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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#V2">reflexive</a> <a href="orders_2.html#V3">transitive</a>  <a href="orders_2.html#L1">RelStr</a> ;<br/><b>let </b><font color="Maroon">X</font> be   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">L</font>;<br/>



<a NAME="E1:77"/>
for <font color="Olive">x</font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L</font> holds <br/> ( <font color="Olive">x</font> <a href="lattice3.html#R1">is_&lt;=_than</a> <font color="Maroon">X</font> iff <font color="Olive">x</font> <a href="lattice3.html#R1">is_&lt;=_than</a>  <a href="waybel_0.html#K4" target="_self">uparrow</a> <font color="Maroon">X</font> )
 
<b>by </b><i/>;<br/>
<b>hence </b><a NAME="E2:77"/>
(  <a href="yellow_0.html#R2">ex_inf_of</a> <font color="Maroon">X</font>,<font color="Maroon">L</font> implies  <a href="yellow_0.html#NK4" target="_self">inf</a> <font color="Maroon">X</font> <a href="hidden.html#R1">=</a>  <a href="yellow_0.html#NK4" target="_self">inf</a> <span class="p1">(<span class="default"><a href="waybel_0.html#K4" target="_self">uparrow</a> <font color="Maroon">X</font></span>)</span> )
 <b>by </b><i><a class="ref" href="yellow_0.html#T49">YELLOW_0:49</a></i>;<br/>


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