">WAYBEL25:def 4</a><br/>

<b>let </b><font color="Maroon">E</font> be  non <a href="xboole_0.html#V1">empty</a> <a href="waybel_0.html#V1">directed</a> <a href="struct_0.html#NM2">Subset</a> of <span class="p1">(<span class="default"><a href="waybel25.html#K1" target="_self">Omega</a> <font color="Maroon">T</font></span>)</span>; <i><font color="Red">:: according to </font></i><a class="ref" href="waybel25.html#D4" target="_self">WAYBEL25:def 4</a><br/>

<a NAME="E3:56"/><i><font color="Green">E44</font></i>: 
 <a href="waybel25.html#K1" target="_self">Omega</a> <font color="Maroon">S</font> <a href="hidden.html#R1">=</a>  <a href="waybel25.html#K1" target="_self">Omega</a> <font color="Maroon">T</font>
 
<b>by </b><i>, </i>;<br/>
<b>hence </b><a NAME="E4:56"/>
 <a href="yellow_0.html#R1">ex_sup_of</a> <font color="Maroon">E</font>, <a href="waybel25.html#K1" target="_self">Omega</a> <font color="Maroon">T</font>
 <b>by </b><i/>;<br/>

<b>let </b><font color="Maroon">V</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>assume </b><a NAME="E5:56"/><i><font color="Green">E47</font></i>: 
 <a href="yellow_0.html#NK3" target="_self">sup</a> <font color="Maroon">E</font> <a href="hidden.html#R2">in</a> <font color="Maroon">V</font>
 ;<br/>

<b>reconsider </b><font color="Maroon">W</font> = <font color="Maroon">V</font> as   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">S</font> <b>by </b><i/>;<br/>
<b>reconsider </b><font color="Maroon">D</font> = <font color="Maroon">E</font> as   <a href="struct_0.html#NM2">Subset</a> of <span class="p1">(<span class="default"><a href="waybel25.html#K1" target="_self">Omega</a> <font color="Maroon">S</font></span>)</span> <b>by </b><i/>;<br/>
<a NAME="E8:56"/>
( <font color="Maroon">W</font> is <a href="pre_topc.html#V3">open</a> &amp;  <a href="yellow_0.html#NK3" target="_self">sup</a> <font color="Maroon">D</font> <a href="hidden.html#R2">in</a> <font color="Maroon">W</font> )
 
<b>by </b><i>, , , <a class="ref" href="tops_3.html#T76">TOPS_3:76</a></i>;<br/>
<b>hence </b><a NAME="E9:56"/>
<font color="Maroon">E</font> <a href="xboole_0.html#NR5" target="_self">meets</a> <font color="Maroon">V</font>
 <b>by </b><i>, </i>;<br/>


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