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<b>let </b><font color="Maroon">X</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">a</font> be   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="yellow_1.html#K3">BoolePoset</a> <font color="Maroon">X</font></span>)</span>;<br/>



<a NAME="E1:11"/><i><font color="Green">E33</font></i>: 
the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="yellow_1.html#K3">BoolePoset</a> <font color="Maroon">X</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="zfmisc_1.html#K1">bool</a> <font color="Maroon">X</font>
 
<b>by </b><i/>;<br/>
<b>then reconsider </b><font color="Maroon">b</font> = <font color="Maroon">X</font> <a href="subset_1.html#K6">\</a> <font color="Maroon">a</font> as   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="yellow_1.html#K3">BoolePoset</a> <font color="Maroon">X</font></span>)</span> ;<br/>
<a NAME="E3:11"/>
<font color="Maroon">b</font> <a href="waybel_1.html#R6">is_a_complement_of</a> <font color="Maroon">a</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="11_1"><b>proof </b></a><div class="add">

<b>thus </b><font color="Maroon">a</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">b</font> = 
<font color="Maroon">a</font> <a href="xboole_0.html#K2">\/</a> <font color="Maroon">b</font>
<b>by </b><i><a class="ref" href="yellow_1.html#T17">YELLOW_1:17</a></i>
<br/>.= 
<font color="Maroon">X</font>
<b>by </b><i>, <a class="ref" href="xboole_1.html#T45">XBOOLE_1:45</a></i>
<br/>.= 
 <a href="yellow_0.html#K4">Top</a> <span class="p1">(<span class="default"><a href="yellow_1.html#K3">BoolePoset</a> <font color="Maroon">X</font></span>)</span>
<b>by </b><i><a class="ref" href="yellow_1.html#T19">YELLOW_1:19</a></i>
; <i><font color="Red">:: according to </font></i><a class="ref" href="waybel_1.html#D23">WAYBEL_1:def 23</a><br/>

<a NAME="E2:11_1"/><i><font color="Green">E42</font></i>: 
<font color="Maroon">a</font> <a href="xboole_0.html#R1">misses</a> <font color="Maroon">b</font>
 
<b>by </b><i><a class="ref" href="xboole_1.html#T79">XBOOLE_1:79</a></i>;<br/>
<b>thus </b><font color="Maroon">a</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">b</font> = 
<font color="Maroon">a</font> <a href="xboole_0.html#K3">/\</a> <font color="Maroon">b</font>
<b>by </b><i><a class="ref" href="yellow_1.html#T17">YELLOW_1:17</a></i>
<br/>.= 
 <a href="xboole_0.html#K1">{}</a> 
<b>by </b><i>, <a class="ref" href="xboole_0.html#D7">XBOOLE_0:def 7</a></i>
<br/>.= 
 <a href="yellow_0.html#K3">Bottom</a> <span class="p1">(<span class="default"><a href="yellow_1.html#K3">BoolePoset</a> <font color="Maroon">X</font></span>)</span>
<b>by </b><i><a class="ref" href="yellow_1.html#T18">YELLOW_1:18</a></i>
;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E4:11"/>
 <a href="waybel_1.html#K7">'not'</a> <font color="Maroon">a</font> <a href="hidden.html#R1">=</a> <font color="Maroon">X</font> <a href="subset_1.html#K6">\</a> <font color="Maroon">a</font>
 <b>by </b><i><a class="ref" href="yellow_5.html#T11">YELLOW_5:11</a></i>;<br/>


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