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<b>let </b><font color="Maroon" title="c1">L</font> be  non <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a> <a href="orders_2.html#V3" title="ORDERS_2:attr.3">reflexive</a> <a href="orders_2.html#V4" title="ORDERS_2:attr.4">transitive</a>  <a href="orders_2.html#L1" title="ORDERS_2:struct.1">RelStr</a> ;<br/><b>let </b><font color="Maroon" title="c2">X</font> be   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">L</font>;<br/>



<a NAME="E1:76"/>
for <font color="Olive" title="b1">x</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">L</font> holds <br/> ( <font color="Olive" title="b1">x</font> <a href="lattice3.html#R1" title="LATTICE3:pred.1">is_&lt;=_than</a> <font color="Maroon" title="c2">X</font> iff <font color="Olive" title="b1">x</font> <a href="lattice3.html#R1" title="LATTICE3:pred.1">is_&lt;=_than</a>  <a href="waybel_0.html#K4" title="WAYBEL_0:func.4">uparrow</a> <font color="Maroon" title="c2">X</font> )
 
<b>by </b><i><a class="ref" href="waybel_0.html#T36" target="_self" title="WAYBEL_0:th.36">Th36</a></i>;<br/>
<b>hence </b><a NAME="E2:76"/>
(  <a href="yellow_0.html#R2" title="YELLOW_0:pred.2">ex_inf_of</a> <font color="Maroon" title="c2">X</font>,<font color="Maroon" title="c1">L</font> iff  <a href="yellow_0.html#R2" title="YELLOW_0:pred.2">ex_inf_of</a>  <a href="waybel_0.html#K4" title="WAYBEL_0:func.4">uparrow</a> <font color="Maroon" title="c2">X</font>,<font color="Maroon" title="c1">L</font> )
 <b>by </b><i><a class="ref" href="yellow_0.html#T48" title="YELLOW_0:th.48">YELLOW_0:48</a></i>;<br/>


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