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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">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>set </b><font color="Maroon">R</font> = <font color="Maroon">L</font> <a href="waybel_4.html#K1" target="_self">-waybelow</a> ;<br/>
<b>assume </b><a NAME="E1:116"/>
<font color="Maroon">x</font> <a href="waybel_3.html#NR2" target="_self">&lt;&lt;</a> <font color="Maroon">y</font>
 ;<br/>

<a NAME="E2:116"/><b>then </b>
<span class="p1"><a href="domain_1.html#K1">[</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">y</font></span><a href="domain_1.html#K1">]</a></span> <a href="hidden.html#R2">in</a> <font color="Maroon">L</font> <a href="waybel_4.html#K1" target="_self">-waybelow</a> 
 
<b>by </b><i/>;<br/>
<b>then consider </b><font color="Maroon">x'</font> being   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L</font><b> such that </b><br/><a NAME="E4:116"/><i><font color="Green">E31</font></i>: 
( <span class="p1"><a href="domain_1.html#K1">[</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">x'</font></span><a href="domain_1.html#K1">]</a></span> <a href="hidden.html#R2">in</a> <font color="Maroon">L</font> <a href="waybel_4.html#K1" target="_self">-waybelow</a>  &amp; <span class="p1"><a href="domain_1.html#K1">[</a><span class="default"><font color="Maroon">x'</font>,<font color="Maroon">y</font></span><a href="domain_1.html#K1">]</a></span> <a href="hidden.html#R2">in</a> <font color="Maroon">L</font> <a href="waybel_4.html#K1" target="_self">-waybelow</a>  )
 <b>by </b><i/>;<br/>
<a NAME="E5:116"/>
( <font color="Maroon">x</font> <a href="waybel_3.html#NR2" target="_self">&lt;&lt;</a> <font color="Maroon">x'</font> &amp; <font color="Maroon">x'</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="waybel_4.html#T11" target="_self">Th11</a>, </i>;<br/>
<b>hence </b><a NAME="E6:116"/>
 ex <font color="Olive">x'</font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L</font> st <br/>( <font color="Maroon">x</font> <a href="waybel_3.html#NR2" target="_self">&lt;&lt;</a> <font color="Olive">x'</font> &amp; <font color="Olive">x'</font> <a href="waybel_3.html#NR2" target="_self">&lt;&lt;</a> <font color="Maroon">y</font> )
 ;<br/>


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