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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#V1" target="_self">auxiliary(i)</a> <a href="waybel_4.html#V3" target="_self">auxiliary(iii)</a> <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="E1:112"/><i><font color="Green">E68</font></i>: 
( <span class="p1"><a href="domain_1.html#K1">[</a><span class="default"><font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</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; <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>3</sub></font> )
 ;<br/>

<a NAME="E2:112"/><b>then </b>
<font color="Maroon">c<sub>2</sub></font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">c<sub>3</sub></font>
 
<b>by </b><i><a class="ref" href="waybel_4.html#D4" target="_self">Def4</a></i>;<br/>
<a NAME="E3:112"/><b>then </b>
<font color="Maroon">c<sub>2</sub></font> <a href="orders_2.html#R2">&lt;</a> <font color="Maroon">c<sub>3</sub></font>
 
<b>by </b><i><a class="txt" href="waybel_4.html#E1:112"><i><font color="Green">E68</font></i></a>, <a class="ref" href="orders_2.html#D10">ORDERS_2:def 10</a></i>;<br/>
<a NAME="E4:112"/><b>then </b>
not <font color="Maroon">c<sub>3</sub></font> <a href="orders_2.html#R2">&lt;</a> <font color="Maroon">c<sub>2</sub></font>
 
<b>by </b><i><a class="ref" href="orders_2.html#T28">ORDERS_2:28</a></i>;<br/>
<a NAME="E5:112"/><b>then </b>
not <font color="Maroon">c<sub>3</sub></font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">c<sub>2</sub></font>
 
<b>by </b><i><a class="txt" href="waybel_4.html#E1:112"><i><font color="Green">E68</font></i></a>, <a class="ref" href="orders_2.html#D10">ORDERS_2:def 10</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="E7:112"/><i><font color="Green">E69</font></i>: 
( <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>3</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>2</sub></font> )
 <b>by </b><i><a class="ref" href="waybel_4.html#T49" target="_self">Th49</a></i>;<br/>
<b>take </b><font color="Maroon">c<sub>6</sub></font> = <font color="Maroon">c<sub>2</sub></font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">c<sub>5</sub></font>;<br/>

<b>thus </b><a NAME="E8:112"/>
<font color="Maroon">c<sub>2</sub></font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">c<sub>6</sub></font>
 <b>by </b><i><a class="ref" href="yellow_0.html#T22">YELLOW_0:22</a></i>;<br/>

<b>thus </b><a NAME="E9:112"/>
<span class="p1"><a href="domain_1.html#K1">[</a><span class="default"><font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>3</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>
 <b>by </b><i><a class="txt" href="waybel_4.html#E1:112"><i><font color="Green">E68</font></i></a>, <a class="txt" href="waybel_4.html#E7:112"><i><font color="Green">E69</font></i></a>, <a class="ref" href="waybel_4.html#D6" target="_self">Def6</a></i>;<br/>

<b>thus </b><a NAME="E10:112"/>
<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>6</sub></font>
 <b>by </b><i><a class="txt" href="waybel_4.html#E7:112"><i><font color="Green">E69</font></i></a>, <a class="ref" href="yellow_0.html#T24">YELLOW_0:24</a></i>;<br/>


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