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<b>let </b><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>set </b><font color="Maroon">OL</font> =  <a href="openlatt.html#K6" target="_self">Open_setLatt</a> <font color="Maroon">T</font>;<br/>
<a NAME="E1:15"/>
the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">T</font> <a href="hidden.html#R2">in</a> the <a href="pre_topc.html#U1">topology</a> of <font color="Maroon">T</font>
 
<b>by </b><i><a class="ref" href="pre_topc.html#D1">PRE_TOPC:def 1</a></i>;<br/>
<b>then reconsider </b><font color="Maroon">B</font> = the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">T</font> as   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="openlatt.html#K6" target="_self">Open_setLatt</a> <font color="Maroon">T</font></span>)</span> ;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="15_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">p</font> be   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="openlatt.html#K6" target="_self">Open_setLatt</a> <font color="Maroon">T</font></span>)</span>;<br/><b>reconsider </b><font color="Maroon">p'</font> = <font color="Maroon">p</font> as    <a href="subset_1.html#M2">Element</a> of  <a href="openlatt.html#K1" target="_self">Topology_of</a> <font color="Maroon">T</font> ;<br/><b>thus </b><font color="Maroon">B</font> <a href="lattices.html#K3">"\/"</a> <font color="Maroon">p</font> = 
the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">T</font> <a href="xboole_0.html#K2">\/</a> <font color="Maroon">p'</font>
<b>by </b><i/>
<br/>.= 
<font color="Maroon">B</font>
<b>by </b><i><a class="ref" href="xboole_1.html#T12">XBOOLE_1:12</a></i>
;<br/><b>hence </b><a NAME="E3:15_1"/>
<font color="Maroon">p</font> <a href="lattices.html#K3">"\/"</a> <font color="Maroon">B</font> <a href="hidden.html#R1">=</a> <font color="Maroon">B</font>
 ;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E4:15"/>
 <a href="lattices.html#K6">Top</a> <span class="p1">(<span class="default"><a href="openlatt.html#K6" target="_self">Open_setLatt</a> <font color="Maroon">T</font></span>)</span> <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">T</font>
 <b>by </b><i><a class="ref" href="lattices.html#D17">LATTICES:def 17</a></i>;<br/>


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