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

<b>let </b><font color="Maroon">c<sub>1</sub></font> be  <a href="setfam_1.html#V2">with_non-empty_element</a>  <a href="hidden.html#M1">set</a> ;<br/>

<a NAME="E1:35"/><i><font color="Green">E25</font></i>: 
ex <font color="Olive">b<sub>1</sub></font> being non <a href="xboole_0.html#V1">empty</a>  <a href="hidden.html#M1">set</a>  st <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>1</sub></font>
 
<b>by </b><i><a class="ref" href="setfam_1.html#D11">SETFAM_1:def 11</a></i>;<br/>
<b>set </b><font color="Maroon">c<sub>2</sub></font> = <font color="Maroon">c<sub>1</sub></font> <a href="waybel34.html#K5" target="_self">-SUP_category</a> ;<br/>
<b>set </b><font color="Maroon">c<sub>3</sub></font> = <font color="Maroon">c<sub>1</sub></font> <a href="waybel34.html#K6" target="_self">LowerAdj</a> ;<br/>
<b>set </b><font color="Maroon">c<sub>4</sub></font> = <font color="Maroon">c<sub>1</sub></font> <a href="waybel34.html#K7" target="_self">UpperAdj</a> ;<br/>
<div><i><font color="Green">E26</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="35_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">c<sub>5</sub></font> be   <a href="altcat_1.html#NM1">object</a> of <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="waybel34.html#K5" target="_self">-SUP_category</a> </span>)</span>;<br/><b>thus </b><span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="waybel34.html#K6" target="_self">LowerAdj</a> </span>)</span> <a href="functor0.html#K3">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="waybel34.html#K7" target="_self">UpperAdj</a> </span>)</span> <a href="functor0.html#K3">.</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> = 
 <a href="yellow21.html#K4">latt</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="waybel34.html#K7" target="_self">UpperAdj</a> </span>)</span> <a href="functor0.html#K3">.</a> <font color="Maroon">c<sub>5</sub></font></span>)</span>
<b>by </b><i><a class="ref" href="waybel34.html#D6" target="_self">Def6</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="waybel34.html#K7" target="_self">UpperAdj</a> </span>)</span> <a href="functor0.html#K3">.</a> <font color="Maroon">c<sub>5</sub></font>

<br/>.= 
 <a href="yellow21.html#K4">latt</a> <font color="Maroon">c<sub>5</sub></font>
<b>by </b><i><a class="ref" href="waybel34.html#D7" target="_self">Def7</a></i>
<br/>.= 
<font color="Maroon">c<sub>5</sub></font>

;<br/></div><b>end;</b></div>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="35_2"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">c<sub>5</sub></font>, <font color="Maroon">c<sub>6</sub></font> be   <a href="altcat_1.html#NM1">object</a> of <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="waybel34.html#K5" target="_self">-SUP_category</a> </span>)</span>;<br/><b>assume </b><a NAME="E1:35_2"/><i><font color="Green">E27</font></i>: 
<span class="p1"><a href="altcat_1.html#K1">&lt;^</a><span class="default"><font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font></span><a href="altcat_1.html#K1">^&gt;</a></span> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a> 
 ;<br/><a NAME="E2:35_2"/><b>then </b><i><font color="Green">E28</font></i>: 
<span class="p1"><a href="altcat_1.html#K1">&lt;^</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="waybel34.html#K7" target="_self">UpperAdj</a> </span>)</span> <a href="functor0.html#K3">.</a> <font color="Maroon">c<sub>6</sub></font></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="waybel34.html#K7" target="_self">UpperAdj</a> </span>)</span> <a href="functor0.html#K3">.</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span><a href="altcat_1.html#K1">^&gt;</a></span> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a> 
 <b>by </b><i><a class="ref" href="functor0.html#D20">FUNCTOR0:def 20</a></i>;<br/><b>let </b><font color="Maroon">c<sub>7</sub></font> be   <a href="altcat_1.html#NM2">Morphism</a> of <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font>;<br/><a NAME="E3:35_2"/><i><font color="Green">E29</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="waybel34.html#K7" target="_self">UpperAdj</a> </span>)</span> <a href="functor0.html#K8">.</a> <font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R1">=</a>  <a href="waybel34.html#K2" target="_self">UpperAdj</a> <span class="p1">(<span class="default"><a href="yellow21.html#K5">@</a> <font color="Maroon">c<sub>7</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="waybel34.html#E1:35_2"><i><font color="Green">E27</font></i></a>, <a class="ref" href="waybel34.html#D7" target="_self">Def7</a></i>;<br/><a NAME="E4:35_2"/><i><font color="Green">E30</font></i>: 
(  <a href="yellow21.html#K5">@</a> <font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>7</sub></font> &amp;  <a href="yellow21.html#K5">@</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="waybel34.html#K7" target="_self">UpperAdj</a> </span>)</span> <a href="functor0.html#K8">.</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="waybel34.html#K7" target="_self">UpperAdj</a> </span>)</span> <a href="functor0.html#K8">.</a> <font color="Maroon">c<sub>7</sub></font> )
 <b>by </b><i><a class="txt" href="waybel34.html#E1:35_2"><i><font color="Green">E27</font></i></a>, <a class="txt" href="waybel34.html#E2:35_2"><i><font color="Green">E28</font></i></a>, <a class="ref" href="yellow21.html#D7">YELLOW21:def 7</a></i>;<br/><a NAME="E5:35_2"/><i><font color="Green">E31</font></i>: 
(  <a href="yellow21.html#K4">latt</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="waybel34.html#K7" target="_self">UpperAdj</a> </span>)</span> <a href="functor0.html#K3">.</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="waybel34.html#K7" target="_self">UpperAdj</a> </span>)</span> <a href="functor0.html#K3">.</a> <font color="Maroon">c<sub>5</sub></font> &amp;  <a href="yellow21.html#K4">latt</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="waybel34.html#K7" target="_self">UpperAdj</a> </span>)</span> <a href="functor0.html#K3">.</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="waybel34.html#K7" target="_self">UpperAdj</a> </span>)</span> <a href="functor0.html#K3">.</a> <font color="Maroon">c<sub>6</sub></font> &amp;  <a href="yellow21.html#K4">latt</a> <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>5</sub></font> &amp;  <a href="yellow21.html#K4">latt</a> <font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>6</sub></font> &amp; <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="waybel34.html#K7" target="_self">UpperAdj</a> </span>)</span> <a href="functor0.html#K3">.</a> <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a>  <a href="yellow21.html#K4">latt</a> <font color="Maroon">c<sub>5</sub></font> &amp; <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="waybel34.html#K7" target="_self">UpperAdj</a> </span>)</span> <a href="functor0.html#K3">.</a> <font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R1">=</a>  <a href="yellow21.html#K4">latt</a> <font color="Maroon">c<sub>6</sub></font> )
 <b>by </b><i><a class="ref" href="waybel34.html#D7" target="_self">Def7</a></i>;<br/><a NAME="E6:35_2"/><i><font color="Green">E32</font></i>: 
(  <a href="yellow21.html#K4">latt</a> <font color="Maroon">c<sub>5</sub></font> is <a href="lattice3.html#V3">complete</a> &amp;  <a href="yellow21.html#K4">latt</a> <font color="Maroon">c<sub>6</sub></font> is <a href="lattice3.html#V3">complete</a> &amp;  <a href="yellow21.html#K5">@</a> <font color="Maroon">c<sub>7</sub></font> is <a href="waybel_0.html#V18">sups-preserving</a> )
 <b>by </b><i><a class="txt" href="waybel34.html#E1:35"><i><font color="Green">E25</font></i></a>, <a class="txt" href="waybel34.html#E1:35_2"><i><font color="Green">E27</font></i></a>, <a class="txt" href="waybel34.html#E4:35_2"><i><font color="Green">E30</font></i></a>, <a class="ref" href="waybel34.html#D5" target="_self">Def5</a></i>;<br/><b>thus </b><span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="waybel34.html#K6" target="_self">LowerAdj</a> </span>)</span> <a href="functor0.html#K8">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="waybel34.html#K7" target="_self">UpperAdj</a> </span>)</span> <a href="functor0.html#K8">.</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> = 
 <a href="waybel34.html#K1" target="_self">LowerAdj</a> <span class="p1">(<span class="default"><a href="yellow21.html#K5">@</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="waybel34.html#K7" target="_self">UpperAdj</a> </span>)</span> <a href="functor0.html#K8">.</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="waybel34.html#E2:35_2"><i><font color="Green">E28</font></i></a>, <a class="ref" href="waybel34.html#D6" target="_self">Def6</a></i>
<br/>.= 
<font color="Maroon">c<sub>7</sub></font>
<b>by </b><i><a class="txt" href="waybel34.html#E3:35_2"><i><font color="Green">E29</font></i></a>, <a class="txt" href="waybel34.html#E4:35_2"><i><font color="Green">E30</font></i></a>, <a class="txt" href="waybel34.html#E5:35_2"><i><font color="Green">E31</font></i></a>, <a class="txt" href="waybel34.html#E6:35_2"><i><font color="Green">E32</font></i></a>, <a class="ref" href="waybel34.html#T11" target="_self">Th11</a></i>
;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E4:35"/>
<span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="waybel34.html#K6" target="_self">LowerAdj</a> </span>)</span> <a href="functor0.html#K15">"</a>  <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>1</sub></font> <a href="waybel34.html#K7" target="_self">UpperAdj</a> 
 <b>by </b><i><a class="txt" href="waybel34.html#E2:35"><i><font color="Green">E26</font></i></a>, <a class="ref" href="yellow20.html#T7">YELLOW20:7</a></i>;<br/>

<b>set </b><font color="Maroon">c<sub>5</sub></font> = <font color="Maroon">c<sub>1</sub></font> <a href="waybel34.html#K4" target="_self">-INF_category</a> ;<br/>
<b>set </b><font color="Maroon">c<sub>6</sub></font> = <font color="Maroon">c<sub>1</sub></font> <a href="waybel34.html#K6" target="_self">LowerAdj</a> ;<br/>
<b>set </b><font color="Maroon">c<sub>7</sub></font> = <font color="Maroon">c<sub>1</sub></font> <a href="waybel34.html#K7" target="_self">UpperAdj</a> ;<br/>
<div><i><font color="Green">E27</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="35_3"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">c<sub>8</sub></font> be   <a href="altcat_1.html#NM1">object</a> of <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="waybel34.html#K4" target="_self">-INF_category</a> </span>)</span>;<br/><b>thus </b><span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="waybel34.html#K7" target="_self">UpperAdj</a> </span>)</span> <a href="functor0.html#K3">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="waybel34.html#K6" target="_self">LowerAdj</a> </span>)</span> <a href="functor0.html#K3">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> = 
 <a href="yellow21.html#K4">latt</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="waybel34.html#K6" target="_self">LowerAdj</a> </span>)</span> <a href="functor0.html#K3">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span>
<b>by </b><i><a class="ref" href="waybel34.html#D7" target="_self">Def7</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="waybel34.html#K6" target="_self">LowerAdj</a> </span>)</span> <a href="functor0.html#K3">.</a> <font color="Maroon">c<sub>8</sub></font>

<br/>.= 
 <a href="yellow21.html#K4">latt</a> <font color="Maroon">c<sub>8</sub></font>
<b>by </b><i><a class="ref" href="waybel34.html#D6" target="_self">Def6</a></i>
<br/>.= 
<font color="Maroon">c<sub>8</sub></font>

;<br/></div><b>end;</b></div>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="35_4"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">c<sub>8</sub></font>, <font color="Maroon">c<sub>9</sub></font> be   <a href="altcat_1.html#NM1">object</a> of <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="waybel34.html#K4" target="_self">-INF_category</a> </span>)</span>;<br/><b>assume </b><a NAME="E1:35_4"/><i><font color="Green">E28</font></i>: 
<span class="p1"><a href="altcat_1.html#K1">&lt;^</a><span class="default"><font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>9</sub></font></span><a href="altcat_1.html#K1">^&gt;</a></span> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a> 
 ;<br/><a NAME="E2:35_4"/><b>then </b><i><font color="Green">E29</font></i>: 
<span class="p1"><a href="altcat_1.html#K1">&lt;^</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="waybel34.html#K6" target="_self">LowerAdj</a> </span>)</span> <a href="functor0.html#K3">.</a> <font color="Maroon">c<sub>9</sub></font></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="waybel34.html#K6" target="_self">LowerAdj</a> </span>)</span> <a href="functor0.html#K3">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span></span><a href="altcat_1.html#K1">^&gt;</a></span> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a> 
 <b>by </b><i><a class="ref" href="functor0.html#D20">FUNCTOR0:def 20</a></i>;<br/><b>let </b><font color="Maroon">c<sub>10</sub></font> be   <a href="altcat_1.html#NM2">Morphism</a> of <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>9</sub></font>;<br/><a NAME="E3:35_4"/><i><font color="Green">E30</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="waybel34.html#K6" target="_self">LowerAdj</a> </span>)</span> <a href="functor0.html#K8">.</a> <font color="Maroon">c<sub>10</sub></font> <a href="hidden.html#R1">=</a>  <a href="waybel34.html#K1" target="_self">LowerAdj</a> <span class="p1">(<span class="default"><a href="yellow21.html#K5">@</a> <font color="Maroon">c<sub>10</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="waybel34.html#E1:35_4"><i><font color="Green">E28</font></i></a>, <a class="ref" href="waybel34.html#D6" target="_self">Def6</a></i>;<br/><a NAME="E4:35_4"/><i><font color="Green">E31</font></i>: 
(  <a href="yellow21.html#K5">@</a> <font color="Maroon">c<sub>10</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>10</sub></font> &amp;  <a href="yellow21.html#K5">@</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="waybel34.html#K6" target="_self">LowerAdj</a> </span>)</span> <a href="functor0.html#K8">.</a> <font color="Maroon">c<sub>10</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="waybel34.html#K6" target="_self">LowerAdj</a> </span>)</span> <a href="functor0.html#K8">.</a> <font color="Maroon">c<sub>10</sub></font> )
 <b>by </b><i><a class="txt" href="waybel34.html#E1:35_4"><i><font color="Green">E28</font></i></a>, <a class="txt" href="waybel34.html#E2:35_4"><i><font color="Green">E29</font></i></a>, <a class="ref" href="yellow21.html#D7">YELLOW21:def 7</a></i>;<br/><a NAME="E5:35_4"/><i><font color="Green">E32</font></i>: 
(  <a href="yellow21.html#K4">latt</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="waybel34.html#K6" target="_self">LowerAdj</a> </span>)</span> <a href="functor0.html#K3">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="waybel34.html#K6" target="_self">LowerAdj</a> </span>)</span> <a href="functor0.html#K3">.</a> <font color="Maroon">c<sub>8</sub></font> &amp;  <a href="yellow21.html#K4">latt</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="waybel34.html#K6" target="_self">LowerAdj</a> </span>)</span> <a href="functor0.html#K3">.</a> <font color="Maroon">c<sub>9</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="waybel34.html#K6" target="_self">LowerAdj</a> </span>)</span> <a href="functor0.html#K3">.</a> <font color="Maroon">c<sub>9</sub></font> &amp;  <a href="yellow21.html#K4">latt</a> <font color="Maroon">c<sub>8</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>8</sub></font> &amp;  <a href="yellow21.html#K4">latt</a> <font color="Maroon">c<sub>9</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>9</sub></font> &amp; <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="waybel34.html#K6" target="_self">LowerAdj</a> </span>)</span> <a href="functor0.html#K3">.</a> <font color="Maroon">c<sub>8</sub></font> <a href="hidden.html#R1">=</a>  <a href="yellow21.html#K4">latt</a> <font color="Maroon">c<sub>8</sub></font> &amp; <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="waybel34.html#K6" target="_self">LowerAdj</a> </span>)</span> <a href="functor0.html#K3">.</a> <font color="Maroon">c<sub>9</sub></font> <a href="hidden.html#R1">=</a>  <a href="yellow21.html#K4">latt</a> <font color="Maroon">c<sub>9</sub></font> )
 <b>by </b><i><a class="ref" href="waybel34.html#D6" target="_self">Def6</a></i>;<br/><a NAME="E6:35_4"/><i><font color="Green">E33</font></i>: 
(  <a href="yellow21.html#K4">latt</a> <font color="Maroon">c<sub>8</sub></font> is <a href="lattice3.html#V3">complete</a> &amp;  <a href="yellow21.html#K4">latt</a> <font color="Maroon">c<sub>9</sub></font> is <a href="lattice3.html#V3">complete</a> &amp;  <a href="yellow21.html#K5">@</a> <font color="Maroon">c<sub>10</sub></font> is <a href="waybel_0.html#V17">infs-preserving</a> )
 <b>by </b><i><a class="txt" href="waybel34.html#E1:35"><i><font color="Green">E25</font></i></a>, <a class="txt" href="waybel34.html#E1:35_4"><i><font color="Green">E28</font></i></a>, <a class="txt" href="waybel34.html#E4:35_4"><i><font color="Green">E31</font></i></a>, <a class="ref" href="waybel34.html#D4" target="_self">Def4</a></i>;<br/><b>thus </b><span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="waybel34.html#K7" target="_self">UpperAdj</a> </span>)</span> <a href="functor0.html#K8">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="waybel34.html#K6" target="_self">LowerAdj</a> </span>)</span> <a href="functor0.html#K8">.</a> <font color="Maroon">c<sub>10</sub></font></span>)</span> = 
 <a href="waybel34.html#K2" target="_self">UpperAdj</a> <span class="p1">(<span class="default"><a href="yellow21.html#K5">@</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="waybel34.html#K6" target="_self">LowerAdj</a> </span>)</span> <a href="functor0.html#K8">.</a> <font color="Maroon">c<sub>10</sub></font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="waybel34.html#E2:35_4"><i><font color="Green">E29</font></i></a>, <a class="ref" href="waybel34.html#D7" target="_self">Def7</a></i>
<br/>.= 
<font color="Maroon">c<sub>10</sub></font>
<b>by </b><i><a class="txt" href="waybel34.html#E3:35_4"><i><font color="Green">E30</font></i></a>, <a class="txt" href="waybel34.html#E4:35_4"><i><font color="Green">E31</font></i></a>, <a class="txt" href="waybel34.html#E5:35_4"><i><font color="Green">E32</font></i></a>, <a class="txt" href="waybel34.html#E6:35_4"><i><font color="Green">E33</font></i></a>, <a class="ref" href="waybel34.html#T10" target="_self">Th10</a></i>
;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E7:35"/>
<span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="waybel34.html#K7" target="_self">UpperAdj</a> </span>)</span> <a href="functor0.html#K15">"</a>  <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>1</sub></font> <a href="waybel34.html#K6" target="_self">LowerAdj</a> 
 <b>by </b><i><a class="txt" href="waybel34.html#E5:35"><i><font color="Green">E27</font></i></a>, <a class="ref" href="yellow20.html#T7">YELLOW20:7</a></i>;<br/>


</div>
