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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>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>let </b><font color="Maroon">q</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>let </b><font color="Maroon">p'</font> be    <a href="subset_1.html#M2">Element</a> of  <a href="openlatt.html#K1" target="_self">Topology_of</a> <font color="Maroon">T</font>, <font color="Maroon">q'</font> be    <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>assume </b><a NAME="E1:11"/><i><font color="Green">E18</font></i>: 
( <font color="Maroon">p</font> <a href="hidden.html#R1">=</a> <font color="Maroon">p'</font> &amp; <font color="Maroon">q</font> <a href="hidden.html#R1">=</a> <font color="Maroon">q'</font> )
 ;<br/>

<div><b>hereby </b>
<div class="add"><b>assume </b><a NAME="E1:11_1"/><i><font color="Green">E19</font></i>: 
<font color="Maroon">p</font> <a href="lattices.html#R3">[=</a> <font color="Maroon">q</font>
 ;<br/><font color="Maroon">p'</font> <a href="openlatt.html#K2" target="_self">\/</a> <font color="Maroon">q'</font> = 
<font color="Maroon">p</font> <a href="lattices.html#K3">"\/"</a> <font color="Maroon">q</font>
<b>by </b><i>, </i>
<br/>.= 
<font color="Maroon">q'</font>
<b>by </b><i>, , <a class="ref" href="lattices.html#D3">LATTICES:def 3</a></i>
;<br/><b>hence </b><a NAME="E3:11_1"/>
<font color="Maroon">p'</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">q'</font>
 <b>by </b><i><a class="ref" href="xboole_1.html#T7">XBOOLE_1:7</a></i>;<br/></div>
<b>end;</b></div>

<b>assume </b><a NAME="E3:11"/><i><font color="Green">E40</font></i>: 
<font color="Maroon">p'</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">q'</font>
 ;<br/>

<font color="Maroon">p</font> <a href="lattices.html#K3">"\/"</a> <font color="Maroon">q</font> = 
<font color="Maroon">p'</font> <a href="openlatt.html#K2" target="_self">\/</a> <font color="Maroon">q'</font>
<b>by </b><i>, </i>
<br/>.= 
<font color="Maroon">q</font>
<b>by </b><i>, , <a class="ref" href="xboole_1.html#T12">XBOOLE_1:12</a></i>
;<br/>
<b>hence </b><a NAME="E5:11"/>
<font color="Maroon">p</font> <a href="lattices.html#R3">[=</a> <font color="Maroon">q</font>
 <b>by </b><i><a class="ref" href="lattices.html#D3">LATTICES:def 3</a></i>;<br/>


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