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<b>let </b><font color="Maroon">c<sub>4</sub></font>, <font color="Maroon">c<sub>5</sub></font> be  <a href="functor0.html#V9">strict</a> <a href="functor0.html#V16">contravariant</a>  <a href="functor0.html#M2">Functor</a> of <font color="Maroon">c<sub>1</sub></font> <a href="waybel34.html#K4" target="_self">-INF_category</a> ,<font color="Maroon">c<sub>1</sub></font> <a href="waybel34.html#K5" target="_self">-SUP_category</a> ;<br/>

<b>assume </b><b>that </b><br/><a NAME="E1:33_2_2"/><i><font color="Green">E28</font></i>: 
for <font color="Olive">b<sub>1</sub></font> being  <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> holds <font color="Maroon">c<sub>4</sub></font> <a href="functor0.html#K3">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a>  <a href="yellow21.html#K4">latt</a> <font color="Olive">b<sub>1</sub></font>
 <b>and </b><br/><a NAME="E2:33_2_2"/><i><font color="Green">E29</font></i>: 
for <font color="Olive">b<sub>1</sub></font>, <font color="Olive">b<sub>2</sub></font> being  <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> st <span class="p1"><a href="altcat_1.html#K1">&lt;^</a><span class="default"><font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>2</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>  holds <br/>for <font color="Olive">b<sub>3</sub></font> being  <a href="altcat_1.html#NM2">Morphism</a> of <font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>2</sub></font> holds <font color="Maroon">c<sub>4</sub></font> <a href="functor0.html#K8">.</a> <font color="Olive">b<sub>3</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="Olive">b<sub>3</sub></font></span>)</span>
 <b>and </b><br/><a NAME="E3:33_2_2"/><i><font color="Green">E30</font></i>: 
for <font color="Olive">b<sub>1</sub></font> being  <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> holds <font color="Maroon">c<sub>5</sub></font> <a href="functor0.html#K3">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a>  <a href="yellow21.html#K4">latt</a> <font color="Olive">b<sub>1</sub></font>
 <b>and </b><br/><a NAME="E4:33_2_2"/><i><font color="Green">E31</font></i>: 
for <font color="Olive">b<sub>1</sub></font>, <font color="Olive">b<sub>2</sub></font> being  <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> st <span class="p1"><a href="altcat_1.html#K1">&lt;^</a><span class="default"><font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>2</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>  holds <br/>for <font color="Olive">b<sub>3</sub></font> being  <a href="altcat_1.html#NM2">Morphism</a> of <font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>2</sub></font> holds <font color="Maroon">c<sub>5</sub></font> <a href="functor0.html#K8">.</a> <font color="Olive">b<sub>3</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="Olive">b<sub>3</sub></font></span>)</span>
 ;<br/>

<div><i><font color="Green">E32</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="33_2_2_1"><b>now </b></a><div class="add"><b>let </b><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#K4" target="_self">-INF_category</a> </span>)</span>;<br/><b>thus </b><font color="Maroon">c<sub>4</sub></font> <a href="functor0.html#K3">.</a> <font color="Maroon">c<sub>6</sub></font> = 
 <a href="yellow21.html#K4">latt</a> <font color="Maroon">c<sub>6</sub></font>
<b>by </b><i><a class="txt" href="waybel34.html#E1:33_2_2"><i><font color="Green">E28</font></i></a></i>
<br/>.= 
<font color="Maroon">c<sub>5</sub></font> <a href="functor0.html#K3">.</a> <font color="Maroon">c<sub>6</sub></font>
<b>by </b><i><a class="txt" href="waybel34.html#E3:33_2_2"><i><font color="Green">E30</font></i></a></i>
;<br/></div><b>end;</b></div>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="33_2_2_2"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">c<sub>6</sub></font>, <font color="Maroon">c<sub>7</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="E1:33_2_2_2"/><i><font color="Green">E33</font></i>: 
<span class="p1"><a href="altcat_1.html#K1">&lt;^</a><span class="default"><font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>7</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/><b>let </b><font color="Maroon">c<sub>8</sub></font> be   <a href="altcat_1.html#NM2">Morphism</a> of <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>7</sub></font>;<br/><b>thus </b><font color="Maroon">c<sub>4</sub></font> <a href="functor0.html#K8">.</a> <font color="Maroon">c<sub>8</sub></font> = 
 <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>8</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="waybel34.html#E2:33_2_2"><i><font color="Green">E29</font></i></a>, <a class="txt" href="waybel34.html#E1:33_2_2_2"><i><font color="Green">E33</font></i></a></i>
<br/>.= 
<font color="Maroon">c<sub>5</sub></font> <a href="functor0.html#K8">.</a> <font color="Maroon">c<sub>8</sub></font>
<b>by </b><i><a class="txt" href="waybel34.html#E4:33_2_2"><i><font color="Green">E31</font></i></a>, <a class="txt" href="waybel34.html#E1:33_2_2_2"><i><font color="Green">E33</font></i></a></i>
;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E7:33_2_2"/>
<font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>5</sub></font>
 <b>by </b><i><a class="txt" href="waybel34.html#E5:33_2_2"><i><font color="Green">E32</font></i></a>, <a class="ref" href="yellow18.html#T2">YELLOW18:2</a></i>;<br/>


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