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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#NM1">Poset</a>;<br/><b>let </b><font color="Maroon">D</font> be  non <a href="xboole_0.html#V1">empty</a> <a href="finset_1.html#V1">finite</a> <a href="waybel_0.html#V2">filtered</a> <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">L</font>;<br/>



<b>assume </b><a NAME="E1:18"/><i><font color="Green">E25</font></i>: 
 <a href="yellow_0.html#R2">ex_inf_of</a> <font color="Maroon">D</font>,<font color="Maroon">L</font>
 ;<br/>

<a NAME="E2:18"/>
<font color="Maroon">D</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">D</font>
 
;<br/>
<b>then consider </b><font color="Maroon">d</font> being   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L</font><b> such that </b><br/><a NAME="E4:18"/><i><font color="Green">E26</font></i>: 
( <font color="Maroon">d</font> <a href="hidden.html#R2">in</a> <font color="Maroon">D</font> &amp; <font color="Maroon">d</font> <a href="lattice3.html#R1">is_&lt;=_than</a> <font color="Maroon">D</font> )
 <b>by </b><i><a class="ref" href="waybel_0.html#T2">WAYBEL_0:2</a></i>;<br/>
<a NAME="E5:18"/>
 <a href="yellow_0.html#NK4" target="_self">inf</a> <font color="Maroon">D</font> <a href="lattice3.html#R1">is_&lt;=_than</a> <font color="Maroon">D</font>
 
<b>by </b><i>, <a class="ref" href="yellow_0.html#T31">YELLOW_0:31</a></i>;<br/>
<a NAME="E6:18"/><b>then </b>
(  <a href="yellow_0.html#NK4" target="_self">inf</a> <font color="Maroon">D</font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">d</font> &amp;  <a href="yellow_0.html#NK4" target="_self">inf</a> <font color="Maroon">D</font> <a href="orders_2.html#NR2" target="_self">&gt;=</a> <font color="Maroon">d</font> )
 
<b>by </b><i>, , <a class="ref" href="lattice3.html#D8">LATTICE3:def 8</a>, <a class="ref" href="yellow_0.html#T31">YELLOW_0:31</a></i>;<br/>
<b>hence </b><a NAME="E7:18"/>
 <a href="yellow_0.html#NK4" target="_self">inf</a> <font color="Maroon">D</font> <a href="hidden.html#R2">in</a> <font color="Maroon">D</font>
 <b>by </b><i>, <a class="ref" href="orders_2.html#T25">ORDERS_2:25</a></i>;<br/>


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