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

<b>let </b><font color="Maroon">c<sub>1</sub></font> be   <a href="cat_4.html#NM2">Cocartesian_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>, <font color="Maroon">c<sub>5</sub></font> be   <a href="cat_1.html#NM1">Object</a> of <font color="Maroon">c<sub>1</sub></font>;<br/><b>let </b><font color="Maroon">c<sub>6</sub></font> be    <a href="cat_1.html#M1">Morphism</a> of <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font>;<br/><b>let </b><font color="Maroon">c<sub>7</sub></font> be    <a href="cat_1.html#M1">Morphism</a> of <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>3</sub></font>;<br/><b>let </b><font color="Maroon">c<sub>8</sub></font> be    <a href="cat_1.html#M1">Morphism</a> of <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>5</sub></font>;<br/>















<b>assume </b><b>that </b><br/><a NAME="E1:94"/><i><font color="Green">E55</font></i>: 
 <a href="cat_1.html#K6">Hom</a> <font color="Maroon">c<sub>2</sub></font>,<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>and </b><br/><a NAME="E2:94"/><i><font color="Green">E56</font></i>: 
 <a href="cat_1.html#K6">Hom</a> <font color="Maroon">c<sub>4</sub></font>,<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>and </b><br/><a NAME="E3:94"/><i><font color="Green">E57</font></i>: 
 <a href="cat_1.html#K6">Hom</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a> 
 ;<br/>

<a NAME="E4:94"/>
(  <a href="cat_1.html#K6">Hom</a> <font color="Maroon">c<sub>2</sub></font>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="cat_4.html#K20" target="_self">+</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>  &amp;  <a href="cat_1.html#K6">Hom</a> <font color="Maroon">c<sub>4</sub></font>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="cat_4.html#K20" target="_self">+</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>  &amp;  <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#K20" target="_self">+</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>  &amp; <font color="Maroon">c<sub>8</sub></font> <a href="cat_1.html#K9">*</a> <span class="p1">(<span class="default"><span class="p2"><a href="cat_4.html#K27" target="_self">[$</a><span class="default"><font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>7</sub></font></span><a href="cat_4.html#K27" target="_self">$]</a></span> <a href="cat_1.html#K9">*</a> <span class="p2">(<span class="default"><a href="cat_4.html#K25" target="_self">in1</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>8</sub></font> <a href="cat_1.html#K9">*</a> <font color="Maroon">c<sub>6</sub></font> &amp; <font color="Maroon">c<sub>8</sub></font> <a href="cat_1.html#K9">*</a> <span class="p1">(<span class="default"><span class="p2"><a href="cat_4.html#K27" target="_self">[$</a><span class="default"><font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>7</sub></font></span><a href="cat_4.html#K27" target="_self">$]</a></span> <a href="cat_1.html#K9">*</a> <span class="p2">(<span class="default"><a href="cat_4.html#K26" target="_self">in2</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>8</sub></font> <a href="cat_1.html#K9">*</a> <font color="Maroon">c<sub>7</sub></font> )
 
<b>by </b><i><a class="txt" href="cat_4.html#E1:94"><i><font color="Green">E55</font></i></a>, <a class="txt" href="cat_4.html#E2:94"><i><font color="Green">E56</font></i></a>, <a class="ref" href="cat_4.html#D29" target="_self">Def29</a>, <a class="ref" href="cat_4.html#T66" target="_self">Th66</a>, <a class="ref" href="cat_4.html#T70" target="_self">Th70</a></i>;<br/>
<a NAME="E5:94"/><b>then </b>
( <span class="p1">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="cat_1.html#K9">*</a> <span class="p2"><a href="cat_4.html#K27" target="_self">[$</a><span class="default"><font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>7</sub></font></span><a href="cat_4.html#K27" target="_self">$]</a></span></span>)</span> <a href="cat_1.html#K9">*</a> <span class="p1">(<span class="default"><a href="cat_4.html#K25" target="_self">in1</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>8</sub></font> <a href="cat_1.html#K9">*</a> <font color="Maroon">c<sub>6</sub></font> &amp; <span class="p1">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="cat_1.html#K9">*</a> <span class="p2"><a href="cat_4.html#K27" target="_self">[$</a><span class="default"><font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>7</sub></font></span><a href="cat_4.html#K27" target="_self">$]</a></span></span>)</span> <a href="cat_1.html#K9">*</a> <span class="p1">(<span class="default"><a href="cat_4.html#K26" target="_self">in2</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>8</sub></font> <a href="cat_1.html#K9">*</a> <font color="Maroon">c<sub>7</sub></font> &amp;  <a href="cat_1.html#K6">Hom</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a>  &amp;  <a href="cat_1.html#K6">Hom</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</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#E1:94"><i><font color="Green">E55</font></i></a>, <a class="txt" href="cat_4.html#E2:94"><i><font color="Green">E56</font></i></a>, <a class="txt" href="cat_4.html#E3:94"><i><font color="Green">E57</font></i></a>, <a class="ref" href="cat_1.html#T52">CAT_1:52</a>, <a class="ref" href="cat_1.html#T54">CAT_1:54</a></i>;<br/>
<b>hence </b><a NAME="E6:94"/>
<span class="p1"><a href="cat_4.html#K27" target="_self">[$</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="cat_1.html#K9">*</a> <font color="Maroon">c<sub>6</sub></font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="cat_1.html#K9">*</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span><a href="cat_4.html#K27" target="_self">$]</a></span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>8</sub></font> <a href="cat_1.html#K9">*</a> <span class="p1"><a href="cat_4.html#K27" target="_self">[$</a><span class="default"><font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>7</sub></font></span><a href="cat_4.html#K27" target="_self">$]</a></span>
 <b>by </b><i><a class="ref" href="cat_4.html#D29" target="_self">Def29</a></i>;<br/>


</div>
