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<b>let </b><font color="Maroon" title="c2">x</font>, <font color="Maroon" title="c3">y</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c1">L</font> <a href="lattice3.html#K7" title="LATTICE3:func.7">~</a> </span>)</span>; <i><font color="Red">:: according to </font></i><a class="ref" href="waybel_0.html#D29" target="_self" title="WAYBEL_0:def.29">WAYBEL_0:def 29</a> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c2">x</font> <a href="orders_2.html#R1" title="ORDERS_2:pred.1">&lt;=</a> <font color="Maroon" title="c3">y</font> or <font color="Maroon" title="c3">y</font> <a href="orders_2.html#R1" title="ORDERS_2:pred.1">&lt;=</a> <font color="Maroon" title="c2">x</font> )</span><br/>

<a NAME="E1:117_1_1"/><i><font color="Green" title="E53">A1</font></i>: 
(  <a href="lattice3.html#K9" title="LATTICE3:func.9">~</a> <font color="Maroon" title="c2">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">x</font> &amp;  <a href="lattice3.html#K9" title="LATTICE3:func.9">~</a> <font color="Maroon" title="c3">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">y</font> &amp; <span class="p1">(<span class="default"><a href="lattice3.html#K9" title="LATTICE3:func.9">~</a> <font color="Maroon" title="c2">x</font></span>)</span> <a href="lattice3.html#K8" title="LATTICE3:func.8">~</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="lattice3.html#K9" title="LATTICE3:func.9">~</a> <font color="Maroon" title="c2">x</font> &amp; <span class="p1">(<span class="default"><a href="lattice3.html#K9" title="LATTICE3:func.9">~</a> <font color="Maroon" title="c3">y</font></span>)</span> <a href="lattice3.html#K8" title="LATTICE3:func.8">~</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="lattice3.html#K9" title="LATTICE3:func.9">~</a> <font color="Maroon" title="c3">y</font> )
 
;<br/>
<a NAME="E2:117_1_1"/>
(  <a href="lattice3.html#K9" title="LATTICE3:func.9">~</a> <font color="Maroon" title="c2">x</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a>  <a href="lattice3.html#K9" title="LATTICE3:func.9">~</a> <font color="Maroon" title="c3">y</font> or  <a href="lattice3.html#K9" title="LATTICE3:func.9">~</a> <font color="Maroon" title="c2">x</font> <a href="orders_2.html#NR2" title="ORDERS_2:NR.2">&gt;=</a>  <a href="lattice3.html#K9" title="LATTICE3:func.9">~</a> <font color="Maroon" title="c3">y</font> )
 
<b>by </b><i><a class="ref" href="waybel_0.html#D29" target="_self" title="WAYBEL_0:def.29">Def29</a></i>;<br/>
<b>hence </b><a NAME="E3:117_1_1"/>
( <font color="Maroon" title="c2">x</font> <a href="orders_2.html#R1" title="ORDERS_2:pred.1">&lt;=</a> <font color="Maroon" title="c3">y</font> or <font color="Maroon" title="c3">y</font> <a href="orders_2.html#R1" title="ORDERS_2:pred.1">&lt;=</a> <font color="Maroon" title="c2">x</font> )
 <b>by </b><i><a class="txt" href="waybel_0.html#E1:117_1_1"><i><font color="Green" title="E53">A1</font></i></a>, <a class="ref" href="lattice3.html#T9" title="LATTICE3:th.9">LATTICE3:9</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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