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<b>let </b><font color="Maroon">L</font> be  non <a href="struct_0.html#V3">empty</a>  <a href="orders_2.html#L1">RelStr</a> ;<br/><b>let </b><font color="Maroon">Y</font> be   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">L</font>;<br/><b>let </b><font color="Maroon">x</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L</font>;<br/>





<b>thus </b><a NAME="E1:22"/>
<span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">x</font></span><a href="domain_1.html#K6">}</a></span> <a href="yellow_4.html#K1" target="_self">"\/"</a> <font color="Maroon">Y</font> <a href="tarski.html#R1">c=</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K10">"\/"</a> <font color="Olive">y</font></span>)</span> where <font color="Olive">y</font> is   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L</font> : <font color="Olive">y</font> <a href="hidden.html#R2">in</a> <font color="Maroon">Y</font> </span>}</span> 
  <i><font color="Red">:: according to </font></i><a class="ref" href="xboole_0.html#D10">XBOOLE_0:def 10</a><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="22_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">q</font> be    <a href="hidden.html#M1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3">TARSKI:def 3</a><br/>

<b>assume </b><a NAME="E1:22_1"/>
<font color="Maroon">q</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">x</font></span><a href="domain_1.html#K6">}</a></span> <a href="yellow_4.html#K1" target="_self">"\/"</a> <font color="Maroon">Y</font>
 ;<br/>

<b>then consider </b><font color="Maroon">s</font> being   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L</font>, <font color="Maroon">t</font> being   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L</font><b> such that </b><br/><a NAME="E3:22_1"/><i><font color="Green">E20</font></i>: 
( <font color="Maroon">q</font> <a href="hidden.html#R1">=</a> <font color="Maroon">s</font> <a href="lattice3.html#K10">"\/"</a> <font color="Maroon">t</font> &amp; <font color="Maroon">s</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">x</font></span><a href="domain_1.html#K6">}</a></span> &amp; <font color="Maroon">t</font> <a href="hidden.html#R2">in</a> <font color="Maroon">Y</font> )
 ;<br/>
<a NAME="E4:22_1"/>
<font color="Maroon">s</font> <a href="hidden.html#R1">=</a> <font color="Maroon">x</font>
 
<b>by </b><i>, <a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/>
<b>hence </b><a NAME="E5:22_1"/>
<font color="Maroon">q</font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K10">"\/"</a> <font color="Olive">y</font></span>)</span> where <font color="Olive">y</font> is   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L</font> : <font color="Olive">y</font> <a href="hidden.html#R2">in</a> <font color="Maroon">Y</font> </span>}</span> 
 <b>by </b><i/>;<br/>


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

<b>let </b><font color="Maroon">q</font> be    <a href="hidden.html#M1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3">TARSKI:def 3</a><br/>

<b>assume </b><a NAME="E2:22"/>
<font color="Maroon">q</font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K10">"\/"</a> <font color="Olive">y</font></span>)</span> where <font color="Olive">y</font> is   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L</font> : <font color="Olive">y</font> <a href="hidden.html#R2">in</a> <font color="Maroon">Y</font> </span>}</span> 
 ;<br/>

<b>then consider </b><font color="Maroon">y</font> being   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L</font><b> such that </b><br/><a NAME="E4:22"/><i><font color="Green">E21</font></i>: 
( <font color="Maroon">q</font> <a href="hidden.html#R1">=</a> <font color="Maroon">x</font> <a href="lattice3.html#K10">"\/"</a> <font color="Maroon">y</font> &amp; <font color="Maroon">y</font> <a href="hidden.html#R2">in</a> <font color="Maroon">Y</font> )
 ;<br/>
<a NAME="E5:22"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">x</font></span><a href="domain_1.html#K6">}</a></span>
 
<b>by </b><i><a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/>
<b>hence </b><a NAME="E6:22"/>
<font color="Maroon">q</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">x</font></span><a href="domain_1.html#K6">}</a></span> <a href="yellow_4.html#K1" target="_self">"\/"</a> <font color="Maroon">Y</font>
 <b>by </b><i/>;<br/>


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