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<b>let </b><font color="Maroon">L</font> be  <a href="yellow_0.html#V1">lower-bounded</a> <a href="waybel_3.html#V3">continuous</a> <a href="waybel_0.html#NM8">LATTICE</a>;<br/><b>let </b><font color="Maroon">B</font> be   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">L</font>;<br/>



<b>assume </b><a NAME="E1:78"/><i><font color="Green">E31</font></i>: 
for <font color="Olive">x</font>, <font color="Olive">y</font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L</font>  st not <font color="Olive">y</font> <a href="orders_2.html#R3">&lt;=</a> <font color="Olive">x</font> holds <br/> ex <font color="Olive">b</font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L</font> st <br/>( <font color="Olive">b</font> <a href="hidden.html#R2">in</a> <font color="Maroon">B</font> &amp; not <font color="Olive">b</font> <a href="orders_2.html#R3">&lt;=</a> <font color="Olive">x</font> &amp; <font color="Olive">b</font> <a href="orders_2.html#R3">&lt;=</a> <font color="Olive">y</font> )
 ;<br/>

<b>let </b><font color="Maroon">x</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L</font>, <font color="Maroon">y</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L</font>;<br/>

<b>assume </b><a NAME="E2:78"/><i><font color="Green">E33</font></i>: 
not <font color="Maroon">y</font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">x</font>
 ;<br/>

<a NAME="E3:78"/>
for <font color="Olive">z</font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L</font> holds <br/> ( not  <a href="waybel_3.html#K1">waybelow</a> <font color="Olive">z</font> is <a href="xboole_0.html#V1">empty</a> &amp;  <a href="waybel_3.html#K1">waybelow</a> <font color="Olive">z</font> is <a href="waybel_0.html#V1">directed</a> )
 
;<br/>
<b>then consider </b><font color="Maroon">y1</font> being   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L</font><b> such that </b><br/><a NAME="E5:78"/><i><font color="Green">E35</font></i>: 
<font color="Maroon">y1</font> <a href="waybel_3.html#NR2" target="_self">&lt;&lt;</a> <font color="Maroon">y</font>
 <b>and </b><br/><a NAME="E6:78"/><i><font color="Green">E36</font></i>: 
not <font color="Maroon">y1</font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">x</font>
 <b>by </b><i>, <a class="ref" href="waybel_3.html#T24">WAYBEL_3:24</a></i>;<br/>
<b>consider </b><font color="Maroon">b</font> being   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L</font><b> such that </b><br/><a NAME="E8:78"/><i><font color="Green">E48</font></i>: 
<font color="Maroon">b</font> <a href="hidden.html#R2">in</a> <font color="Maroon">B</font>
 <b>and </b><br/><a NAME="E9:78"/><i><font color="Green">E50</font></i>: 
not <font color="Maroon">b</font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">x</font>
 <b>and </b><br/><a NAME="E10:78"/><i><font color="Green">E52</font></i>: 
<font color="Maroon">b</font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">y1</font>
 <b>by </b><i><a class="ref" href="waybel23.html#T2" target="_self">Th2</a>, <a class="ref" href="waybel23.html#T3" target="_self">Th3</a></i>;<br/>
<b>take </b>
<font color="Maroon">b</font>
;<br/>

<b>thus </b><a NAME="E11:78"/>
( <font color="Maroon">b</font> <a href="hidden.html#R2">in</a> <font color="Maroon">B</font> &amp; not <font color="Maroon">b</font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">x</font> &amp; <font color="Maroon">b</font> <a href="waybel_3.html#NR2" target="_self">&lt;&lt;</a> <font color="Maroon">y</font> )
 <b>by </b><i>, , , <a class="ref" href="waybel23.html#T5" target="_self">Th5</a>, <a class="ref" href="waybel_3.html#T2">WAYBEL_3:2</a></i>;<br/>


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