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<b>let </b><font color="Maroon">L</font> be   <a href="waybel_0.html#NM7">sup-Semilattice</a>;<br/><b>let </b><font color="Maroon">I</font> be  <a href="waybel_0.html#V1">directed</a> <a href="waybel_0.html#V12">lower</a> <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">L</font>;<br/>



<b>thus </b><a NAME="E1:35"/>
<font color="Maroon">I</font> <a href="yellow_4.html#K2">"\/"</a> <font color="Maroon">I</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">I</font>
  <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="35_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">x</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="E1:35_1"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">I</font> <a href="yellow_4.html#K2">"\/"</a> <font color="Maroon">I</font>
 ;<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>, <font color="Maroon">z</font> being   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L</font><b> such that </b><br/><a NAME="E3:35_1"/><i><font color="Green">E25</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">y</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">z</font>
 <b>and </b><br/><a NAME="E4:35_1"/><i><font color="Green">E26</font></i>: 
( <font color="Maroon">y</font> <a href="hidden.html#R2">in</a> <font color="Maroon">I</font> &amp; <font color="Maroon">z</font> <a href="hidden.html#R2">in</a> <font color="Maroon">I</font> )
 ;<br/>
<b>consider </b><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="E6:35_1"/><i><font color="Green">E28</font></i>: 
<font color="Maroon">t</font> <a href="hidden.html#R2">in</a> <font color="Maroon">I</font>
 <b>and </b><br/><a NAME="E7:35_1"/><i><font color="Green">E29</font></i>: 
( <font color="Maroon">t</font> <a href="orders_2.html#NR2" target="_self">&gt;=</a> <font color="Maroon">y</font> &amp; <font color="Maroon">t</font> <a href="orders_2.html#NR2" target="_self">&gt;=</a> <font color="Maroon">z</font> )
 <b>by </b><i>, <a class="ref" href="waybel_0.html#D1">WAYBEL_0:def 1</a></i>;<br/>
<a NAME="E8:35_1"/>
<font color="Maroon">y</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">z</font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">t</font>
 
<b>by </b><i>, <a class="ref" href="yellow_0.html#T22">YELLOW_0:22</a></i>;<br/>
<b>hence </b><a NAME="E9:35_1"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">I</font>
 <b>by </b><i><a class="txt" href="waybel12.html#E1"><i><font color="Green">Lemma18</font></i></a>, , <a class="ref" href="waybel_0.html#D19">WAYBEL_0:def 19</a></i>;<br/>


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

<b>thus </b><a NAME="E2:35"/>
<font color="Maroon">I</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">I</font> <a href="yellow_4.html#K2">"\/"</a> <font color="Maroon">I</font>
 <b>by </b><i><a class="ref" href="yellow_4.html#T13">YELLOW_4:13</a></i>;<br/>


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