<?xml version="1.0"?>
<div class="add">

<b>let </b><font color="Maroon">L</font> be   <a href="waybel_0.html#NM8">LATTICE</a>;<br/>

<b>assume </b><a NAME="E1:20"/><i><font color="Green">E35</font></i>: 
<font color="Maroon">L</font> is <a href="yellow11.html#V1" target="_self">modular</a>
 ;<br/>

<b>thus </b><a NAME="E2:20"/>
( <font color="Maroon">L</font> is <a href="waybel_1.html#V2">distributive</a> implies for <font color="Olive">a</font>, <font color="Olive">b</font>, <font color="Olive">c</font>, <font color="Olive">d</font>, <font color="Olive">e</font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L</font>  holds <br/>(  not <font color="Olive">a</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Olive">b</font> or  not <font color="Olive">a</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Olive">c</font> or  not <font color="Olive">a</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Olive">d</font> or  not <font color="Olive">a</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Olive">e</font> or  not <font color="Olive">b</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Olive">c</font> or  not <font color="Olive">b</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Olive">d</font> or  not <font color="Olive">b</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Olive">e</font> or  not <font color="Olive">c</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Olive">d</font> or  not <font color="Olive">c</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Olive">e</font> or  not <font color="Olive">d</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Olive">e</font> or  not <font color="Olive">a</font> <a href="lattice3.html#K12">"/\"</a> <font color="Olive">b</font> <a href="hidden.html#R1">=</a> <font color="Olive">a</font> or  not <font color="Olive">a</font> <a href="lattice3.html#K12">"/\"</a> <font color="Olive">c</font> <a href="hidden.html#R1">=</a> <font color="Olive">a</font> or  not <font color="Olive">a</font> <a href="lattice3.html#K12">"/\"</a> <font color="Olive">d</font> <a href="hidden.html#R1">=</a> <font color="Olive">a</font> or  not <font color="Olive">b</font> <a href="lattice3.html#K12">"/\"</a> <font color="Olive">e</font> <a href="hidden.html#R1">=</a> <font color="Olive">b</font> or  not <font color="Olive">c</font> <a href="lattice3.html#K12">"/\"</a> <font color="Olive">e</font> <a href="hidden.html#R1">=</a> <font color="Olive">c</font> or  not <font color="Olive">d</font> <a href="lattice3.html#K12">"/\"</a> <font color="Olive">e</font> <a href="hidden.html#R1">=</a> <font color="Olive">d</font> or  not <font color="Olive">b</font> <a href="lattice3.html#K12">"/\"</a> <font color="Olive">c</font> <a href="hidden.html#R1">=</a> <font color="Olive">a</font> or  not <font color="Olive">b</font> <a href="lattice3.html#K12">"/\"</a> <font color="Olive">d</font> <a href="hidden.html#R1">=</a> <font color="Olive">a</font> or  not <font color="Olive">c</font> <a href="lattice3.html#K12">"/\"</a> <font color="Olive">d</font> <a href="hidden.html#R1">=</a> <font color="Olive">a</font> or  not <font color="Olive">b</font> <a href="lattice3.html#K13">"\/"</a> <font color="Olive">c</font> <a href="hidden.html#R1">=</a> <font color="Olive">e</font> or  not <font color="Olive">b</font> <a href="lattice3.html#K13">"\/"</a> <font color="Olive">d</font> <a href="hidden.html#R1">=</a> <font color="Olive">e</font> or  not <font color="Olive">c</font> <a href="lattice3.html#K13">"\/"</a> <font color="Olive">d</font> <a href="hidden.html#R1">=</a> <font color="Olive">e</font> ) )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="20_1"><b>proof </b></a><div class="add">

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="20_1_1"><b>now </b></a><div class="add"><b>given </b><font color="Maroon">a</font> being   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L</font>, <font color="Maroon">b</font> being   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L</font>, <font color="Maroon">c</font> being   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L</font>, <font color="Maroon">d</font> being   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L</font>, <font color="Maroon">e</font> being   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L</font><b> such that </b><a NAME="E1:20_1_1"/><i><font color="Green">E36</font></i>: 
( <font color="Maroon">a</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">b</font> &amp; <font color="Maroon">a</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c</font> &amp; <font color="Maroon">a</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">d</font> &amp; <font color="Maroon">a</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">e</font> &amp; <font color="Maroon">b</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c</font> &amp; <font color="Maroon">b</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">d</font> &amp; <font color="Maroon">b</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">e</font> &amp; <font color="Maroon">c</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">d</font> &amp; <font color="Maroon">c</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">e</font> &amp; <font color="Maroon">d</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">e</font> )
 <b>and </b><br/><a NAME="E2:20_1_1"/><i><font color="Green">E37</font></i>: 
( <font color="Maroon">a</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">b</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a</font> &amp; <font color="Maroon">a</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">c</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a</font> &amp; <font color="Maroon">a</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">d</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a</font> &amp; <font color="Maroon">b</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">e</font> <a href="hidden.html#R1">=</a> <font color="Maroon">b</font> &amp; <font color="Maroon">c</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">e</font> <a href="hidden.html#R1">=</a> <font color="Maroon">c</font> &amp; <font color="Maroon">d</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">e</font> <a href="hidden.html#R1">=</a> <font color="Maroon">d</font> &amp; <font color="Maroon">b</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">c</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a</font> &amp; <font color="Maroon">b</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">d</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a</font> &amp; <font color="Maroon">c</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">d</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a</font> &amp; <font color="Maroon">b</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">c</font> <a href="hidden.html#R1">=</a> <font color="Maroon">e</font> &amp; <font color="Maroon">b</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">d</font> <a href="hidden.html#R1">=</a> <font color="Maroon">e</font> &amp; <font color="Maroon">c</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">d</font> <a href="hidden.html#R1">=</a> <font color="Maroon">e</font> )
 ;<br/><a NAME="E3:20_1_1"/>
<span class="p1">(<span class="default"><font color="Maroon">b</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">c</font></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p1">(<span class="default"><font color="Maroon">b</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">d</font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">a</font>
 <b>by </b><i>, <a class="ref" href="yellow_5.html#T1">YELLOW_5:1</a></i>;<br/><b>hence </b><a NAME="E4:20_1_1"/>
not <font color="Maroon">L</font> is <a href="waybel_1.html#V2">distributive</a>
 <b>by </b><i>, , <a class="ref" href="waybel_1.html#D3">WAYBEL_1:def 3</a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E2:20_1"/>
( <font color="Maroon">L</font> is <a href="waybel_1.html#V2">distributive</a> implies for <font color="Olive">a</font>, <font color="Olive">b</font>, <font color="Olive">c</font>, <font color="Olive">d</font>, <font color="Olive">e</font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L</font>  holds <br/>(  not <font color="Olive">a</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Olive">b</font> or  not <font color="Olive">a</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Olive">c</font> or  not <font color="Olive">a</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Olive">d</font> or  not <font color="Olive">a</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Olive">e</font> or  not <font color="Olive">b</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Olive">c</font> or  not <font color="Olive">b</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Olive">d</font> or  not <font color="Olive">b</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Olive">e</font> or  not <font color="Olive">c</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Olive">d</font> or  not <font color="Olive">c</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Olive">e</font> or  not <font color="Olive">d</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Olive">e</font> or  not <font color="Olive">a</font> <a href="lattice3.html#K12">"/\"</a> <font color="Olive">b</font> <a href="hidden.html#R1">=</a> <font color="Olive">a</font> or  not <font color="Olive">a</font> <a href="lattice3.html#K12">"/\"</a> <font color="Olive">c</font> <a href="hidden.html#R1">=</a> <font color="Olive">a</font> or  not <font color="Olive">a</font> <a href="lattice3.html#K12">"/\"</a> <font color="Olive">d</font> <a href="hidden.html#R1">=</a> <font color="Olive">a</font> or  not <font color="Olive">b</font> <a href="lattice3.html#K12">"/\"</a> <font color="Olive">e</font> <a href="hidden.html#R1">=</a> <font color="Olive">b</font> or  not <font color="Olive">c</font> <a href="lattice3.html#K12">"/\"</a> <font color="Olive">e</font> <a href="hidden.html#R1">=</a> <font color="Olive">c</font> or  not <font color="Olive">d</font> <a href="lattice3.html#K12">"/\"</a> <font color="Olive">e</font> <a href="hidden.html#R1">=</a> <font color="Olive">d</font> or  not <font color="Olive">b</font> <a href="lattice3.html#K12">"/\"</a> <font color="Olive">c</font> <a href="hidden.html#R1">=</a> <font color="Olive">a</font> or  not <font color="Olive">b</font> <a href="lattice3.html#K12">"/\"</a> <font color="Olive">d</font> <a href="hidden.html#R1">=</a> <font color="Olive">a</font> or  not <font color="Olive">c</font> <a href="lattice3.html#K12">"/\"</a> <font color="Olive">d</font> <a href="hidden.html#R1">=</a> <font color="Olive">a</font> or  not <font color="Olive">b</font> <a href="lattice3.html#K13">"\/"</a> <font color="Olive">c</font> <a href="hidden.html#R1">=</a> <font color="Olive">e</font> or  not <font color="Olive">b</font> <a href="lattice3.html#K13">"\/"</a> <font color="Olive">d</font> <a href="hidden.html#R1">=</a> <font color="Olive">e</font> or  not <font color="Olive">c</font> <a href="lattice3.html#K13">"\/"</a> <font color="Olive">d</font> <a href="hidden.html#R1">=</a> <font color="Olive">e</font> ) )
 ;<br/>


</div><b>end;</b></div>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="20_2"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:20_2"/>
not <font color="Maroon">L</font> is <a href="waybel_1.html#V2">distributive</a>
 ;<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>, <font color="Maroon">y</font> being   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L</font>, <font color="Maroon">z</font> being   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L</font><b> such that </b><br/><a NAME="E3:20_2"/><i><font color="Green">E41</font></i>: 
<font color="Maroon">x</font> <a href="lattice3.html#K12">"/\"</a> <span class="p1">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">z</font></span>)</span> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <span class="p1">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">y</font></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p1">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">z</font></span>)</span>
 <b>by </b><i><a class="ref" href="waybel_1.html#D3">WAYBEL_1:def 3</a></i>;<br/><b>set </b><font color="Maroon">b</font> = <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">y</font></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p2">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">z</font></span>)</span></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p1">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">x</font></span>)</span>;<br/><b>set </b><font color="Maroon">t</font> = <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">y</font></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p2">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">z</font></span>)</span></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p1">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">x</font></span>)</span>;<br/><a NAME="E4:20_2"/><i><font color="Green">E42</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">y</font></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p2">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">z</font></span>)</span></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p1">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">x</font></span>)</span> <a href="orders_2.html#R3">&lt;=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">y</font></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p2">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">z</font></span>)</span></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p1">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">x</font></span>)</span>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="20_2_1"><b>proof </b></a><div class="add">

<a NAME="E1:20_2_1"/><i><font color="Green">E43</font></i>: 
( <font color="Maroon">x</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">y</font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">x</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">y</font> &amp; <font color="Maroon">x</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">y</font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">y</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">z</font> &amp; <font color="Maroon">x</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">y</font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">z</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">x</font> )
 
<b>by </b><i><a class="ref" href="yellow_5.html#T5">YELLOW_5:5</a></i>;<br/>
<a NAME="E2:20_2_1"/><i><font color="Green">E44</font></i>: 
( <font color="Maroon">y</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">z</font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">x</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">y</font> &amp; <font color="Maroon">y</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">z</font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">y</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">z</font> &amp; <font color="Maroon">y</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">z</font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">z</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">x</font> )
 
<b>by </b><i><a class="ref" href="yellow_5.html#T5">YELLOW_5:5</a></i>;<br/>
<a NAME="E3:20_2_1"/><i><font color="Green">E45</font></i>: 
( <font color="Maroon">z</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">x</font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">x</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">y</font> &amp; <font color="Maroon">z</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">x</font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">y</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">z</font> &amp; <font color="Maroon">z</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">x</font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">z</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">x</font> )
 
<b>by </b><i><a class="ref" href="yellow_5.html#T5">YELLOW_5:5</a></i>;<br/>
<a NAME="E4:20_2_1"/>
<span class="p1">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">y</font></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p1">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">y</font></span>)</span> <a href="orders_2.html#R3">&lt;=</a> <span class="p1">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">y</font></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p1">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">z</font></span>)</span>
 
<b>by </b><i>, <a class="ref" href="yellow_3.html#T2">YELLOW_3:2</a></i>;<br/>
<a NAME="E5:20_2_1"/><b>then </b>
<font color="Maroon">x</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">y</font> <a href="orders_2.html#R3">&lt;=</a> <span class="p1">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">y</font></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p1">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">z</font></span>)</span>
 
<b>by </b><i><a class="ref" href="yellow_5.html#T2">YELLOW_5:2</a></i>;<br/>
<a NAME="E6:20_2_1"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">y</font></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p1">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">y</font></span>)</span> <a href="orders_2.html#R3">&lt;=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">y</font></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p2">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">z</font></span>)</span></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p1">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">x</font></span>)</span>
 
<b>by </b><i>, <a class="ref" href="yellow_3.html#T2">YELLOW_3:2</a></i>;<br/>
<a NAME="E7:20_2_1"/><b>then </b><i><font color="Green">E49</font></i>: 
<font color="Maroon">x</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">y</font> <a href="orders_2.html#R3">&lt;=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">y</font></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p2">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">z</font></span>)</span></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p1">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">x</font></span>)</span>
 
<b>by </b><i><a class="ref" href="yellow_5.html#T2">YELLOW_5:2</a></i>;<br/>
<a NAME="E8:20_2_1"/>
<span class="p1">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">z</font></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p1">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">z</font></span>)</span> <a href="orders_2.html#R3">&lt;=</a> <span class="p1">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">y</font></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p1">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">z</font></span>)</span>
 
<b>by </b><i>, <a class="ref" href="yellow_3.html#T2">YELLOW_3:2</a></i>;<br/>
<a NAME="E9:20_2_1"/><b>then </b>
<font color="Maroon">y</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">z</font> <a href="orders_2.html#R3">&lt;=</a> <span class="p1">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">y</font></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p1">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">z</font></span>)</span>
 
<b>by </b><i><a class="ref" href="yellow_5.html#T2">YELLOW_5:2</a></i>;<br/>
<a NAME="E10:20_2_1"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">z</font></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p1">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">z</font></span>)</span> <a href="orders_2.html#R3">&lt;=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">y</font></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p2">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">z</font></span>)</span></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p1">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">x</font></span>)</span>
 
<b>by </b><i>, <a class="ref" href="yellow_3.html#T2">YELLOW_3:2</a></i>;<br/>
<a NAME="E11:20_2_1"/><b>then </b><i><font color="Green">E50</font></i>: 
<font color="Maroon">y</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">z</font> <a href="orders_2.html#R3">&lt;=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">y</font></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p2">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">z</font></span>)</span></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p1">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">x</font></span>)</span>
 
<b>by </b><i><a class="ref" href="yellow_5.html#T2">YELLOW_5:2</a></i>;<br/>
<a NAME="E12:20_2_1"/>
<span class="p1">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">x</font></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p1">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">x</font></span>)</span> <a href="orders_2.html#R3">&lt;=</a> <span class="p1">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">y</font></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p1">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">z</font></span>)</span>
 
<b>by </b><i>, <a class="ref" href="yellow_3.html#T2">YELLOW_3:2</a></i>;<br/>
<a NAME="E13:20_2_1"/><b>then </b>
<font color="Maroon">z</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">x</font> <a href="orders_2.html#R3">&lt;=</a> <span class="p1">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">y</font></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p1">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">z</font></span>)</span>
 
<b>by </b><i><a class="ref" href="yellow_5.html#T2">YELLOW_5:2</a></i>;<br/>
<a NAME="E14:20_2_1"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">x</font></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p1">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">x</font></span>)</span> <a href="orders_2.html#R3">&lt;=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">y</font></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p2">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">z</font></span>)</span></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p1">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">x</font></span>)</span>
 
<b>by </b><i>, <a class="ref" href="yellow_3.html#T2">YELLOW_3:2</a></i>;<br/>
<a NAME="E15:20_2_1"/><b>then </b><i><font color="Green">E51</font></i>: 
<font color="Maroon">z</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">x</font> <a href="orders_2.html#R3">&lt;=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">y</font></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p2">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">z</font></span>)</span></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p1">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">x</font></span>)</span>
 
<b>by </b><i><a class="ref" href="yellow_5.html#T2">YELLOW_5:2</a></i>;<br/>
<a NAME="E16:20_2_1"/>
<span class="p1">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">y</font></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p1">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">z</font></span>)</span> <a href="orders_2.html#R3">&lt;=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">y</font></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p3">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">z</font></span>)</span></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p2">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">x</font></span>)</span></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">y</font></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p3">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">z</font></span>)</span></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p2">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">x</font></span>)</span></span>)</span>
 
<b>by </b><i>, <a class="ref" href="yellow11.html#T1" target="_self">Th1</a>, <a class="ref" href="yellow_3.html#T3">YELLOW_3:3</a></i>;<br/>
<a NAME="E17:20_2_1"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">y</font></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p1">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">z</font></span>)</span> <a href="orders_2.html#R3">&lt;=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">y</font></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p2">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">z</font></span>)</span></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p1">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">x</font></span>)</span>
 
<b>by </b><i><a class="ref" href="yellow_5.html#T1">YELLOW_5:1</a></i>;<br/>
<a NAME="E18:20_2_1"/><b>then </b>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">y</font></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p2">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">z</font></span>)</span></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p1">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">x</font></span>)</span> <a href="orders_2.html#R3">&lt;=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">y</font></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p3">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">z</font></span>)</span></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p2">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">x</font></span>)</span></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">y</font></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p3">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">z</font></span>)</span></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p2">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">x</font></span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="yellow11.html#T2" target="_self">Th2</a>, <a class="ref" href="yellow_3.html#T3">YELLOW_3:3</a></i>;<br/>
<b>hence </b><a NAME="E19:20_2_1"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">y</font></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p2">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">z</font></span>)</span></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p1">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">x</font></span>)</span> <a href="orders_2.html#R3">&lt;=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">y</font></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p2">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">z</font></span>)</span></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p1">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">x</font></span>)</span>
 <b>by </b><i><a class="ref" href="yellow_5.html#T1">YELLOW_5:1</a></i>;<br/>


</div><b>end;</b></div><a NAME="E5:20_2"/><i><font color="Green">E52</font></i>: 
( <font color="Maroon">z</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">x</font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">x</font> &amp; <font color="Maroon">x</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">y</font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">x</font> )
 <b>by </b><i><a class="ref" href="yellow_0.html#T23">YELLOW_0:23</a></i>;<br/><a NAME="E6:20_2"/>
( <font color="Maroon">y</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">z</font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">z</font> &amp; <font color="Maroon">x</font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">x</font> )
 <b>by </b><i><a class="ref" href="yellow_0.html#T23">YELLOW_0:23</a></i>;<br/><a NAME="E7:20_2"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">z</font></span>)</span> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">x</font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">z</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">x</font>
 <b>by </b><i><a class="ref" href="yellow_3.html#T2">YELLOW_3:2</a></i>;<br/><a NAME="E8:20_2"/><b>then </b><i><font color="Green">E53</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">z</font></span>)</span> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">x</font></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p1">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">x</font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">z</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">x</font>
 <b>by </b><i><a class="ref" href="yellow_5.html#T8">YELLOW_5:8</a></i>;<br/><i><font color="Green">E54</font></i>: <font color="Maroon">x</font> <a href="lattice3.html#K12">"/\"</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">y</font></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p3">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">z</font></span>)</span></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p2">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">x</font></span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K12">"/\"</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">y</font></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p3">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">z</font></span>)</span></span>)</span></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p1">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">x</font></span>)</span>
<b>by </b><i><a class="ref" href="lattice3.html#T16">LATTICE3:16</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K12">"/\"</a> <span class="p3">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">y</font></span>)</span></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p2">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">z</font></span>)</span></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p1">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">x</font></span>)</span>
<b>by </b><i><a class="ref" href="lattice3.html#T16">LATTICE3:16</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K12">"/\"</a> <span class="p2">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">z</font></span>)</span></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p1">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">x</font></span>)</span>
<b>by </b><i><a class="ref" href="lattice3.html#T18">LATTICE3:18</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K12">"/\"</a> <span class="p2">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">x</font></span>)</span></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p1">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">z</font></span>)</span>
<b>by </b><i><a class="ref" href="lattice3.html#T16">LATTICE3:16</a></i>
<br/>.= 
<font color="Maroon">x</font> <a href="lattice3.html#K12">"/\"</a> <span class="p1">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">z</font></span>)</span>
<b>by </b><i><a class="ref" href="lattice3.html#T18">LATTICE3:18</a></i>
;<br/><a NAME="E10:20_2"/><i><font color="Green">E55</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">y</font></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p2">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">z</font></span>)</span></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p1">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">x</font></span>)</span> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">y</font></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p2">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">z</font></span>)</span></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p1">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">x</font></span>)</span>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="20_2_3"><b>proof </b></a><div class="add">

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="20_2_3_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:20_2_3_1"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">y</font></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p2">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">z</font></span>)</span></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p1">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">x</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">y</font></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p2">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">z</font></span>)</span></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p1">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">x</font></span>)</span>
 ;<br/><b>then </b><font color="Maroon">x</font> <a href="lattice3.html#K12">"/\"</a> <span class="p1">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">z</font></span>)</span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">y</font></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">z</font></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p3">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">x</font></span>)</span></span>)</span></span>)</span> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">x</font>
<b>by </b><i>, <a class="ref" href="lattice3.html#T14">LATTICE3:14</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">y</font></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">z</font></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p3">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">x</font></span>)</span></span>)</span> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">x</font></span>)</span>
<b>by </b><i>, , </i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">y</font></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p1">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">x</font></span>)</span>
<b>by </b><i>, , , </i>
;<br/><b>hence </b><a NAME="E3:20_2_3_1"/>
contradiction
 <b>by </b><i/>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E2:20_2_3"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">y</font></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p2">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">z</font></span>)</span></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p1">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">x</font></span>)</span> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">y</font></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p2">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">z</font></span>)</span></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p1">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">x</font></span>)</span>
 ;<br/>


</div><b>end;</b></div><b>set </b><font color="Maroon">x1</font> = <span class="p1">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K13">"\/"</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">y</font></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p4">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">z</font></span>)</span></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p3">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">x</font></span>)</span></span>)</span></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">y</font></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p3">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">z</font></span>)</span></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p2">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">x</font></span>)</span></span>)</span>;<br/><b>set </b><font color="Maroon">y1</font> = <span class="p1">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K13">"\/"</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">y</font></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p4">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">z</font></span>)</span></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p3">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">x</font></span>)</span></span>)</span></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">y</font></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p3">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">z</font></span>)</span></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p2">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">x</font></span>)</span></span>)</span>;<br/><b>set </b><font color="Maroon">z1</font> = <span class="p1">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K13">"\/"</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">y</font></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p4">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">z</font></span>)</span></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p3">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">x</font></span>)</span></span>)</span></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">y</font></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p3">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">z</font></span>)</span></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p2">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">x</font></span>)</span></span>)</span>;<br/><i><font color="Green">E56</font></i>: <font color="Maroon">x</font> <a href="lattice3.html#K12">"/\"</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">y</font></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p3">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">z</font></span>)</span></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p2">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">x</font></span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K12">"/\"</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">y</font></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p3">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">z</font></span>)</span></span>)</span></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p1">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">x</font></span>)</span>
<b>by </b><i><a class="ref" href="lattice3.html#T16">LATTICE3:16</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K12">"/\"</a> <span class="p3">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">y</font></span>)</span></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p2">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">z</font></span>)</span></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p1">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">x</font></span>)</span>
<b>by </b><i><a class="ref" href="lattice3.html#T16">LATTICE3:16</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K12">"/\"</a> <span class="p2">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">z</font></span>)</span></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p1">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">x</font></span>)</span>
<b>by </b><i><a class="ref" href="lattice3.html#T18">LATTICE3:18</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">x</font></span>)</span> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">x</font></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p1">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">z</font></span>)</span>
<b>by </b><i><a class="ref" href="lattice3.html#T16">LATTICE3:16</a></i>
<br/>.= 
<font color="Maroon">x</font> <a href="lattice3.html#K12">"/\"</a> <span class="p1">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">z</font></span>)</span>
<b>by </b><i><a class="ref" href="lattice3.html#T18">LATTICE3:18</a></i>
;<br/><i><font color="Green">E57</font></i>: <font color="Maroon">y</font> <a href="lattice3.html#K12">"/\"</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">y</font></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p3">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">z</font></span>)</span></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p2">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">x</font></span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K12">"/\"</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">y</font></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p3">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">z</font></span>)</span></span>)</span></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p1">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">x</font></span>)</span>
<b>by </b><i><a class="ref" href="lattice3.html#T16">LATTICE3:16</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K12">"/\"</a> <span class="p3">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">y</font></span>)</span></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p2">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">z</font></span>)</span></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p1">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">x</font></span>)</span>
<b>by </b><i><a class="ref" href="lattice3.html#T16">LATTICE3:16</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K12">"/\"</a> <span class="p2">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">z</font></span>)</span></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p1">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">x</font></span>)</span>
<b>by </b><i><a class="ref" href="lattice3.html#T18">LATTICE3:18</a></i>
<br/>.= 
<font color="Maroon">y</font> <a href="lattice3.html#K12">"/\"</a> <span class="p1">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">z</font></span>)</span>
<b>by </b><i><a class="ref" href="lattice3.html#T18">LATTICE3:18</a></i>
;<br/><i><font color="Green">E58</font></i>: <font color="Maroon">z</font> <a href="lattice3.html#K12">"/\"</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">y</font></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p3">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">z</font></span>)</span></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p2">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">x</font></span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K12">"/\"</a> <span class="p2">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">x</font></span>)</span></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">y</font></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p2">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">z</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="lattice3.html#T16">LATTICE3:16</a></i>
<br/>.= 
<font color="Maroon">z</font> <a href="lattice3.html#K12">"/\"</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">z</font></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p2">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">y</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="lattice3.html#T18">LATTICE3:18</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K12">"/\"</a> <span class="p2">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">z</font></span>)</span></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p1">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">y</font></span>)</span>
<b>by </b><i><a class="ref" href="lattice3.html#T16">LATTICE3:16</a></i>
<br/>.= 
<font color="Maroon">z</font> <a href="lattice3.html#K12">"/\"</a> <span class="p1">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">y</font></span>)</span>
<b>by </b><i><a class="ref" href="lattice3.html#T18">LATTICE3:18</a></i>
;<br/><i><font color="Green">E59</font></i>: <font color="Maroon">x</font> <a href="lattice3.html#K13">"\/"</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">y</font></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p3">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">z</font></span>)</span></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p2">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">x</font></span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K13">"\/"</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">y</font></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p3">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">z</font></span>)</span></span>)</span></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p1">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">x</font></span>)</span>
<b>by </b><i><a class="ref" href="lattice3.html#T14">LATTICE3:14</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K13">"\/"</a> <span class="p3">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">y</font></span>)</span></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p2">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">z</font></span>)</span></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p1">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">x</font></span>)</span>
<b>by </b><i><a class="ref" href="lattice3.html#T14">LATTICE3:14</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K13">"\/"</a> <span class="p2">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">z</font></span>)</span></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p1">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">x</font></span>)</span>
<b>by </b><i><a class="ref" href="lattice3.html#T17">LATTICE3:17</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">x</font></span>)</span> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">x</font></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p1">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">z</font></span>)</span>
<b>by </b><i><a class="ref" href="lattice3.html#T14">LATTICE3:14</a></i>
<br/>.= 
<font color="Maroon">x</font> <a href="lattice3.html#K13">"\/"</a> <span class="p1">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">z</font></span>)</span>
<b>by </b><i><a class="ref" href="lattice3.html#T17">LATTICE3:17</a></i>
;<br/><i><font color="Green">E60</font></i>: <font color="Maroon">y</font> <a href="lattice3.html#K13">"\/"</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">y</font></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p3">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">z</font></span>)</span></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p2">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">x</font></span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K13">"\/"</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">y</font></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p3">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">z</font></span>)</span></span>)</span></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p1">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">x</font></span>)</span>
<b>by </b><i><a class="ref" href="lattice3.html#T14">LATTICE3:14</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K13">"\/"</a> <span class="p3">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">y</font></span>)</span></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p2">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">z</font></span>)</span></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p1">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">x</font></span>)</span>
<b>by </b><i><a class="ref" href="lattice3.html#T14">LATTICE3:14</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K13">"\/"</a> <span class="p2">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">z</font></span>)</span></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p1">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">x</font></span>)</span>
<b>by </b><i><a class="ref" href="lattice3.html#T17">LATTICE3:17</a></i>
<br/>.= 
<font color="Maroon">y</font> <a href="lattice3.html#K13">"\/"</a> <span class="p1">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">z</font></span>)</span>
<b>by </b><i><a class="ref" href="lattice3.html#T17">LATTICE3:17</a></i>
;<br/><i><font color="Green">E61</font></i>: <font color="Maroon">z</font> <a href="lattice3.html#K13">"\/"</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">y</font></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p3">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">z</font></span>)</span></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p2">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">x</font></span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K13">"\/"</a> <span class="p2">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">x</font></span>)</span></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">y</font></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p2">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">z</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="lattice3.html#T14">LATTICE3:14</a></i>
<br/>.= 
<font color="Maroon">z</font> <a href="lattice3.html#K13">"\/"</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">z</font></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p2">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">y</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="lattice3.html#T17">LATTICE3:17</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K13">"\/"</a> <span class="p2">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">z</font></span>)</span></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p1">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">y</font></span>)</span>
<b>by </b><i><a class="ref" href="lattice3.html#T14">LATTICE3:14</a></i>
<br/>.= 
<font color="Maroon">z</font> <a href="lattice3.html#K13">"\/"</a> <span class="p1">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">y</font></span>)</span>
<b>by </b><i><a class="ref" href="lattice3.html#T17">LATTICE3:17</a></i>
;<br/><a NAME="E17:20_2"/><i><font color="Green">E62</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">y</font></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p2">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">z</font></span>)</span></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p1">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">x</font></span>)</span> <a href="orders_2.html#R3">&lt;=</a> <span class="p1">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K12">"/\"</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">y</font></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p4">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">z</font></span>)</span></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p3">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">x</font></span>)</span></span>)</span></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p1">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K12">"/\"</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">y</font></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p4">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">z</font></span>)</span></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p3">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">x</font></span>)</span></span>)</span></span>)</span>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="20_2_10"><b>proof </b></a><div class="add">

<a NAME="E1:20_2_10"/>
( <span class="p1">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">y</font></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p1">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">z</font></span>)</span> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">x</font> <a href="lattice3.html#K12">"/\"</a> <span class="p1">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">z</font></span>)</span> &amp; <span class="p1">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">y</font></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p1">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">z</font></span>)</span> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">y</font> <a href="lattice3.html#K12">"/\"</a> <span class="p1">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">z</font></span>)</span> )
 
<b>by </b><i/>;<br/>
<a NAME="E2:20_2_10"/><b>then </b>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">y</font></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p2">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">z</font></span>)</span></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">y</font></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p2">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">z</font></span>)</span></span>)</span> <a href="orders_2.html#R3">&lt;=</a> <span class="p1">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K12">"/\"</a> <span class="p2">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">z</font></span>)</span></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p1">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K12">"/\"</a> <span class="p2">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">z</font></span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="yellow_3.html#T3">YELLOW_3:3</a></i>;<br/>
<a NAME="E3:20_2_10"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">z</font></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">y</font></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">y</font></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p3">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">z</font></span>)</span></span>)</span></span>)</span> <a href="orders_2.html#R3">&lt;=</a> <span class="p1">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K12">"/\"</a> <span class="p2">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">z</font></span>)</span></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p1">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K12">"/\"</a> <span class="p2">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">z</font></span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="lattice3.html#T14">LATTICE3:14</a></i>;<br/>
<a NAME="E4:20_2_10"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">z</font></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">y</font></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p3">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">y</font></span>)</span></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p2">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">z</font></span>)</span></span>)</span> <a href="orders_2.html#R3">&lt;=</a> <span class="p1">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K12">"/\"</a> <span class="p2">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">z</font></span>)</span></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p1">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K12">"/\"</a> <span class="p2">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">z</font></span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="lattice3.html#T14">LATTICE3:14</a></i>;<br/>
<a NAME="E5:20_2_10"/><b>then </b>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">y</font></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p3">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">y</font></span>)</span></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p2">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">z</font></span>)</span></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p1">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">z</font></span>)</span> <a href="orders_2.html#R3">&lt;=</a> <span class="p1">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K12">"/\"</a> <span class="p2">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">z</font></span>)</span></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p1">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K12">"/\"</a> <span class="p2">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">z</font></span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="lattice3.html#T14">LATTICE3:14</a></i>;<br/>
<a NAME="E6:20_2_10"/><b>then </b>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">y</font></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p2">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">z</font></span>)</span></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p1">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">z</font></span>)</span> <a href="orders_2.html#R3">&lt;=</a> <span class="p1">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K12">"/\"</a> <span class="p2">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">z</font></span>)</span></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p1">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K12">"/\"</a> <span class="p2">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">z</font></span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="yellow_5.html#T1">YELLOW_5:1</a></i>;<br/>
<b>hence </b><a NAME="E7:20_2_10"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">y</font></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p2">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">z</font></span>)</span></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p1">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">x</font></span>)</span> <a href="orders_2.html#R3">&lt;=</a> <span class="p1">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K12">"/\"</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">y</font></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p4">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">z</font></span>)</span></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p3">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">x</font></span>)</span></span>)</span></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p1">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K12">"/\"</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">y</font></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p4">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">z</font></span>)</span></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p3">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">x</font></span>)</span></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="yellow11.html#T1" target="_self">Th1</a>, <a class="ref" href="yellow11.html#T2" target="_self">Th2</a>, <a class="ref" href="lattice3.html#T14">LATTICE3:14</a></i>;<br/>


</div><b>end;</b></div><a NAME="E18:20_2"/><i><font color="Green">E63</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">y</font></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p2">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">z</font></span>)</span></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p1">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">x</font></span>)</span> <a href="orders_2.html#R3">&lt;=</a> <span class="p1">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K12">"/\"</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">y</font></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p4">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">z</font></span>)</span></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p3">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">x</font></span>)</span></span>)</span></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p1">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K12">"/\"</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">y</font></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p4">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">z</font></span>)</span></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p3">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">x</font></span>)</span></span>)</span></span>)</span>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="20_2_11"><b>proof </b></a><div class="add">

<a NAME="E1:20_2_11"/>
( <span class="p1">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">z</font></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p1">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">y</font></span>)</span> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">x</font> <a href="lattice3.html#K12">"/\"</a> <span class="p1">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">y</font></span>)</span> &amp; <span class="p1">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">z</font></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p1">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">y</font></span>)</span> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">z</font> <a href="lattice3.html#K12">"/\"</a> <span class="p1">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">y</font></span>)</span> )
 
<b>by </b><i/>;<br/>
<a NAME="E2:20_2_11"/><b>then </b>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">z</font></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p2">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">y</font></span>)</span></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">z</font></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p2">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">y</font></span>)</span></span>)</span> <a href="orders_2.html#R3">&lt;=</a> <span class="p1">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K12">"/\"</a> <span class="p2">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">y</font></span>)</span></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p1">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K12">"/\"</a> <span class="p2">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">y</font></span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="yellow_3.html#T3">YELLOW_3:3</a></i>;<br/>
<a NAME="E3:20_2_11"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">y</font></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">z</font></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">z</font></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p3">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">y</font></span>)</span></span>)</span></span>)</span> <a href="orders_2.html#R3">&lt;=</a> <span class="p1">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K12">"/\"</a> <span class="p2">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">y</font></span>)</span></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p1">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K12">"/\"</a> <span class="p2">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">y</font></span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="lattice3.html#T14">LATTICE3:14</a></i>;<br/>
<a NAME="E4:20_2_11"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">y</font></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">z</font></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p3">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">z</font></span>)</span></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p2">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">y</font></span>)</span></span>)</span> <a href="orders_2.html#R3">&lt;=</a> <span class="p1">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K12">"/\"</a> <span class="p2">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">y</font></span>)</span></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p1">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K12">"/\"</a> <span class="p2">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">y</font></span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="lattice3.html#T14">LATTICE3:14</a></i>;<br/>
<a NAME="E5:20_2_11"/><b>then </b>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">z</font></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p3">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">z</font></span>)</span></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p2">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">y</font></span>)</span></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p1">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">y</font></span>)</span> <a href="orders_2.html#R3">&lt;=</a> <span class="p1">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K12">"/\"</a> <span class="p2">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">y</font></span>)</span></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p1">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K12">"/\"</a> <span class="p2">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">y</font></span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="lattice3.html#T14">LATTICE3:14</a></i>;<br/>
<a NAME="E6:20_2_11"/><b>then </b>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">z</font></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p2">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">y</font></span>)</span></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p1">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">y</font></span>)</span> <a href="orders_2.html#R3">&lt;=</a> <span class="p1">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K12">"/\"</a> <span class="p2">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">y</font></span>)</span></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p1">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K12">"/\"</a> <span class="p2">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">y</font></span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="yellow_5.html#T1">YELLOW_5:1</a></i>;<br/>
<b>hence </b><a NAME="E7:20_2_11"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">y</font></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p2">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">z</font></span>)</span></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p1">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">x</font></span>)</span> <a href="orders_2.html#R3">&lt;=</a> <span class="p1">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K12">"/\"</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">y</font></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p4">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">z</font></span>)</span></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p3">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">x</font></span>)</span></span>)</span></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p1">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K12">"/\"</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">y</font></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p4">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">z</font></span>)</span></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p3">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">x</font></span>)</span></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="yellow11.html#T1" target="_self">Th1</a>, <a class="ref" href="yellow11.html#T3" target="_self">Th3</a>, <a class="ref" href="lattice3.html#T14">LATTICE3:14</a></i>;<br/>


</div><b>end;</b></div><a NAME="E19:20_2"/><i><font color="Green">E64</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">y</font></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p2">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">z</font></span>)</span></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p1">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">x</font></span>)</span> <a href="orders_2.html#R3">&lt;=</a> <span class="p1">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K12">"/\"</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">y</font></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p4">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">z</font></span>)</span></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p3">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">x</font></span>)</span></span>)</span></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p1">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K12">"/\"</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">y</font></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p4">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">z</font></span>)</span></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p3">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">x</font></span>)</span></span>)</span></span>)</span>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="20_2_12"><b>proof </b></a><div class="add">

<a NAME="E1:20_2_12"/>
( <span class="p1">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">y</font></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p1">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">x</font></span>)</span> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">z</font> <a href="lattice3.html#K12">"/\"</a> <span class="p1">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">x</font></span>)</span> &amp; <span class="p1">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">y</font></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p1">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">x</font></span>)</span> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">y</font> <a href="lattice3.html#K12">"/\"</a> <span class="p1">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">x</font></span>)</span> )
 
<b>by </b><i/>;<br/>
<a NAME="E2:20_2_12"/><b>then </b>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">y</font></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p2">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">x</font></span>)</span></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">y</font></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p2">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">x</font></span>)</span></span>)</span> <a href="orders_2.html#R3">&lt;=</a> <span class="p1">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K12">"/\"</a> <span class="p2">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">x</font></span>)</span></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p1">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K12">"/\"</a> <span class="p2">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">x</font></span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="yellow_3.html#T3">YELLOW_3:3</a></i>;<br/>
<a NAME="E3:20_2_12"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">x</font></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">y</font></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">y</font></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p3">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">x</font></span>)</span></span>)</span></span>)</span> <a href="orders_2.html#R3">&lt;=</a> <span class="p1">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K12">"/\"</a> <span class="p2">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">x</font></span>)</span></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p1">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K12">"/\"</a> <span class="p2">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">x</font></span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="lattice3.html#T14">LATTICE3:14</a></i>;<br/>
<a NAME="E4:20_2_12"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">x</font></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">y</font></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p3">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">y</font></span>)</span></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p2">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">x</font></span>)</span></span>)</span> <a href="orders_2.html#R3">&lt;=</a> <span class="p1">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K12">"/\"</a> <span class="p2">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">x</font></span>)</span></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p1">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K12">"/\"</a> <span class="p2">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">x</font></span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="lattice3.html#T14">LATTICE3:14</a></i>;<br/>
<a NAME="E5:20_2_12"/><b>then </b>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">y</font></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p3">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">y</font></span>)</span></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p2">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">x</font></span>)</span></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p1">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">x</font></span>)</span> <a href="orders_2.html#R3">&lt;=</a> <span class="p1">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K12">"/\"</a> <span class="p2">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">x</font></span>)</span></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p1">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K12">"/\"</a> <span class="p2">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">x</font></span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="lattice3.html#T14">LATTICE3:14</a></i>;<br/>
<a NAME="E6:20_2_12"/><b>then </b>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">y</font></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p2">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">x</font></span>)</span></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p1">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">x</font></span>)</span> <a href="orders_2.html#R3">&lt;=</a> <span class="p1">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K12">"/\"</a> <span class="p2">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">x</font></span>)</span></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p1">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K12">"/\"</a> <span class="p2">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">x</font></span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="yellow_5.html#T1">YELLOW_5:1</a></i>;<br/>
<b>hence </b><a NAME="E7:20_2_12"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">y</font></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p2">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">z</font></span>)</span></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p1">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">x</font></span>)</span> <a href="orders_2.html#R3">&lt;=</a> <span class="p1">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K12">"/\"</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">y</font></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p4">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">z</font></span>)</span></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p3">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">x</font></span>)</span></span>)</span></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p1">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K12">"/\"</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">y</font></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p4">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">z</font></span>)</span></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p3">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">x</font></span>)</span></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="yellow11.html#T2" target="_self">Th2</a>, <a class="ref" href="yellow11.html#T3" target="_self">Th3</a>, <a class="ref" href="lattice3.html#T14">LATTICE3:14</a></i>;<br/>


</div><b>end;</b></div><a NAME="E20:20_2"/><i><font color="Green">E65</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K13">"\/"</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">y</font></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p4">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">z</font></span>)</span></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p3">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">x</font></span>)</span></span>)</span></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p1">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K13">"\/"</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">y</font></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p4">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">z</font></span>)</span></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p3">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">x</font></span>)</span></span>)</span></span>)</span> <a href="orders_2.html#R3">&lt;=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">y</font></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p2">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">z</font></span>)</span></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p1">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">x</font></span>)</span>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="20_2_13"><b>proof </b></a><div class="add">

<a NAME="E1:20_2_13"/>
( <font color="Maroon">x</font> <a href="lattice3.html#K13">"\/"</a> <span class="p1">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">z</font></span>)</span> <a href="orders_2.html#R3">&lt;=</a> <span class="p1">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">y</font></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p1">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">z</font></span>)</span> &amp; <font color="Maroon">y</font> <a href="lattice3.html#K13">"\/"</a> <span class="p1">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">z</font></span>)</span> <a href="orders_2.html#R3">&lt;=</a> <span class="p1">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">x</font></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p1">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">z</font></span>)</span> )
 
<b>by </b><i/>;<br/>
<a NAME="E2:20_2_13"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K13">"\/"</a> <span class="p2">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">z</font></span>)</span></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p1">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K13">"\/"</a> <span class="p2">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">z</font></span>)</span></span>)</span> <a href="orders_2.html#R3">&lt;=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">y</font></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p2">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">z</font></span>)</span></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">x</font></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p2">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">z</font></span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="yellow_3.html#T2">YELLOW_3:2</a></i>;<br/>
<a NAME="E3:20_2_13"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K13">"\/"</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">y</font></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p4">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">z</font></span>)</span></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p3">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">x</font></span>)</span></span>)</span></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p1">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K13">"\/"</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">y</font></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p4">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">z</font></span>)</span></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p3">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">x</font></span>)</span></span>)</span></span>)</span> <a href="orders_2.html#R3">&lt;=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">z</font></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p3">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">y</font></span>)</span></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p2">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">y</font></span>)</span></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p1">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">z</font></span>)</span>
 
<b>by </b><i><a class="ref" href="yellow11.html#T4" target="_self">Th4</a>, <a class="txt" href="yellow11.html#E5"><i><font color="Green">Lemma26</font></i></a>, <a class="ref" href="lattice3.html#T16">LATTICE3:16</a></i>;<br/>
<a NAME="E4:20_2_13"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K13">"\/"</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">y</font></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p4">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">z</font></span>)</span></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p3">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">x</font></span>)</span></span>)</span></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p1">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K13">"\/"</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">y</font></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p4">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">z</font></span>)</span></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p3">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">x</font></span>)</span></span>)</span></span>)</span> <a href="orders_2.html#R3">&lt;=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">z</font></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">y</font></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p3">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">y</font></span>)</span></span>)</span></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p1">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">z</font></span>)</span>
 
<b>by </b><i><a class="ref" href="lattice3.html#T16">LATTICE3:16</a></i>;<br/>
<a NAME="E5:20_2_13"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K13">"\/"</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">y</font></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p4">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">z</font></span>)</span></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p3">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">x</font></span>)</span></span>)</span></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p1">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K13">"\/"</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">y</font></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p4">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">z</font></span>)</span></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p3">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">x</font></span>)</span></span>)</span></span>)</span> <a href="orders_2.html#R3">&lt;=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">z</font></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p2">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">y</font></span>)</span></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p1">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">z</font></span>)</span>
 
<b>by </b><i><a class="ref" href="yellow_5.html#T2">YELLOW_5:2</a></i>;<br/>
<b>hence </b><a NAME="E6:20_2_13"/>
<span class="p1">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K13">"\/"</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">y</font></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p4">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">z</font></span>)</span></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p3">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">x</font></span>)</span></span>)</span></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p1">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K13">"\/"</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">y</font></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p4">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">z</font></span>)</span></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p3">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">x</font></span>)</span></span>)</span></span>)</span> <a href="orders_2.html#R3">&lt;=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">y</font></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p2">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">z</font></span>)</span></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p1">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">x</font></span>)</span>
 <b>by </b><i><a class="ref" href="lattice3.html#T16">LATTICE3:16</a></i>;<br/>


</div><b>end;</b></div><a NAME="E21:20_2"/><i><font color="Green">E66</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K13">"\/"</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">y</font></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p4">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">z</font></span>)</span></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p3">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">x</font></span>)</span></span>)</span></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p1">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K13">"\/"</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">y</font></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p4">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">z</font></span>)</span></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p3">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">x</font></span>)</span></span>)</span></span>)</span> <a href="orders_2.html#R3">&lt;=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">y</font></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p2">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">z</font></span>)</span></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p1">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">x</font></span>)</span>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="20_2_14"><b>proof </b></a><div class="add">

<a NAME="E1:20_2_14"/>
( <font color="Maroon">x</font> <a href="lattice3.html#K13">"\/"</a> <span class="p1">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">y</font></span>)</span> <a href="orders_2.html#R3">&lt;=</a> <span class="p1">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">z</font></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p1">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">y</font></span>)</span> &amp; <font color="Maroon">z</font> <a href="lattice3.html#K13">"\/"</a> <span class="p1">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">y</font></span>)</span> <a href="orders_2.html#R3">&lt;=</a> <span class="p1">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">x</font></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p1">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">y</font></span>)</span> )
 
<b>by </b><i/>;<br/>
<a NAME="E2:20_2_14"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K13">"\/"</a> <span class="p2">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">y</font></span>)</span></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p1">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K13">"\/"</a> <span class="p2">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">y</font></span>)</span></span>)</span> <a href="orders_2.html#R3">&lt;=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">z</font></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p2">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">y</font></span>)</span></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">x</font></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p2">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">y</font></span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="yellow_3.html#T2">YELLOW_3:2</a></i>;<br/>
<a NAME="E3:20_2_14"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K13">"\/"</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">y</font></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p4">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">z</font></span>)</span></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p3">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">x</font></span>)</span></span>)</span></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p1">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K13">"\/"</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">y</font></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p4">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">z</font></span>)</span></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p3">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">x</font></span>)</span></span>)</span></span>)</span> <a href="orders_2.html#R3">&lt;=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">y</font></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p3">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">z</font></span>)</span></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p2">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">z</font></span>)</span></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p1">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">y</font></span>)</span>
 
<b>by </b><i><a class="ref" href="yellow11.html#T4" target="_self">Th4</a>, <a class="ref" href="yellow11.html#T5" target="_self">Th5</a>, <a class="ref" href="lattice3.html#T16">LATTICE3:16</a></i>;<br/>
<a NAME="E4:20_2_14"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K13">"\/"</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">y</font></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p4">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">z</font></span>)</span></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p3">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">x</font></span>)</span></span>)</span></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p1">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K13">"\/"</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">y</font></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p4">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">z</font></span>)</span></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p3">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">x</font></span>)</span></span>)</span></span>)</span> <a href="orders_2.html#R3">&lt;=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">y</font></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">z</font></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p3">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">z</font></span>)</span></span>)</span></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p1">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">y</font></span>)</span>
 
<b>by </b><i><a class="ref" href="lattice3.html#T16">LATTICE3:16</a></i>;<br/>
<a NAME="E5:20_2_14"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K13">"\/"</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">y</font></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p4">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">z</font></span>)</span></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p3">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">x</font></span>)</span></span>)</span></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p1">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K13">"\/"</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">y</font></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p4">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">z</font></span>)</span></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p3">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">x</font></span>)</span></span>)</span></span>)</span> <a href="orders_2.html#R3">&lt;=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">y</font></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p2">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">z</font></span>)</span></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p1">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">y</font></span>)</span>
 
<b>by </b><i><a class="ref" href="yellow_5.html#T2">YELLOW_5:2</a></i>;<br/>
<b>hence </b><a NAME="E6:20_2_14"/>
<span class="p1">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K13">"\/"</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">y</font></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p4">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">z</font></span>)</span></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p3">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">x</font></span>)</span></span>)</span></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p1">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K13">"\/"</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">y</font></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p4">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">z</font></span>)</span></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p3">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">x</font></span>)</span></span>)</span></span>)</span> <a href="orders_2.html#R3">&lt;=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">y</font></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p2">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">z</font></span>)</span></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p1">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">x</font></span>)</span>
 <b>by </b><i><a class="ref" href="lattice3.html#T16">LATTICE3:16</a></i>;<br/>


</div><b>end;</b></div><a NAME="E22:20_2"/><i><font color="Green">E67</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K13">"\/"</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">y</font></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p4">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">z</font></span>)</span></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p3">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">x</font></span>)</span></span>)</span></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p1">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K13">"\/"</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">y</font></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p4">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">z</font></span>)</span></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p3">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">x</font></span>)</span></span>)</span></span>)</span> <a href="orders_2.html#R3">&lt;=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">y</font></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p2">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">z</font></span>)</span></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p1">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">x</font></span>)</span>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="20_2_15"><b>proof </b></a><div class="add">

<a NAME="E1:20_2_15"/>
( <font color="Maroon">z</font> <a href="lattice3.html#K13">"\/"</a> <span class="p1">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">x</font></span>)</span> <a href="orders_2.html#R3">&lt;=</a> <span class="p1">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">y</font></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p1">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">x</font></span>)</span> &amp; <font color="Maroon">y</font> <a href="lattice3.html#K13">"\/"</a> <span class="p1">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">x</font></span>)</span> <a href="orders_2.html#R3">&lt;=</a> <span class="p1">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">z</font></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p1">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">x</font></span>)</span> )
 
<b>by </b><i/>;<br/>
<a NAME="E2:20_2_15"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K13">"\/"</a> <span class="p2">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">x</font></span>)</span></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p1">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K13">"\/"</a> <span class="p2">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">x</font></span>)</span></span>)</span> <a href="orders_2.html#R3">&lt;=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">y</font></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p2">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">x</font></span>)</span></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">z</font></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p2">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">x</font></span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="yellow_3.html#T2">YELLOW_3:2</a></i>;<br/>
<a NAME="E3:20_2_15"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K13">"\/"</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">y</font></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p4">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">z</font></span>)</span></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p3">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">x</font></span>)</span></span>)</span></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p1">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K13">"\/"</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">y</font></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p4">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">z</font></span>)</span></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p3">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">x</font></span>)</span></span>)</span></span>)</span> <a href="orders_2.html#R3">&lt;=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">x</font></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p3">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">y</font></span>)</span></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p2">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">y</font></span>)</span></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p1">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">x</font></span>)</span>
 
<b>by </b><i><a class="txt" href="yellow11.html#E5"><i><font color="Green">Lemma26</font></i></a>, <a class="ref" href="yellow11.html#T5" target="_self">Th5</a>, <a class="ref" href="lattice3.html#T16">LATTICE3:16</a></i>;<br/>
<a NAME="E4:20_2_15"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K13">"\/"</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">y</font></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p4">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">z</font></span>)</span></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p3">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">x</font></span>)</span></span>)</span></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p1">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K13">"\/"</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">y</font></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p4">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">z</font></span>)</span></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p3">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">x</font></span>)</span></span>)</span></span>)</span> <a href="orders_2.html#R3">&lt;=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">x</font></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">y</font></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p3">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">y</font></span>)</span></span>)</span></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p1">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">x</font></span>)</span>
 
<b>by </b><i><a class="ref" href="lattice3.html#T16">LATTICE3:16</a></i>;<br/>
<a NAME="E5:20_2_15"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K13">"\/"</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">y</font></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p4">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">z</font></span>)</span></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p3">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">x</font></span>)</span></span>)</span></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p1">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K13">"\/"</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">y</font></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p4">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">z</font></span>)</span></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p3">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">x</font></span>)</span></span>)</span></span>)</span> <a href="orders_2.html#R3">&lt;=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">x</font></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p2">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">y</font></span>)</span></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p1">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">x</font></span>)</span>
 
<b>by </b><i><a class="ref" href="yellow_5.html#T2">YELLOW_5:2</a></i>;<br/>
<b>hence </b><a NAME="E6:20_2_15"/>
<span class="p1">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K13">"\/"</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">y</font></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p4">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">z</font></span>)</span></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p3">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">x</font></span>)</span></span>)</span></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p1">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K13">"\/"</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">y</font></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p4">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">z</font></span>)</span></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p3">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">x</font></span>)</span></span>)</span></span>)</span> <a href="orders_2.html#R3">&lt;=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">y</font></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p2">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">z</font></span>)</span></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p1">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">x</font></span>)</span>
 <b>by </b><i><a class="ref" href="lattice3.html#T16">LATTICE3:16</a></i>;<br/>


</div><b>end;</b></div><a NAME="E23:20_2"/>
( <font color="Maroon">x</font> <a href="lattice3.html#K12">"/\"</a> <span class="p1">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">z</font></span>)</span> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">x</font> &amp; <font color="Maroon">x</font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">x</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">z</font> )
 <b>by </b><i><a class="ref" href="yellow_0.html#T22">YELLOW_0:22</a>, <a class="ref" href="yellow_0.html#T23">YELLOW_0:23</a></i>;<br/><a NAME="E24:20_2"/><b>then </b><i><font color="Green">E68</font></i>: 
<font color="Maroon">x</font> <a href="lattice3.html#K12">"/\"</a> <span class="p1">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">z</font></span>)</span> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">x</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">z</font>
 <b>by </b><i><a class="ref" href="yellow_0.html#D2">YELLOW_0:def 2</a></i>;<br/><a NAME="E25:20_2"/>
( <font color="Maroon">x</font> <a href="lattice3.html#K12">"/\"</a> <span class="p1">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">y</font></span>)</span> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">x</font> &amp; <font color="Maroon">x</font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">x</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">y</font> )
 <b>by </b><i><a class="ref" href="yellow_0.html#T22">YELLOW_0:22</a>, <a class="ref" href="yellow_0.html#T23">YELLOW_0:23</a></i>;<br/><a NAME="E26:20_2"/><b>then </b><i><font color="Green">E70</font></i>: 
<font color="Maroon">x</font> <a href="lattice3.html#K12">"/\"</a> <span class="p1">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">y</font></span>)</span> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">x</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">y</font>
 <b>by </b><i><a class="ref" href="yellow_0.html#D2">YELLOW_0:def 2</a></i>;<br/><a NAME="E27:20_2"/>
( <font color="Maroon">z</font> <a href="lattice3.html#K12">"/\"</a> <span class="p1">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">x</font></span>)</span> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">z</font> &amp; <font color="Maroon">z</font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">z</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">x</font> )
 <b>by </b><i><a class="ref" href="yellow_0.html#T22">YELLOW_0:22</a>, <a class="ref" href="yellow_0.html#T23">YELLOW_0:23</a></i>;<br/><a NAME="E28:20_2"/><b>then </b><i><font color="Green">E71</font></i>: 
<font color="Maroon">z</font> <a href="lattice3.html#K12">"/\"</a> <span class="p1">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">x</font></span>)</span> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">z</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">x</font>
 <b>by </b><i><a class="ref" href="yellow_0.html#D2">YELLOW_0:def 2</a></i>;<br/><a NAME="E29:20_2"/>
( <font color="Maroon">x</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">z</font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">x</font> &amp; <font color="Maroon">x</font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">x</font> <a href="lattice3.html#K13">"\/"</a> <span class="p1">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">z</font></span>)</span> )
 <b>by </b><i><a class="ref" href="yellow_0.html#T22">YELLOW_0:22</a>, <a class="ref" href="yellow_0.html#T23">YELLOW_0:23</a></i>;<br/><a NAME="E30:20_2"/><b>then </b><i><font color="Green">E72</font></i>: 
<font color="Maroon">x</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">z</font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">x</font> <a href="lattice3.html#K13">"\/"</a> <span class="p1">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">z</font></span>)</span>
 <b>by </b><i><a class="ref" href="yellow_0.html#D2">YELLOW_0:def 2</a></i>;<br/><a NAME="E31:20_2"/>
( <font color="Maroon">x</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">y</font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">x</font> &amp; <font color="Maroon">x</font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">x</font> <a href="lattice3.html#K13">"\/"</a> <span class="p1">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">y</font></span>)</span> )
 <b>by </b><i><a class="ref" href="yellow_0.html#T22">YELLOW_0:22</a>, <a class="ref" href="yellow_0.html#T23">YELLOW_0:23</a></i>;<br/><a NAME="E32:20_2"/><b>then </b><i><font color="Green">E73</font></i>: 
<font color="Maroon">x</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">y</font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">x</font> <a href="lattice3.html#K13">"\/"</a> <span class="p1">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">y</font></span>)</span>
 <b>by </b><i><a class="ref" href="yellow_0.html#D2">YELLOW_0:def 2</a></i>;<br/><a NAME="E33:20_2"/>
( <font color="Maroon">z</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">x</font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">z</font> &amp; <font color="Maroon">z</font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">z</font> <a href="lattice3.html#K13">"\/"</a> <span class="p1">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">x</font></span>)</span> )
 <b>by </b><i><a class="ref" href="yellow_0.html#T22">YELLOW_0:22</a>, <a class="ref" href="yellow_0.html#T23">YELLOW_0:23</a></i>;<br/><a NAME="E34:20_2"/><b>then </b><i><font color="Green">E74</font></i>: 
<font color="Maroon">z</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">x</font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">z</font> <a href="lattice3.html#K13">"\/"</a> <span class="p1">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">x</font></span>)</span>
 <b>by </b><i><a class="ref" href="yellow_0.html#D2">YELLOW_0:def 2</a></i>;<br/><a NAME="E35:20_2"/><i><font color="Green">E75</font></i>: 
<font color="Maroon">y</font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">y</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">z</font>
 <b>by </b><i><a class="ref" href="yellow_0.html#T22">YELLOW_0:22</a></i>;<br/><a NAME="E36:20_2"/><i><font color="Green">E76</font></i>: 
<font color="Maroon">z</font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">z</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">y</font>
 <b>by </b><i><a class="ref" href="yellow_0.html#T22">YELLOW_0:22</a></i>;<br/><a NAME="E37:20_2"/><i><font color="Green">E77</font></i>: 
<font color="Maroon">y</font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">y</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">x</font>
 <b>by </b><i><a class="ref" href="yellow_0.html#T22">YELLOW_0:22</a></i>;<br/><a NAME="E38:20_2"/><i><font color="Green">E78</font></i>: 
<font color="Maroon">y</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">z</font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">y</font>
 <b>by </b><i><a class="ref" href="yellow_0.html#T23">YELLOW_0:23</a></i>;<br/><a NAME="E39:20_2"/><i><font color="Green">E79</font></i>: 
<font color="Maroon">z</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">y</font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">z</font>
 <b>by </b><i><a class="ref" href="yellow_0.html#T23">YELLOW_0:23</a></i>;<br/><a NAME="E40:20_2"/><i><font color="Green">E80</font></i>: 
<font color="Maroon">y</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">x</font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">y</font>
 <b>by </b><i><a class="ref" href="yellow_0.html#T23">YELLOW_0:23</a></i>;<br/><a NAME="E41:20_2"/><i><font color="Green">E81</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K13">"\/"</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">y</font></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p4">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">z</font></span>)</span></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p3">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">x</font></span>)</span></span>)</span></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">y</font></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p3">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">z</font></span>)</span></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p2">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">x</font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K12">"/\"</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">y</font></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p4">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">z</font></span>)</span></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p3">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">x</font></span>)</span></span>)</span></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">y</font></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p3">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">z</font></span>)</span></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p2">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">x</font></span>)</span></span>)</span>
 <b>by </b><i>, , </i>;<br/><a NAME="E42:20_2"/><i><font color="Green">E82</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K13">"\/"</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">y</font></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p4">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">z</font></span>)</span></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p3">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">x</font></span>)</span></span>)</span></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">y</font></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p3">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">z</font></span>)</span></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p2">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">x</font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K12">"/\"</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">y</font></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p4">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">z</font></span>)</span></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p3">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">x</font></span>)</span></span>)</span></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">y</font></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p3">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">z</font></span>)</span></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p2">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">x</font></span>)</span></span>)</span>
 <b>by </b><i>, , </i>;<br/><i><font color="Green">E83</font></i>: <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K13">"\/"</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">y</font></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p5">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">z</font></span>)</span></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p4">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">x</font></span>)</span></span>)</span></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">y</font></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p4">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">z</font></span>)</span></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p3">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">x</font></span>)</span></span>)</span></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K13">"\/"</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">y</font></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p5">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">z</font></span>)</span></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p4">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">x</font></span>)</span></span>)</span></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">y</font></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p4">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">z</font></span>)</span></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p3">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">x</font></span>)</span></span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K12">"/\"</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">y</font></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p5">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">z</font></span>)</span></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p4">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">x</font></span>)</span></span>)</span></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">y</font></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p4">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">z</font></span>)</span></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p3">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">x</font></span>)</span></span>)</span></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K12">"/\"</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">y</font></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p5">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">z</font></span>)</span></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p4">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">x</font></span>)</span></span>)</span></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">y</font></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p4">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">z</font></span>)</span></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p3">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">x</font></span>)</span></span>)</span></span>)</span>
<b>by </b><i>, , , </i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K12">"/\"</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">y</font></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p4">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">z</font></span>)</span></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p3">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">x</font></span>)</span></span>)</span></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">y</font></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p4">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">z</font></span>)</span></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p3">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">x</font></span>)</span></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K12">"/\"</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">y</font></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p0">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">z</font></span>)</span></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p5">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">x</font></span>)</span></span>)</span></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">y</font></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p5">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">z</font></span>)</span></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p4">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">x</font></span>)</span></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="lattice3.html#T14">LATTICE3:14</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K12">"/\"</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">y</font></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p4">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">z</font></span>)</span></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p3">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">x</font></span>)</span></span>)</span></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">y</font></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p5">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">z</font></span>)</span></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p4">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">x</font></span>)</span></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">y</font></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p5">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">z</font></span>)</span></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p4">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">x</font></span>)</span></span>)</span></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p2">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K12">"/\"</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">y</font></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p5">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">z</font></span>)</span></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p4">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">x</font></span>)</span></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="lattice3.html#T14">LATTICE3:14</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K12">"/\"</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">y</font></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p4">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">z</font></span>)</span></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p3">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">x</font></span>)</span></span>)</span></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K12">"/\"</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">y</font></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p5">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">z</font></span>)</span></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p4">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">x</font></span>)</span></span>)</span></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">y</font></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p4">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">z</font></span>)</span></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p3">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">x</font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="yellow_5.html#T1">YELLOW_5:1</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K12">"/\"</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">y</font></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p5">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">z</font></span>)</span></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p4">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">x</font></span>)</span></span>)</span></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p2">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K12">"/\"</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">y</font></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p5">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">z</font></span>)</span></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p4">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">x</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">y</font></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p3">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">z</font></span>)</span></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p2">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">x</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="lattice3.html#T14">LATTICE3:14</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K12">"/\"</a> <span class="p2">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">z</font></span>)</span></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p1">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K12">"/\"</a> <span class="p2">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">z</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="yellow11.html#T1" target="_self">Th1</a>, <a class="ref" href="yellow11.html#T2" target="_self">Th2</a>, , <a class="ref" href="yellow_5.html#T8">YELLOW_5:8</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K13">"\/"</a> <span class="p2">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K12">"/\"</a> <span class="p3">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">z</font></span>)</span></span>)</span></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p1">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">z</font></span>)</span>
<b>by </b><i>, <a class="ref" href="yellow11.html#T8" target="_self">Th8</a>, </i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">y</font></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p2">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">z</font></span>)</span></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p1">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">x</font></span>)</span>
<b>by </b><i>, , </i>
;<br/><i><font color="Green">E84</font></i>: <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K13">"\/"</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">y</font></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p5">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">z</font></span>)</span></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p4">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">x</font></span>)</span></span>)</span></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">y</font></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p4">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">z</font></span>)</span></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p3">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">x</font></span>)</span></span>)</span></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K13">"\/"</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">y</font></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p5">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">z</font></span>)</span></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p4">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">x</font></span>)</span></span>)</span></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">y</font></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p4">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">z</font></span>)</span></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p3">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">x</font></span>)</span></span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K13">"\/"</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">y</font></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p4">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">z</font></span>)</span></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p3">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">x</font></span>)</span></span>)</span></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">y</font></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p4">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">z</font></span>)</span></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p3">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">x</font></span>)</span></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K13">"\/"</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">y</font></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p0">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">z</font></span>)</span></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p5">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">x</font></span>)</span></span>)</span></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">y</font></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p5">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">z</font></span>)</span></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p4">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">x</font></span>)</span></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="lattice3.html#T16">LATTICE3:16</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K13">"\/"</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">y</font></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p4">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">z</font></span>)</span></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p3">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">x</font></span>)</span></span>)</span></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">y</font></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p5">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">z</font></span>)</span></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p4">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">x</font></span>)</span></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">y</font></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p5">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">z</font></span>)</span></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p4">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">x</font></span>)</span></span>)</span></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p2">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K13">"\/"</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">y</font></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p5">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">z</font></span>)</span></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p4">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">x</font></span>)</span></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="lattice3.html#T16">LATTICE3:16</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K13">"\/"</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">y</font></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p4">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">z</font></span>)</span></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p3">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">x</font></span>)</span></span>)</span></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K13">"\/"</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">y</font></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p5">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">z</font></span>)</span></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p4">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">x</font></span>)</span></span>)</span></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">y</font></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p4">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">z</font></span>)</span></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p3">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">x</font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="yellow_5.html#T2">YELLOW_5:2</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K13">"\/"</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">y</font></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p5">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">z</font></span>)</span></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p4">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">x</font></span>)</span></span>)</span></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p2">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K13">"\/"</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">y</font></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p5">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">z</font></span>)</span></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p4">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">x</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">y</font></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p3">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">z</font></span>)</span></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p2">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">x</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="lattice3.html#T16">LATTICE3:16</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K13">"\/"</a> <span class="p2">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">z</font></span>)</span></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p1">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K13">"\/"</a> <span class="p2">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">z</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="yellow11.html#T4" target="_self">Th4</a>, <a class="txt" href="yellow11.html#E5"><i><font color="Green">Lemma26</font></i></a>, <a class="ref" href="yellow11.html#T6" target="_self">Th6</a>, <a class="ref" href="yellow_5.html#T10">YELLOW_5:10</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K12">"/\"</a> <span class="p2">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K13">"\/"</a> <span class="p3">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">z</font></span>)</span></span>)</span></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p1">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">z</font></span>)</span>
<b>by </b><i>, , </i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">y</font></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p2">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">z</font></span>)</span></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p1">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">x</font></span>)</span>
<b>by </b><i>, , </i>
;<br/><i><font color="Green">E85</font></i>: <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K13">"\/"</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">y</font></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p5">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">z</font></span>)</span></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p4">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">x</font></span>)</span></span>)</span></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">y</font></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p4">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">z</font></span>)</span></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p3">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">x</font></span>)</span></span>)</span></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K13">"\/"</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">y</font></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p5">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">z</font></span>)</span></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p4">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">x</font></span>)</span></span>)</span></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">y</font></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p4">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">z</font></span>)</span></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p3">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">x</font></span>)</span></span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K12">"/\"</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">y</font></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p5">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">z</font></span>)</span></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p4">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">x</font></span>)</span></span>)</span></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">y</font></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p4">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">z</font></span>)</span></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p3">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">x</font></span>)</span></span>)</span></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K12">"/\"</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">y</font></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p5">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">z</font></span>)</span></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p4">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">x</font></span>)</span></span>)</span></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">y</font></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p4">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">z</font></span>)</span></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p3">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">x</font></span>)</span></span>)</span></span>)</span>
<b>by </b><i>, , , </i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K12">"/\"</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">y</font></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p4">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">z</font></span>)</span></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p3">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">x</font></span>)</span></span>)</span></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">y</font></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p4">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">z</font></span>)</span></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p3">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">x</font></span>)</span></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K12">"/\"</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">y</font></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p0">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">z</font></span>)</span></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p5">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">x</font></span>)</span></span>)</span></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">y</font></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p5">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">z</font></span>)</span></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p4">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">x</font></span>)</span></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="lattice3.html#T14">LATTICE3:14</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K12">"/\"</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">y</font></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p4">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">z</font></span>)</span></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p3">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">x</font></span>)</span></span>)</span></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">y</font></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p5">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">z</font></span>)</span></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p4">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">x</font></span>)</span></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">y</font></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p5">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">z</font></span>)</span></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p4">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">x</font></span>)</span></span>)</span></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p2">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K12">"/\"</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">y</font></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p5">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">z</font></span>)</span></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p4">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">x</font></span>)</span></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="lattice3.html#T14">LATTICE3:14</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K12">"/\"</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">y</font></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p4">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">z</font></span>)</span></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p3">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">x</font></span>)</span></span>)</span></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K12">"/\"</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">y</font></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p5">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">z</font></span>)</span></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p4">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">x</font></span>)</span></span>)</span></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">y</font></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p4">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">z</font></span>)</span></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p3">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">x</font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="yellow_5.html#T1">YELLOW_5:1</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K12">"/\"</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">y</font></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p5">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">z</font></span>)</span></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p4">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">x</font></span>)</span></span>)</span></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p2">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K12">"/\"</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">y</font></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p5">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">z</font></span>)</span></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p4">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">x</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">y</font></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p3">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">z</font></span>)</span></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p2">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">x</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="lattice3.html#T14">LATTICE3:14</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K12">"/\"</a> <span class="p2">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">y</font></span>)</span></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p1">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K12">"/\"</a> <span class="p2">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">y</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="yellow11.html#T1" target="_self">Th1</a>, <a class="ref" href="yellow11.html#T3" target="_self">Th3</a>, , <a class="ref" href="yellow_5.html#T8">YELLOW_5:8</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K13">"\/"</a> <span class="p2">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K12">"/\"</a> <span class="p3">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">y</font></span>)</span></span>)</span></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p1">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">y</font></span>)</span>
<b>by </b><i>, <a class="txt" href="yellow11.html#E1:20"><i><font color="Green">E35</font></i></a>, </i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">x</font></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p2">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">y</font></span>)</span></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p1">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">y</font></span>)</span>
<b>by </b><i>, <a class="txt" href="yellow11.html#E3:20_2"><i><font color="Green">E41</font></i></a>, </i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">y</font></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p2">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">z</font></span>)</span></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p1">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">x</font></span>)</span>
<b>by </b><i><a class="ref" href="lattice3.html#T16">LATTICE3:16</a></i>
;<br/><i><font color="Green">E86</font></i>: <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K13">"\/"</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">y</font></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p5">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">z</font></span>)</span></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p4">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">x</font></span>)</span></span>)</span></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">y</font></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p4">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">z</font></span>)</span></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p3">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">x</font></span>)</span></span>)</span></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K13">"\/"</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">y</font></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p5">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">z</font></span>)</span></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p4">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">x</font></span>)</span></span>)</span></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">y</font></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p4">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">z</font></span>)</span></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p3">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">x</font></span>)</span></span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K13">"\/"</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">y</font></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p4">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">z</font></span>)</span></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p3">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">x</font></span>)</span></span>)</span></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">y</font></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p4">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">z</font></span>)</span></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p3">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">x</font></span>)</span></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K13">"\/"</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">y</font></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p0">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">z</font></span>)</span></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p5">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">x</font></span>)</span></span>)</span></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">y</font></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p5">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">z</font></span>)</span></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p4">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">x</font></span>)</span></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="lattice3.html#T16">LATTICE3:16</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K13">"\/"</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">y</font></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p4">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">z</font></span>)</span></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p3">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">x</font></span>)</span></span>)</span></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">y</font></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p5">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">z</font></span>)</span></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p4">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">x</font></span>)</span></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">y</font></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p5">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">z</font></span>)</span></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p4">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">x</font></span>)</span></span>)</span></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p2">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K13">"\/"</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">y</font></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p5">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">z</font></span>)</span></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p4">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">x</font></span>)</span></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="lattice3.html#T16">LATTICE3:16</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K13">"\/"</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">y</font></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p4">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">z</font></span>)</span></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p3">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">x</font></span>)</span></span>)</span></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K13">"\/"</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">y</font></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p5">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">z</font></span>)</span></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p4">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">x</font></span>)</span></span>)</span></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">y</font></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p4">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">z</font></span>)</span></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p3">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">x</font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="yellow_5.html#T2">YELLOW_5:2</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K13">"\/"</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">y</font></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p5">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">z</font></span>)</span></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p4">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">x</font></span>)</span></span>)</span></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p2">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K13">"\/"</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">y</font></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p5">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">z</font></span>)</span></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p4">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">x</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">y</font></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p3">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">z</font></span>)</span></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p2">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">x</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="lattice3.html#T16">LATTICE3:16</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K13">"\/"</a> <span class="p2">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">y</font></span>)</span></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p1">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K13">"\/"</a> <span class="p2">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">y</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="yellow11.html#T4" target="_self">Th4</a>, <a class="ref" href="yellow11.html#T5" target="_self">Th5</a>, , <a class="ref" href="yellow_5.html#T10">YELLOW_5:10</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K12">"/\"</a> <span class="p2">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K13">"\/"</a> <span class="p3">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">y</font></span>)</span></span>)</span></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p1">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">y</font></span>)</span>
<b>by </b><i>, , </i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">x</font></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p2">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">y</font></span>)</span></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p1">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">y</font></span>)</span>
<b>by </b><i>, , </i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">y</font></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p2">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">z</font></span>)</span></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p1">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">x</font></span>)</span>
<b>by </b><i><a class="ref" href="lattice3.html#T14">LATTICE3:14</a></i>
;<br/><i><font color="Green">E87</font></i>: <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K13">"\/"</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">y</font></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p5">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">z</font></span>)</span></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p4">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">x</font></span>)</span></span>)</span></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">y</font></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p4">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">z</font></span>)</span></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p3">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">x</font></span>)</span></span>)</span></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K13">"\/"</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">y</font></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p5">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">z</font></span>)</span></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p4">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">x</font></span>)</span></span>)</span></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">y</font></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p4">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">z</font></span>)</span></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p3">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">x</font></span>)</span></span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K12">"/\"</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">y</font></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p5">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">z</font></span>)</span></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p4">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">x</font></span>)</span></span>)</span></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">y</font></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p4">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">z</font></span>)</span></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p3">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">x</font></span>)</span></span>)</span></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K12">"/\"</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">y</font></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p5">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">z</font></span>)</span></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p4">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">x</font></span>)</span></span>)</span></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">y</font></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p4">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">z</font></span>)</span></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p3">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">x</font></span>)</span></span>)</span></span>)</span>
<b>by </b><i>, , , </i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K12">"/\"</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">y</font></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p4">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">z</font></span>)</span></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p3">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">x</font></span>)</span></span>)</span></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">y</font></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p4">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">z</font></span>)</span></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p3">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">x</font></span>)</span></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K12">"/\"</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">y</font></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p0">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">z</font></span>)</span></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p5">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">x</font></span>)</span></span>)</span></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">y</font></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p5">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">z</font></span>)</span></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p4">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">x</font></span>)</span></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="lattice3.html#T14">LATTICE3:14</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K12">"/\"</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">y</font></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p4">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">z</font></span>)</span></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p3">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">x</font></span>)</span></span>)</span></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">y</font></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p5">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">z</font></span>)</span></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p4">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">x</font></span>)</span></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">y</font></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p5">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">z</font></span>)</span></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p4">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">x</font></span>)</span></span>)</span></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p2">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K12">"/\"</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">y</font></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p5">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">z</font></span>)</span></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p4">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">x</font></span>)</span></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="lattice3.html#T14">LATTICE3:14</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K12">"/\"</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">y</font></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p4">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">z</font></span>)</span></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p3">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">x</font></span>)</span></span>)</span></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K12">"/\"</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">y</font></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p5">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">z</font></span>)</span></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p4">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">x</font></span>)</span></span>)</span></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">y</font></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p4">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">z</font></span>)</span></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p3">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">x</font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="yellow_5.html#T1">YELLOW_5:1</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K12">"/\"</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">y</font></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p5">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">z</font></span>)</span></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p4">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">x</font></span>)</span></span>)</span></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p2">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K12">"/\"</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">y</font></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p5">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">z</font></span>)</span></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p4">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">x</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">y</font></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p3">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">z</font></span>)</span></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p2">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">x</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="lattice3.html#T14">LATTICE3:14</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K12">"/\"</a> <span class="p2">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">x</font></span>)</span></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p1">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K12">"/\"</a> <span class="p2">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">x</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="yellow11.html#T2" target="_self">Th2</a>, <a class="ref" href="yellow11.html#T3" target="_self">Th3</a>, , <a class="ref" href="yellow_5.html#T8">YELLOW_5:8</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K13">"\/"</a> <span class="p2">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K12">"/\"</a> <span class="p3">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">x</font></span>)</span></span>)</span></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p1">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">x</font></span>)</span>
<b>by </b><i>, , </i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">y</font></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p2">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">z</font></span>)</span></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p1">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">x</font></span>)</span>
<b>by </b><i>, <a class="txt" href="yellow11.html#E4:20_2"><i><font color="Green">E42</font></i></a>, </i>
;<br/><i><font color="Green">E88</font></i>: <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K13">"\/"</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">y</font></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p5">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">z</font></span>)</span></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p4">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">x</font></span>)</span></span>)</span></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">y</font></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p4">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">z</font></span>)</span></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p3">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">x</font></span>)</span></span>)</span></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K13">"\/"</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">y</font></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p5">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">z</font></span>)</span></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p4">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">x</font></span>)</span></span>)</span></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">y</font></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p4">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">z</font></span>)</span></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p3">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">x</font></span>)</span></span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K13">"\/"</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">y</font></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p4">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">z</font></span>)</span></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p3">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">x</font></span>)</span></span>)</span></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">y</font></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p4">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">z</font></span>)</span></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p3">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">x</font></span>)</span></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K13">"\/"</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">y</font></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p0">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">z</font></span>)</span></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p5">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">x</font></span>)</span></span>)</span></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">y</font></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p5">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">z</font></span>)</span></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p4">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">x</font></span>)</span></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="lattice3.html#T16">LATTICE3:16</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K13">"\/"</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">y</font></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p4">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">z</font></span>)</span></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p3">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">x</font></span>)</span></span>)</span></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">y</font></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p5">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">z</font></span>)</span></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p4">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">x</font></span>)</span></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">y</font></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p5">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">z</font></span>)</span></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p4">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">x</font></span>)</span></span>)</span></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p2">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K13">"\/"</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">y</font></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p5">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">z</font></span>)</span></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p4">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">x</font></span>)</span></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="lattice3.html#T16">LATTICE3:16</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K13">"\/"</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">y</font></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p4">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">z</font></span>)</span></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p3">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">x</font></span>)</span></span>)</span></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K13">"\/"</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">y</font></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p5">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">z</font></span>)</span></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p4">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">x</font></span>)</span></span>)</span></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">y</font></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p4">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">z</font></span>)</span></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p3">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">x</font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="yellow_5.html#T2">YELLOW_5:2</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K13">"\/"</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">y</font></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p5">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">z</font></span>)</span></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p4">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">x</font></span>)</span></span>)</span></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p2">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K13">"\/"</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">y</font></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p5">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">z</font></span>)</span></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p4">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">x</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">y</font></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p3">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">z</font></span>)</span></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p2">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">x</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="lattice3.html#T16">LATTICE3:16</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K13">"\/"</a> <span class="p2">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">x</font></span>)</span></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p1">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K13">"\/"</a> <span class="p2">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">x</font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="yellow11.html#E5"><i><font color="Green">Lemma26</font></i></a>, <a class="ref" href="yellow11.html#T5" target="_self">Th5</a>, <a class="ref" href="yellow11.html#T7" target="_self">Th7</a>, <a class="ref" href="yellow_5.html#T10">YELLOW_5:10</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K12">"/\"</a> <span class="p2">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K13">"\/"</a> <span class="p3">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">x</font></span>)</span></span>)</span></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p1">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">x</font></span>)</span>
<b>by </b><i>, , </i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">y</font></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p2">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">z</font></span>)</span></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p1">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">x</font></span>)</span>
<b>by </b><i>, , </i>
;<br/><a NAME="E49:20_2"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">y</font></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p2">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">z</font></span>)</span></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p1">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">x</font></span>)</span> <a href="orders_2.html#R3">&lt;=</a> <span class="p1">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K13">"\/"</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">y</font></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p4">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">z</font></span>)</span></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p3">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">x</font></span>)</span></span>)</span></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">y</font></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p3">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">z</font></span>)</span></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p2">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">x</font></span>)</span></span>)</span>
 <b>by </b><i>, <a class="ref" href="yellow_0.html#T23">YELLOW_0:23</a></i>;<br/><a NAME="E50:20_2"/><b>then </b><i><font color="Green">E89</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">y</font></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p3">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">z</font></span>)</span></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p2">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">x</font></span>)</span></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K13">"\/"</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">y</font></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p5">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">z</font></span>)</span></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p4">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">x</font></span>)</span></span>)</span></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">y</font></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p4">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">z</font></span>)</span></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p3">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">x</font></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K13">"\/"</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">y</font></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p4">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">z</font></span>)</span></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p3">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">x</font></span>)</span></span>)</span></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">y</font></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p3">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">z</font></span>)</span></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p2">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">x</font></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="yellow_5.html#T8">YELLOW_5:8</a></i>;<br/><a NAME="E51:20_2"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">y</font></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p2">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">z</font></span>)</span></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p1">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">x</font></span>)</span> <a href="orders_2.html#R3">&lt;=</a> <span class="p1">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K13">"\/"</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">y</font></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p4">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">z</font></span>)</span></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p3">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">x</font></span>)</span></span>)</span></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">y</font></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p3">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">z</font></span>)</span></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p2">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">x</font></span>)</span></span>)</span>
 <b>by </b><i>, <a class="ref" href="yellow_0.html#T23">YELLOW_0:23</a></i>;<br/><a NAME="E52:20_2"/><b>then </b><i><font color="Green">E90</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">y</font></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p3">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">z</font></span>)</span></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p2">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">x</font></span>)</span></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K13">"\/"</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">y</font></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p5">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">z</font></span>)</span></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p4">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">x</font></span>)</span></span>)</span></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">y</font></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p4">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">z</font></span>)</span></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p3">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">x</font></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K13">"\/"</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">y</font></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p4">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">z</font></span>)</span></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p3">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">x</font></span>)</span></span>)</span></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">y</font></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p3">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">z</font></span>)</span></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p2">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">x</font></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="yellow_5.html#T8">YELLOW_5:8</a></i>;<br/><a NAME="E53:20_2"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">y</font></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p2">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">z</font></span>)</span></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p1">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">x</font></span>)</span> <a href="orders_2.html#R3">&lt;=</a> <span class="p1">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K13">"\/"</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">y</font></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p4">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">z</font></span>)</span></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p3">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">x</font></span>)</span></span>)</span></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">y</font></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p3">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">z</font></span>)</span></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p2">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">x</font></span>)</span></span>)</span>
 <b>by </b><i>, <a class="ref" href="yellow_0.html#T23">YELLOW_0:23</a></i>;<br/><a NAME="E54:20_2"/><b>then </b><i><font color="Green">E91</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">y</font></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p3">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">z</font></span>)</span></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p2">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">x</font></span>)</span></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K13">"\/"</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">y</font></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p5">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">z</font></span>)</span></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p4">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">x</font></span>)</span></span>)</span></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">y</font></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p4">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">z</font></span>)</span></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p3">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">x</font></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K13">"\/"</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">y</font></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p4">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">z</font></span>)</span></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p3">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">x</font></span>)</span></span>)</span></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">y</font></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p3">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">z</font></span>)</span></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p2">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">x</font></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="yellow_5.html#T8">YELLOW_5:8</a></i>;<br/><a NAME="E55:20_2"/>
<span class="p1">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K13">"\/"</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">y</font></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p4">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">z</font></span>)</span></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p3">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">x</font></span>)</span></span>)</span></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">y</font></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p3">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">z</font></span>)</span></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p2">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">x</font></span>)</span></span>)</span> <a href="orders_2.html#R3">&lt;=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">y</font></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p2">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">z</font></span>)</span></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p1">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">x</font></span>)</span>
 <b>by </b><i><a class="ref" href="yellow_0.html#T23">YELLOW_0:23</a></i>;<br/><a NAME="E56:20_2"/><b>then </b><i><font color="Green">E92</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">y</font></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p3">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">z</font></span>)</span></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p2">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">x</font></span>)</span></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K13">"\/"</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">y</font></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p5">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">z</font></span>)</span></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p4">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">x</font></span>)</span></span>)</span></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">y</font></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p4">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">z</font></span>)</span></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p3">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">x</font></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K13">"\/"</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">y</font></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p4">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">z</font></span>)</span></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p3">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">x</font></span>)</span></span>)</span></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">y</font></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p3">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">z</font></span>)</span></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p2">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">x</font></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="yellow_5.html#T10">YELLOW_5:10</a></i>;<br/><a NAME="E57:20_2"/>
<span class="p1">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K13">"\/"</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">y</font></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p4">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">z</font></span>)</span></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p3">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">x</font></span>)</span></span>)</span></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">y</font></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p3">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">z</font></span>)</span></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p2">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">x</font></span>)</span></span>)</span> <a href="orders_2.html#R3">&lt;=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">y</font></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p2">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">z</font></span>)</span></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p1">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">x</font></span>)</span>
 <b>by </b><i><a class="ref" href="yellow_0.html#T23">YELLOW_0:23</a></i>;<br/><a NAME="E58:20_2"/><b>then </b><i><font color="Green">E93</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">y</font></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p3">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">z</font></span>)</span></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p2">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">x</font></span>)</span></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K13">"\/"</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">y</font></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p5">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">z</font></span>)</span></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p4">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">x</font></span>)</span></span>)</span></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">y</font></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p4">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">z</font></span>)</span></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p3">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">x</font></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K13">"\/"</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">y</font></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p4">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">z</font></span>)</span></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p3">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">x</font></span>)</span></span>)</span></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">y</font></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p3">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">z</font></span>)</span></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p2">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">x</font></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="yellow_5.html#T10">YELLOW_5:10</a></i>;<br/><a NAME="E59:20_2"/>
<span class="p1">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K13">"\/"</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">y</font></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p4">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">z</font></span>)</span></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p3">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">x</font></span>)</span></span>)</span></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">y</font></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p3">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">z</font></span>)</span></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p2">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">x</font></span>)</span></span>)</span> <a href="orders_2.html#R3">&lt;=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">y</font></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p2">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">z</font></span>)</span></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p1">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">x</font></span>)</span>
 <b>by </b><i><a class="ref" href="yellow_0.html#T23">YELLOW_0:23</a></i>;<br/><a NAME="E60:20_2"/><b>then </b><i><font color="Green">E94</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">y</font></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p3">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">z</font></span>)</span></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p2">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">x</font></span>)</span></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K13">"\/"</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">y</font></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p5">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">z</font></span>)</span></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p4">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">x</font></span>)</span></span>)</span></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">y</font></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p4">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">z</font></span>)</span></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p3">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">x</font></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K13">"\/"</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">y</font></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p4">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">z</font></span>)</span></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p3">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">x</font></span>)</span></span>)</span></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">y</font></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p3">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">z</font></span>)</span></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p2">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">x</font></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="yellow_5.html#T10">YELLOW_5:10</a></i>;<br/><b>thus </b><a NAME="E61:20_2"/>
 ex <font color="Olive">a</font>, <font color="Olive">b</font>, <font color="Olive">c</font>, <font color="Olive">d</font>, <font color="Olive">e</font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L</font> st <br/>( <font color="Olive">a</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Olive">b</font> &amp; <font color="Olive">a</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Olive">c</font> &amp; <font color="Olive">a</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Olive">d</font> &amp; <font color="Olive">a</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Olive">e</font> &amp; <font color="Olive">b</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Olive">c</font> &amp; <font color="Olive">b</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Olive">d</font> &amp; <font color="Olive">b</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Olive">e</font> &amp; <font color="Olive">c</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Olive">d</font> &amp; <font color="Olive">c</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Olive">e</font> &amp; <font color="Olive">d</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Olive">e</font> &amp; <font color="Olive">a</font> <a href="lattice3.html#K12">"/\"</a> <font color="Olive">b</font> <a href="hidden.html#R1">=</a> <font color="Olive">a</font> &amp; <font color="Olive">a</font> <a href="lattice3.html#K12">"/\"</a> <font color="Olive">c</font> <a href="hidden.html#R1">=</a> <font color="Olive">a</font> &amp; <font color="Olive">a</font> <a href="lattice3.html#K12">"/\"</a> <font color="Olive">d</font> <a href="hidden.html#R1">=</a> <font color="Olive">a</font> &amp; <font color="Olive">b</font> <a href="lattice3.html#K12">"/\"</a> <font color="Olive">e</font> <a href="hidden.html#R1">=</a> <font color="Olive">b</font> &amp; <font color="Olive">c</font> <a href="lattice3.html#K12">"/\"</a> <font color="Olive">e</font> <a href="hidden.html#R1">=</a> <font color="Olive">c</font> &amp; <font color="Olive">d</font> <a href="lattice3.html#K12">"/\"</a> <font color="Olive">e</font> <a href="hidden.html#R1">=</a> <font color="Olive">d</font> &amp; <font color="Olive">b</font> <a href="lattice3.html#K12">"/\"</a> <font color="Olive">c</font> <a href="hidden.html#R1">=</a> <font color="Olive">a</font> &amp; <font color="Olive">b</font> <a href="lattice3.html#K12">"/\"</a> <font color="Olive">d</font> <a href="hidden.html#R1">=</a> <font color="Olive">a</font> &amp; <font color="Olive">c</font> <a href="lattice3.html#K12">"/\"</a> <font color="Olive">d</font> <a href="hidden.html#R1">=</a> <font color="Olive">a</font> &amp; <font color="Olive">b</font> <a href="lattice3.html#K13">"\/"</a> <font color="Olive">c</font> <a href="hidden.html#R1">=</a> <font color="Olive">e</font> &amp; <font color="Olive">b</font> <a href="lattice3.html#K13">"\/"</a> <font color="Olive">d</font> <a href="hidden.html#R1">=</a> <font color="Olive">e</font> &amp; <font color="Olive">c</font> <a href="lattice3.html#K13">"\/"</a> <font color="Olive">d</font> <a href="hidden.html#R1">=</a> <font color="Olive">e</font> )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="20_2_22"><b>proof </b></a><div class="add">

<b>reconsider </b><font color="Maroon">b</font> = <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">y</font></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p2">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">z</font></span>)</span></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p1">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">x</font></span>)</span>, <font color="Maroon">x1</font> = <span class="p1">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K13">"\/"</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">y</font></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p4">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">z</font></span>)</span></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p3">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">x</font></span>)</span></span>)</span></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">y</font></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p3">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">z</font></span>)</span></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p2">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">x</font></span>)</span></span>)</span>, <font color="Maroon">y1</font> = <span class="p1">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K13">"\/"</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">y</font></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p4">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">z</font></span>)</span></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p3">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">x</font></span>)</span></span>)</span></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">y</font></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p3">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">z</font></span>)</span></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p2">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">x</font></span>)</span></span>)</span>, <font color="Maroon">z1</font> = <span class="p1">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K13">"\/"</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">y</font></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p4">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">z</font></span>)</span></span>)</span> <a href="lattice3.html#K13">"\/"</a> <span class="p3">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">x</font></span>)</span></span>)</span></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">y</font></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p3">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">z</font></span>)</span></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p2">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">x</font></span>)</span></span>)</span>, <font color="Maroon">t</font> = <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">x</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">y</font></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p2">(<span class="default"><font color="Maroon">y</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">z</font></span>)</span></span>)</span> <a href="lattice3.html#K12">"/\"</a> <span class="p1">(<span class="default"><font color="Maroon">z</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">x</font></span>)</span> as   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L</font> ;<br/>
<b>take </b>
<font color="Maroon">b</font>
;<br/>

<b>take </b>
<font color="Maroon">x1</font>
;<br/>

<b>take </b>
<font color="Maroon">y1</font>
;<br/>

<b>take </b>
<font color="Maroon">z1</font>
;<br/>

<b>take </b>
<font color="Maroon">t</font>
;<br/>

<b>thus </b><a NAME="E2:20_2_22"/>
<font color="Maroon">b</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">x1</font>
 <b>by </b><i>, , , <a class="txt" href="yellow11.html#E8:20_2"><i><font color="Green">E53</font></i></a>, <a class="txt" href="yellow11.html#E10:20_2"><i><font color="Green">E55</font></i></a>, <a class="txt" href="yellow11.html#E11:20_2"><i><font color="Green">E56</font></i></a>, <a class="ref" href="yellow_5.html#T2">YELLOW_5:2</a></i>;<br/>

<b>thus </b><a NAME="E3:20_2_22"/>
<font color="Maroon">b</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">y1</font>
 <b>by </b><i>, , , <a class="txt" href="yellow11.html#E5:20_2"><i><font color="Green">E52</font></i></a>, <a class="txt" href="yellow11.html#E9:20_2"><i><font color="Green">E54</font></i></a>, <a class="txt" href="yellow11.html#E11:20_2"><i><font color="Green">E56</font></i></a>, <a class="ref" href="yellow_5.html#T2">YELLOW_5:2</a></i>;<br/>

<b>thus </b><a NAME="E4:20_2_22"/>
<font color="Maroon">b</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">z1</font>
 <b>by </b><i>, , , <a class="txt" href="yellow11.html#E5:20_2"><i><font color="Green">E52</font></i></a>, <a class="txt" href="yellow11.html#E9:20_2"><i><font color="Green">E54</font></i></a>, <a class="txt" href="yellow11.html#E10:20_2"><i><font color="Green">E55</font></i></a>, <a class="ref" href="yellow_5.html#T2">YELLOW_5:2</a></i>;<br/>

<b>thus </b><a NAME="E5:20_2_22"/>
<font color="Maroon">b</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">t</font>
 <b>by </b><i/>;<br/>

<b>thus </b><a NAME="E6:20_2_22"/>
<font color="Maroon">x1</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">y1</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="20_2_22_1"><b>proof </b></a><div class="add">

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="20_2_22_1_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:20_2_22_1_1"/>
<font color="Maroon">x1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">y1</font>
 ;<br/><a NAME="E2:20_2_22_1_1"/><b>then </b>
( <font color="Maroon">x1</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">y1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">x1</font> &amp; <font color="Maroon">x1</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">y1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">x1</font> )
 <b>by </b><i><a class="ref" href="yellow_5.html#T1">YELLOW_5:1</a>, <a class="ref" href="yellow_5.html#T2">YELLOW_5:2</a></i>;<br/><b>hence </b><a NAME="E3:20_2_22_1_1"/>
contradiction
 <b>by </b><i>, , </i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E2:20_2_22_1"/>
<font color="Maroon">x1</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">y1</font>
 ;<br/>


</div><b>end;</b></div>

<b>thus </b><a NAME="E7:20_2_22"/>
<font color="Maroon">x1</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">z1</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="20_2_22_2"><b>proof </b></a><div class="add">

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="20_2_22_2_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:20_2_22_2_1"/>
<font color="Maroon">x1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">z1</font>
 ;<br/><a NAME="E2:20_2_22_2_1"/><b>then </b>
( <font color="Maroon">x1</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">z1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">x1</font> &amp; <font color="Maroon">x1</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">z1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">x1</font> )
 <b>by </b><i><a class="ref" href="yellow_5.html#T1">YELLOW_5:1</a>, <a class="ref" href="yellow_5.html#T2">YELLOW_5:2</a></i>;<br/><b>hence </b><a NAME="E3:20_2_22_2_1"/>
contradiction
 <b>by </b><i>, , </i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E2:20_2_22_2"/>
<font color="Maroon">x1</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">z1</font>
 ;<br/>


</div><b>end;</b></div>

<b>thus </b><a NAME="E8:20_2_22"/>
<font color="Maroon">x1</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">t</font>
 <b>by </b><i>, , , <a class="txt" href="yellow11.html#E5:20_2"><i><font color="Green">E52</font></i></a>, <a class="txt" href="yellow11.html#E13:20_2"><i><font color="Green">E58</font></i></a>, <a class="txt" href="yellow11.html#E14:20_2"><i><font color="Green">E59</font></i></a>, <a class="ref" href="yellow_5.html#T1">YELLOW_5:1</a></i>;<br/>

<b>thus </b><a NAME="E9:20_2_22"/>
<font color="Maroon">y1</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">z1</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="20_2_22_3"><b>proof </b></a><div class="add">

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="20_2_22_3_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:20_2_22_3_1"/>
<font color="Maroon">y1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">z1</font>
 ;<br/><a NAME="E2:20_2_22_3_1"/><b>then </b>
( <font color="Maroon">y1</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">z1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">y1</font> &amp; <font color="Maroon">y1</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">z1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">y1</font> )
 <b>by </b><i><a class="ref" href="yellow_5.html#T1">YELLOW_5:1</a>, <a class="ref" href="yellow_5.html#T2">YELLOW_5:2</a></i>;<br/><b>hence </b><a NAME="E3:20_2_22_3_1"/>
contradiction
 <b>by </b><i>, <a class="txt" href="yellow11.html#E5:20_2"><i><font color="Green">E52</font></i></a>, <a class="txt" href="yellow11.html#E8:20_2"><i><font color="Green">E53</font></i></a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E2:20_2_22_3"/>
<font color="Maroon">y1</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">z1</font>
 ;<br/>


</div><b>end;</b></div>

<b>thus </b><a NAME="E10:20_2_22"/>
<font color="Maroon">y1</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">t</font>
 <b>by </b><i>, , , <a class="txt" href="yellow11.html#E8:20_2"><i><font color="Green">E53</font></i></a>, <a class="txt" href="yellow11.html#E12:20_2"><i><font color="Green">E57</font></i></a>, <a class="txt" href="yellow11.html#E14:20_2"><i><font color="Green">E59</font></i></a>, <a class="ref" href="yellow_5.html#T1">YELLOW_5:1</a></i>;<br/>

<b>thus </b><a NAME="E11:20_2_22"/>
<font color="Maroon">z1</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">t</font>
 <b>by </b><i>, , , <a class="txt" href="yellow11.html#E8:20_2"><i><font color="Green">E53</font></i></a>, <a class="txt" href="yellow11.html#E12:20_2"><i><font color="Green">E57</font></i></a>, <a class="txt" href="yellow11.html#E13:20_2"><i><font color="Green">E58</font></i></a>, <a class="ref" href="yellow_5.html#T1">YELLOW_5:1</a></i>;<br/>

<b>thus </b><a NAME="E12:20_2_22"/>
<font color="Maroon">b</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">x1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">b</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="20_2_22_4"><b>proof </b></a><div class="add">

<a NAME="E1:20_2_22_4"/>
<font color="Maroon">b</font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">x1</font>
 
<b>by </b><i>, <a class="ref" href="yellow_0.html#T23">YELLOW_0:23</a></i>;<br/>
<b>hence </b><a NAME="E2:20_2_22_4"/>
<font color="Maroon">b</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">x1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">b</font>
 <b>by </b><i><a class="ref" href="yellow_5.html#T10">YELLOW_5:10</a></i>;<br/>


</div><b>end;</b></div>

<b>thus </b><a NAME="E13:20_2_22"/>
<font color="Maroon">b</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">y1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">b</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="20_2_22_5"><b>proof </b></a><div class="add">

<a NAME="E1:20_2_22_5"/>
<font color="Maroon">b</font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">y1</font>
 
<b>by </b><i>, <a class="ref" href="yellow_0.html#T23">YELLOW_0:23</a></i>;<br/>
<b>hence </b><a NAME="E2:20_2_22_5"/>
<font color="Maroon">b</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">y1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">b</font>
 <b>by </b><i><a class="ref" href="yellow_5.html#T10">YELLOW_5:10</a></i>;<br/>


</div><b>end;</b></div>

<b>thus </b><a NAME="E14:20_2_22"/>
<font color="Maroon">b</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">z1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">b</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="20_2_22_6"><b>proof </b></a><div class="add">

<a NAME="E1:20_2_22_6"/>
<font color="Maroon">b</font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">z1</font>
 
<b>by </b><i>, <a class="ref" href="yellow_0.html#T23">YELLOW_0:23</a></i>;<br/>
<b>hence </b><a NAME="E2:20_2_22_6"/>
<font color="Maroon">b</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">z1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">b</font>
 <b>by </b><i><a class="ref" href="yellow_5.html#T10">YELLOW_5:10</a></i>;<br/>


</div><b>end;</b></div>

<b>thus </b><a NAME="E15:20_2_22"/>
<font color="Maroon">x1</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">t</font> <a href="hidden.html#R1">=</a> <font color="Maroon">x1</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="20_2_22_7"><b>proof </b></a><div class="add">

<a NAME="E1:20_2_22_7"/>
<font color="Maroon">x1</font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">t</font>
 
<b>by </b><i>, <a class="ref" href="yellow_0.html#T22">YELLOW_0:22</a></i>;<br/>
<b>hence </b><a NAME="E2:20_2_22_7"/>
<font color="Maroon">x1</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">t</font> <a href="hidden.html#R1">=</a> <font color="Maroon">x1</font>
 <b>by </b><i><a class="ref" href="yellow_5.html#T10">YELLOW_5:10</a></i>;<br/>


</div><b>end;</b></div>

<b>thus </b><a NAME="E16:20_2_22"/>
<font color="Maroon">y1</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">t</font> <a href="hidden.html#R1">=</a> <font color="Maroon">y1</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="20_2_22_8"><b>proof </b></a><div class="add">

<a NAME="E1:20_2_22_8"/>
<font color="Maroon">y1</font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">t</font>
 
<b>by </b><i>, <a class="ref" href="yellow_0.html#T22">YELLOW_0:22</a></i>;<br/>
<b>hence </b><a NAME="E2:20_2_22_8"/>
<font color="Maroon">y1</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">t</font> <a href="hidden.html#R1">=</a> <font color="Maroon">y1</font>
 <b>by </b><i><a class="ref" href="yellow_5.html#T10">YELLOW_5:10</a></i>;<br/>


</div><b>end;</b></div>

<b>thus </b><a NAME="E17:20_2_22"/>
<font color="Maroon">z1</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">t</font> <a href="hidden.html#R1">=</a> <font color="Maroon">z1</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="20_2_22_9"><b>proof </b></a><div class="add">

<a NAME="E1:20_2_22_9"/>
<font color="Maroon">z1</font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">t</font>
 
<b>by </b><i>, <a class="ref" href="yellow_0.html#T22">YELLOW_0:22</a></i>;<br/>
<b>hence </b><a NAME="E2:20_2_22_9"/>
<font color="Maroon">z1</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">t</font> <a href="hidden.html#R1">=</a> <font color="Maroon">z1</font>
 <b>by </b><i><a class="ref" href="yellow_5.html#T10">YELLOW_5:10</a></i>;<br/>


</div><b>end;</b></div>

<b>thus </b><a NAME="E18:20_2_22"/>
<font color="Maroon">x1</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">y1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">b</font>
 <b>by </b><i/>;<br/>

<b>thus </b><a NAME="E19:20_2_22"/>
<font color="Maroon">x1</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">z1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">b</font>
 <b>by </b><i/>;<br/>

<b>thus </b><a NAME="E20:20_2_22"/>
<font color="Maroon">y1</font> <a href="lattice3.html#K12">"/\"</a> <font color="Maroon">z1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">b</font>
 <b>by </b><i><a class="txt" href="yellow11.html#E8:20_2"><i><font color="Green">E53</font></i></a></i>;<br/>

<b>thus </b><a NAME="E21:20_2_22"/>
<font color="Maroon">x1</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">y1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">t</font>
 <b>by </b><i/>;<br/>

<b>thus </b><a NAME="E22:20_2_22"/>
<font color="Maroon">x1</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">z1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">t</font>
 <b>by </b><i/>;<br/>

<b>thus </b><a NAME="E23:20_2_22"/>
<font color="Maroon">y1</font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">z1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">t</font>
 <b>by </b><i><a class="txt" href="yellow11.html#E5:20_2"><i><font color="Green">E52</font></i></a></i>;<br/>


</div><b>end;</b></div></div><b>end;</b></div>
<b>hence </b><a NAME="E4:20"/>
( ( for <font color="Olive">a</font>, <font color="Olive">b</font>, <font color="Olive">c</font>, <font color="Olive">d</font>, <font color="Olive">e</font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L</font>  holds <br/>(  not <font color="Olive">a</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Olive">b</font> or  not <font color="Olive">a</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Olive">c</font> or  not <font color="Olive">a</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Olive">d</font> or  not <font color="Olive">a</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Olive">e</font> or  not <font color="Olive">b</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Olive">c</font> or  not <font color="Olive">b</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Olive">d</font> or  not <font color="Olive">b</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Olive">e</font> or  not <font color="Olive">c</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Olive">d</font> or  not <font color="Olive">c</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Olive">e</font> or  not <font color="Olive">d</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Olive">e</font> or  not <font color="Olive">a</font> <a href="lattice3.html#K12">"/\"</a> <font color="Olive">b</font> <a href="hidden.html#R1">=</a> <font color="Olive">a</font> or  not <font color="Olive">a</font> <a href="lattice3.html#K12">"/\"</a> <font color="Olive">c</font> <a href="hidden.html#R1">=</a> <font color="Olive">a</font> or  not <font color="Olive">a</font> <a href="lattice3.html#K12">"/\"</a> <font color="Olive">d</font> <a href="hidden.html#R1">=</a> <font color="Olive">a</font> or  not <font color="Olive">b</font> <a href="lattice3.html#K12">"/\"</a> <font color="Olive">e</font> <a href="hidden.html#R1">=</a> <font color="Olive">b</font> or  not <font color="Olive">c</font> <a href="lattice3.html#K12">"/\"</a> <font color="Olive">e</font> <a href="hidden.html#R1">=</a> <font color="Olive">c</font> or  not <font color="Olive">d</font> <a href="lattice3.html#K12">"/\"</a> <font color="Olive">e</font> <a href="hidden.html#R1">=</a> <font color="Olive">d</font> or  not <font color="Olive">b</font> <a href="lattice3.html#K12">"/\"</a> <font color="Olive">c</font> <a href="hidden.html#R1">=</a> <font color="Olive">a</font> or  not <font color="Olive">b</font> <a href="lattice3.html#K12">"/\"</a> <font color="Olive">d</font> <a href="hidden.html#R1">=</a> <font color="Olive">a</font> or  not <font color="Olive">c</font> <a href="lattice3.html#K12">"/\"</a> <font color="Olive">d</font> <a href="hidden.html#R1">=</a> <font color="Olive">a</font> or  not <font color="Olive">b</font> <a href="lattice3.html#K13">"\/"</a> <font color="Olive">c</font> <a href="hidden.html#R1">=</a> <font color="Olive">e</font> or  not <font color="Olive">b</font> <a href="lattice3.html#K13">"\/"</a> <font color="Olive">d</font> <a href="hidden.html#R1">=</a> <font color="Olive">e</font> or  not <font color="Olive">c</font> <a href="lattice3.html#K13">"\/"</a> <font color="Olive">d</font> <a href="hidden.html#R1">=</a> <font color="Olive">e</font> ) ) implies <font color="Maroon">L</font> is <a href="waybel_1.html#V2">distributive</a> )
 ;<br/>


</div>
