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<b>let </b><font color="Maroon">L</font> be  <a href="lattice3.html#V3">complete</a> <a href="waybel_0.html#NM8">LATTICE</a>;<br/><b>let </b><font color="Maroon">a</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L</font>;<br/><b>let </b><font color="Maroon">b</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L</font>;<br/>





<b>assume </b><b>that </b><br/><a NAME="E1:34"/><i><font color="Green">E34</font></i>: 
<font color="Maroon">L</font> is <a href="waybel_3.html#V3">continuous</a>
 <b>and </b><br/><a NAME="E2:34"/><i><font color="Green">E36</font></i>: 
for <font color="Olive">c</font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L</font>  st <font color="Olive">c</font> <a href="waybel_3.html#NR2" target="_self">&lt;&lt;</a> <font color="Maroon">a</font> holds <br/><font color="Olive">c</font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">b</font>
 ;<br/>

<a NAME="E3:34"/><i><font color="Green">E38</font></i>: 
( <font color="Maroon">L</font> is <a href="lattice3.html#V3">complete</a> &amp; <font color="Maroon">L</font> is <a href="waybel_3.html#V2">satisfying_axiom_of_approximation</a> )
 
<b>by </b><i>, <a class="ref" href="waybel_3.html#D6">WAYBEL_3:def 6</a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="34_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">c</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L</font>;<br/><b>assume </b><a NAME="E1:34_1"/>
<font color="Maroon">c</font> <a href="hidden.html#R2">in</a>  <a href="waybel_3.html#K1">waybelow</a> <font color="Maroon">a</font>
 ;<br/><a NAME="E2:34_1"/><b>then </b>
<font color="Maroon">c</font> <a href="waybel_3.html#NR2" target="_self">&lt;&lt;</a> <font color="Maroon">a</font>
 <b>by </b><i><a class="ref" href="waybel_3.html#T7">WAYBEL_3:7</a></i>;<br/><b>hence </b><a NAME="E3:34_1"/>
<font color="Maroon">c</font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">b</font>
 <b>by </b><i/>;<br/></div><b>end;</b></div>
<a NAME="E5:34"/><b>then </b>
 <a href="waybel_3.html#K1">waybelow</a> <font color="Maroon">a</font> <a href="lattice3.html#R2">is_&lt;=_than</a> <font color="Maroon">b</font>
 
<b>by </b><i><a class="ref" href="lattice3.html#D9">LATTICE3:def 9</a></i>;<br/>
<a NAME="E6:34"/><b>then </b>
 <a href="yellow_0.html#NK3" target="_self">sup</a> <span class="p1">(<span class="default"><a href="waybel_3.html#K1">waybelow</a> <font color="Maroon">a</font></span>)</span> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">b</font>
 
<b>by </b><i><a class="ref" href="yellow_0.html#T32">YELLOW_0:32</a></i>;<br/>
<b>hence </b><a NAME="E7:34"/>
<font color="Maroon">a</font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">b</font>
 <b>by </b><i>, <a class="ref" href="waybel_3.html#D5">WAYBEL_3:def 5</a></i>;<br/>


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