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<b>let </b><font color="Maroon">c<sub>1</sub></font> be  <a href="lattice3.html#V3">complete</a> <a href="waybel_0.html#NM8">LATTICE</a>;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font>, <font color="Maroon">c<sub>3</sub></font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>1</sub></font>;<br/><b>let </b><font color="Maroon">c<sub>4</sub></font> be  <a href="waybel_4.html#V6" target="_self">approximating</a> <a href="alg_1.html#NM1">Relation</a> of <font color="Maroon">c<sub>1</sub></font>;<br/>







<b>assume </b><a NAME="E1:111"/><i><font color="Green">E67</font></i>: 
not <font color="Maroon">c<sub>2</sub></font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">c<sub>3</sub></font>
 ;<br/>

<a NAME="E2:111"/>
( <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a>  <a href="yellow_0.html#NK3" target="_self">sup</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="waybel_4.html#K5" target="_self">-below</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> &amp;  <a href="yellow_0.html#R1">ex_sup_of</a> <font color="Maroon">c<sub>4</sub></font> <a href="waybel_4.html#K5" target="_self">-below</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>1</sub></font> )
 
<b>by </b><i><a class="ref" href="waybel_4.html#D18" target="_self">Def18</a>, <a class="ref" href="yellow_0.html#T17">YELLOW_0:17</a></i>;<br/>
<a NAME="E3:111"/><b>then </b>
( <font color="Maroon">c<sub>3</sub></font> <a href="lattice3.html#NR4" target="_self">is_&gt;=_than</a> <font color="Maroon">c<sub>4</sub></font> <a href="waybel_4.html#K5" target="_self">-below</a> <font color="Maroon">c<sub>2</sub></font> implies <font color="Maroon">c<sub>3</sub></font> <a href="orders_2.html#NR2" target="_self">&gt;=</a> <font color="Maroon">c<sub>2</sub></font> )
 
<b>by </b><i><a class="ref" href="yellow_0.html#D9">YELLOW_0:def 9</a></i>;<br/>
<b>then consider </b><font color="Maroon">c<sub>5</sub></font> being   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>1</sub></font><b> such that </b><br/><a NAME="E5:111"/><i><font color="Green">E68</font></i>: 
( <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>4</sub></font> <a href="waybel_4.html#K5" target="_self">-below</a> <font color="Maroon">c<sub>2</sub></font> &amp; not <font color="Maroon">c<sub>5</sub></font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">c<sub>3</sub></font> )
 <b>by </b><i><a class="txt" href="waybel_4.html#E1:111"><i><font color="Green">E67</font></i></a>, <a class="ref" href="lattice3.html#D9">LATTICE3:def 9</a></i>;<br/>
<b>take </b>
<font color="Maroon">c<sub>5</sub></font>
;<br/>

<b>thus </b><a NAME="E6:111"/>
( <span class="p1"><a href="domain_1.html#K1">[</a><span class="default"><font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>2</sub></font></span><a href="domain_1.html#K1">]</a></span> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>4</sub></font> &amp; not <font color="Maroon">c<sub>5</sub></font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">c<sub>3</sub></font> )
 <b>by </b><i><a class="txt" href="waybel_4.html#E5:111"><i><font color="Green">E68</font></i></a>, <a class="ref" href="waybel_4.html#T13" target="_self">Th13</a></i>;<br/>


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