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<b>let </b><font color="Maroon">R</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#V4">antisymmetric</a> <a href="waybel_0.html#V24">up-complete</a>  <a href="waybel_9.html#L1">TopRelStr</a> ;<br/><b>let </b><font color="Maroon">S</font> be  non <a href="xboole_0.html#V1">empty</a> <a href="waybel_0.html#V1">directed</a> <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">R</font>;<br/><b>let </b><font color="Maroon">a</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">R</font>;<br/>





<b>assume </b><a NAME="E1:26"/><i><font color="Green">E32</font></i>: 
<font color="Maroon">a</font> <a href="hidden.html#R2">in</a> <font color="Maroon">S</font>
 ;<br/>

<a NAME="E2:26"/>
 <a href="yellow_0.html#R1">ex_sup_of</a> <font color="Maroon">S</font>,<font color="Maroon">R</font>
 
<b>by </b><i><a class="ref" href="waybel_0.html#T75">WAYBEL_0:75</a></i>;<br/>
<a NAME="E3:26"/><b>then </b>
<font color="Maroon">S</font> <a href="lattice3.html#R2">is_&lt;=_than</a>  <a href="yellow_0.html#K1">"\/"</a> <font color="Maroon">S</font>,<font color="Maroon">R</font>
 
<b>by </b><i><a class="ref" href="yellow_0.html#T30">YELLOW_0:30</a></i>;<br/>
<b>hence </b><a NAME="E4:26"/>
<font color="Maroon">a</font> <a href="orders_2.html#R3">&lt;=</a>  <a href="yellow_0.html#K1">"\/"</a> <font color="Maroon">S</font>,<font color="Maroon">R</font>
 <b>by </b><i>, <a class="ref" href="lattice3.html#D9">LATTICE3:def 9</a></i>;<br/>


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