<?xml version="1.0"?>
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<b>let </b><font color="Maroon">c<sub>1</sub></font> be   <a href="cat_4.html#NM1">Cartesian_category</a>;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font>, <font color="Maroon">c<sub>3</sub></font>, <font color="Maroon">c<sub>4</sub></font> be   <a href="cat_1.html#NM1">Object</a> of <font color="Maroon">c<sub>1</sub></font>;<br/>







<a NAME="E1:51"/><i><font color="Green">E30</font></i>: 
 <a href="cat_1.html#K6">Hom</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="cat_4.html#K2" target="_self">[x]</a> <font color="Maroon">c<sub>3</sub></font></span>)</span>,<font color="Maroon">c<sub>2</sub></font> <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="cat_4.html#T21" target="_self">Th21</a></i>;<br/>
<a NAME="E2:51"/><i><font color="Green">E31</font></i>: 
 <a href="cat_1.html#K6">Hom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="cat_4.html#K2" target="_self">[x]</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="cat_4.html#K2" target="_self">[x]</a> <font color="Maroon">c<sub>4</sub></font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="cat_4.html#K2" target="_self">[x]</a> <font color="Maroon">c<sub>3</sub></font></span>)</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="cat_4.html#T21" target="_self">Th21</a></i>;<br/>
<a NAME="E3:51"/><b>then </b><i><font color="Green">E32</font></i>: 
 <a href="cat_1.html#K6">Hom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="cat_4.html#K2" target="_self">[x]</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="cat_4.html#K2" target="_self">[x]</a> <font color="Maroon">c<sub>4</sub></font></span>)</span>,<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a> 
 
<b>by </b><i><a class="txt" href="cat_4.html#E1:51"><i><font color="Green">E30</font></i></a>, <a class="ref" href="cat_1.html#T52">CAT_1:52</a></i>;<br/>
<a NAME="E4:51"/>
 <a href="cat_1.html#K6">Hom</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="cat_4.html#K2" target="_self">[x]</a> <font color="Maroon">c<sub>3</sub></font></span>)</span>,<font color="Maroon">c<sub>3</sub></font> <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="cat_4.html#T21" target="_self">Th21</a></i>;<br/>
<a NAME="E5:51"/><b>then </b><i><font color="Green">E33</font></i>: 
 <a href="cat_1.html#K6">Hom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="cat_4.html#K2" target="_self">[x]</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="cat_4.html#K2" target="_self">[x]</a> <font color="Maroon">c<sub>4</sub></font></span>)</span>,<font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a> 
 
<b>by </b><i><a class="txt" href="cat_4.html#E2:51"><i><font color="Green">E31</font></i></a>, <a class="ref" href="cat_1.html#T52">CAT_1:52</a></i>;<br/>
<a NAME="E6:51"/>
 <a href="cat_1.html#K6">Hom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="cat_4.html#K2" target="_self">[x]</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="cat_4.html#K2" target="_self">[x]</a> <font color="Maroon">c<sub>4</sub></font></span>)</span>,<font color="Maroon">c<sub>4</sub></font> <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="cat_4.html#T21" target="_self">Th21</a></i>;<br/>
<a NAME="E7:51"/><b>then </b>
 <a href="cat_1.html#K6">Hom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="cat_4.html#K2" target="_self">[x]</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="cat_4.html#K2" target="_self">[x]</a> <font color="Maroon">c<sub>4</sub></font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="cat_4.html#K2" target="_self">[x]</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a> 
 
<b>by </b><i><a class="txt" href="cat_4.html#E5:51"><i><font color="Green">E33</font></i></a>, <a class="ref" href="cat_4.html#T25" target="_self">Th25</a></i>;<br/>
<b>hence </b><a NAME="E8:51"/>
 <a href="cat_1.html#K6">Hom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="cat_4.html#K2" target="_self">[x]</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="cat_4.html#K2" target="_self">[x]</a> <font color="Maroon">c<sub>4</sub></font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="cat_4.html#K2" target="_self">[x]</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="cat_4.html#K2" target="_self">[x]</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a> 
 <b>by </b><i><a class="txt" href="cat_4.html#E3:51"><i><font color="Green">E32</font></i></a>, <a class="ref" href="cat_4.html#T25" target="_self">Th25</a></i>;<br/>

<a NAME="E9:51"/><i><font color="Green">E34</font></i>: 
 <a href="cat_1.html#K6">Hom</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="cat_4.html#K2" target="_self">[x]</a> <font color="Maroon">c<sub>4</sub></font></span>)</span>,<font color="Maroon">c<sub>3</sub></font> <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="cat_4.html#T21" target="_self">Th21</a></i>;<br/>
<a NAME="E10:51"/><i><font color="Green">E35</font></i>: 
 <a href="cat_1.html#K6">Hom</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="cat_4.html#K2" target="_self">[x]</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="cat_4.html#K2" target="_self">[x]</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="cat_4.html#K2" target="_self">[x]</a> <font color="Maroon">c<sub>4</sub></font></span>)</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="cat_4.html#T21" target="_self">Th21</a></i>;<br/>
<a NAME="E11:51"/><b>then </b><i><font color="Green">E36</font></i>: 
 <a href="cat_1.html#K6">Hom</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="cat_4.html#K2" target="_self">[x]</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="cat_4.html#K2" target="_self">[x]</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span>,<font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a> 
 
<b>by </b><i><a class="txt" href="cat_4.html#E9:51"><i><font color="Green">E34</font></i></a>, <a class="ref" href="cat_1.html#T52">CAT_1:52</a></i>;<br/>
<a NAME="E12:51"/>
 <a href="cat_1.html#K6">Hom</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="cat_4.html#K2" target="_self">[x]</a> <font color="Maroon">c<sub>4</sub></font></span>)</span>,<font color="Maroon">c<sub>4</sub></font> <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="cat_4.html#T21" target="_self">Th21</a></i>;<br/>
<a NAME="E13:51"/><b>then </b><i><font color="Green">E37</font></i>: 
 <a href="cat_1.html#K6">Hom</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="cat_4.html#K2" target="_self">[x]</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="cat_4.html#K2" target="_self">[x]</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span>,<font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a> 
 
<b>by </b><i><a class="txt" href="cat_4.html#E10:51"><i><font color="Green">E35</font></i></a>, <a class="ref" href="cat_1.html#T52">CAT_1:52</a></i>;<br/>
<a NAME="E14:51"/>
 <a href="cat_1.html#K6">Hom</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="cat_4.html#K2" target="_self">[x]</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="cat_4.html#K2" target="_self">[x]</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span>,<font color="Maroon">c<sub>2</sub></font> <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="cat_4.html#T21" target="_self">Th21</a></i>;<br/>
<a NAME="E15:51"/><b>then </b>
 <a href="cat_1.html#K6">Hom</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="cat_4.html#K2" target="_self">[x]</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="cat_4.html#K2" target="_self">[x]</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="cat_4.html#K2" target="_self">[x]</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a> 
 
<b>by </b><i><a class="txt" href="cat_4.html#E11:51"><i><font color="Green">E36</font></i></a>, <a class="ref" href="cat_4.html#T25" target="_self">Th25</a></i>;<br/>
<b>hence </b><a NAME="E16:51"/>
 <a href="cat_1.html#K6">Hom</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="cat_4.html#K2" target="_self">[x]</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="cat_4.html#K2" target="_self">[x]</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="cat_4.html#K2" target="_self">[x]</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="cat_4.html#K2" target="_self">[x]</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a> 
 <b>by </b><i><a class="txt" href="cat_4.html#E13:51"><i><font color="Green">E37</font></i></a>, <a class="ref" href="cat_4.html#T25" target="_self">Th25</a></i>;<br/>


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