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<b>let </b><font color="Maroon">c<sub>1</sub></font>, <font color="Maroon">c<sub>2</sub></font>, <font color="Maroon">c<sub>3</sub></font> be   <a href="cat_1.html#NM4">Category</a>;<br/><b>let </b><font color="Maroon">c<sub>4</sub></font> be    <a href="cat_1.html#M2" target="_self">Functor</a> of <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font>;<br/><b>let </b><font color="Maroon">c<sub>5</sub></font> be    <a href="cat_1.html#M2" target="_self">Functor</a> of <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font>;<br/>









<b>assume </b><b>that </b><br/><a NAME="E1:105"/><i><font color="Green">E70</font></i>: 
<font color="Maroon">c<sub>4</sub></font> is <a href="cat_1.html#V9" target="_self">full</a>
 <b>and </b><br/><a NAME="E2:105"/><i><font color="Green">E71</font></i>: 
<font color="Maroon">c<sub>5</sub></font> is <a href="cat_1.html#V9" target="_self">full</a>
 ;<br/>

<b>let </b><font color="Maroon">c<sub>6</sub></font>, <font color="Maroon">c<sub>7</sub></font> be   <a href="cat_1.html#NM1">Object</a> of <font color="Maroon">c<sub>1</sub></font>; <i><font color="Red">:: according to </font></i><a class="ref" href="cat_1.html#D23" target="_self">CAT_1:def 23</a><br/>

<b>assume </b><a NAME="E3:105"/><i><font color="Green">E72</font></i>: 
 <a href="cat_1.html#K6" target="_self">Hom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="cat_1.html#K14" target="_self">*</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="cat_1.html#K13" target="_self">.</a> <font color="Maroon">c<sub>6</sub></font></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="cat_1.html#K14" target="_self">*</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="cat_1.html#K13" target="_self">.</a> <font color="Maroon">c<sub>7</sub></font></span>)</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="cat_1.html#M1" target="_self">Morphism</a> of <span class="p1">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="cat_1.html#K14" target="_self">*</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="cat_1.html#K13" target="_self">.</a> <font color="Maroon">c<sub>6</sub></font>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="cat_1.html#K14" target="_self">*</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="cat_1.html#K13" target="_self">.</a> <font color="Maroon">c<sub>7</sub></font>;<br/>

<a NAME="E4:105"/><i><font color="Green">E73</font></i>: 
( <span class="p1">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="cat_1.html#K14" target="_self">*</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="cat_1.html#K13" target="_self">.</a> <font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>5</sub></font> <a href="cat_1.html#K13" target="_self">.</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="cat_1.html#K13" target="_self">.</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> &amp; <span class="p1">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="cat_1.html#K14" target="_self">*</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="cat_1.html#K13" target="_self">.</a> <font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>5</sub></font> <a href="cat_1.html#K13" target="_self">.</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="cat_1.html#K13" target="_self">.</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> )
 
<b>by </b><i><a class="ref" href="cat_1.html#T113" target="_self">Th113</a></i>;<br/>
<b>then consider </b><font color="Maroon">c<sub>9</sub></font> being    <a href="cat_1.html#M1" target="_self">Morphism</a> of <font color="Maroon">c<sub>4</sub></font> <a href="cat_1.html#K13" target="_self">.</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>4</sub></font> <a href="cat_1.html#K13" target="_self">.</a> <font color="Maroon">c<sub>7</sub></font><b> such that </b><br/><a NAME="E6:105"/><i><font color="Green">E74</font></i>: 
<font color="Maroon">c<sub>8</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>5</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>9</sub></font>
 <b>by </b><i><a class="txt" href="cat_1.html#E2:105"><i><font color="Green">E71</font></i></a>, <a class="txt" href="cat_1.html#E3:105"><i><font color="Green">E72</font></i></a>, <a class="ref" href="cat_1.html#D23" target="_self">Def23</a></i>;<br/>
<a NAME="E7:105"/><i><font color="Green">E75</font></i>: 
 <a href="cat_1.html#K6" target="_self">Hom</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="cat_1.html#K13" target="_self">.</a> <font color="Maroon">c<sub>6</sub></font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="cat_1.html#K13" target="_self">.</a> <font color="Maroon">c<sub>7</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_1.html#E2:105"><i><font color="Green">E71</font></i></a>, <a class="txt" href="cat_1.html#E3:105"><i><font color="Green">E72</font></i></a>, <a class="txt" href="cat_1.html#E4:105"><i><font color="Green">E73</font></i></a>, <a class="ref" href="cat_1.html#D23" target="_self">Def23</a></i>;<br/>
<b>hence </b><a NAME="E8:105"/>
 <a href="cat_1.html#K6" target="_self">Hom</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>7</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_1.html#E1:105"><i><font color="Green">E70</font></i></a>, <a class="ref" href="cat_1.html#D23" target="_self">Def23</a></i>;<br/>

<b>consider </b><font color="Maroon">c<sub>10</sub></font> being    <a href="cat_1.html#M1" target="_self">Morphism</a> of <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>7</sub></font><b> such that </b><br/><a NAME="E10:105"/><i><font color="Green">E76</font></i>: 
<font color="Maroon">c<sub>9</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>4</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>10</sub></font>
 <b>by </b><i><a class="txt" href="cat_1.html#E1:105"><i><font color="Green">E70</font></i></a>, <a class="txt" href="cat_1.html#E7:105"><i><font color="Green">E75</font></i></a>, <a class="ref" href="cat_1.html#D23" target="_self">Def23</a></i>;<br/>
<b>take </b>
<font color="Maroon">c<sub>10</sub></font>
;<br/>

<b>thus </b><a NAME="E11:105"/>
<font color="Maroon">c<sub>8</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="cat_1.html#K14" target="_self">*</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>10</sub></font>
 <b>by </b><i><a class="txt" href="cat_1.html#E6:105"><i><font color="Green">E74</font></i></a>, <a class="txt" href="cat_1.html#E10:105"><i><font color="Green">E76</font></i></a>, <a class="ref" href="funct_2.html#T21">FUNCT_2:21</a></i>;<br/>


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