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<b>let </b><font color="Maroon">c<sub>1</sub></font> be   <a href="cat_1.html#NM4">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" target="_self">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" target="_self">Morphism</a> of <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font>;<br/><b>let </b><font color="Maroon">c<sub>8</sub></font> be    <a href="cat_1.html#M1" target="_self">Morphism</a> of <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font>;<br/>















<b>assume </b><b>that </b><br/><a NAME="E1:42"/><i><font color="Green">E28</font></i>: 
 <a href="cat_1.html#K6" target="_self">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="E2:42"/><i><font color="Green">E29</font></i>: 
 <a href="cat_1.html#K6" target="_self">Hom</a> <font color="Maroon">c<sub>3</sub></font>,<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>and </b><br/><a NAME="E3:42"/><i><font color="Green">E30</font></i>: 
 <a href="cat_1.html#K6" target="_self">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> 
 ;<br/>

<b>reconsider </b><font color="Maroon">c<sub>9</sub></font> = <font color="Maroon">c<sub>6</sub></font> as   <a href="cat_1.html#NM2">Morphism</a> of <font color="Maroon">c<sub>1</sub></font> ;<br/>
<b>reconsider </b><font color="Maroon">c<sub>10</sub></font> = <font color="Maroon">c<sub>7</sub></font> as   <a href="cat_1.html#NM2">Morphism</a> of <font color="Maroon">c<sub>1</sub></font> ;<br/>
<b>reconsider </b><font color="Maroon">c<sub>11</sub></font> = <font color="Maroon">c<sub>8</sub></font> as   <a href="cat_1.html#NM2">Morphism</a> of <font color="Maroon">c<sub>1</sub></font> ;<br/>
<a NAME="E7:42"/>
( <font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R2">in</a>  <a href="cat_1.html#K6" target="_self">Hom</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font> &amp; <font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R2">in</a>  <a href="cat_1.html#K6" target="_self">Hom</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font> &amp; <font color="Maroon">c<sub>8</sub></font> <a href="hidden.html#R2">in</a>  <a href="cat_1.html#K6" target="_self">Hom</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font> )
 
<b>by </b><i><a class="txt" href="cat_1.html#E1:42"><i><font color="Green">E28</font></i></a>, <a class="txt" href="cat_1.html#E2:42"><i><font color="Green">E29</font></i></a>, <a class="txt" href="cat_1.html#E3:42"><i><font color="Green">E30</font></i></a>, <a class="ref" href="cat_1.html#D7" target="_self">Def7</a></i>;<br/>
<a NAME="E8:42"/><b>then </b><i><font color="Green">E31</font></i>: 
(  <a href="cat_1.html#K2" target="_self">dom</a> <font color="Maroon">c<sub>8</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>4</sub></font> &amp;  <a href="cat_1.html#K3" target="_self">cod</a> <font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>4</sub></font> &amp;  <a href="cat_1.html#K2" target="_self">dom</a> <font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font> &amp;  <a href="cat_1.html#K3" target="_self">cod</a> <font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font> )
 
<b>by </b><i><a class="ref" href="cat_1.html#T18" target="_self">Th18</a></i>;<br/>
<a NAME="E9:42"/><i><font color="Green">E32</font></i>: 
 <a href="cat_1.html#K6" target="_self">Hom</a> <font color="Maroon">c<sub>2</sub></font>,<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_1.html#E1:42"><i><font color="Green">E28</font></i></a>, <a class="txt" href="cat_1.html#E2:42"><i><font color="Green">E29</font></i></a>, <a class="ref" href="cat_1.html#T51" target="_self">Th51</a></i>;<br/>
<a NAME="E10:42"/>
 <a href="cat_1.html#K6" target="_self">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> 
 
<b>by </b><i><a class="txt" href="cat_1.html#E2:42"><i><font color="Green">E29</font></i></a>, <a class="txt" href="cat_1.html#E3:42"><i><font color="Green">E30</font></i></a>, <a class="ref" href="cat_1.html#T51" target="_self">Th51</a></i>;<br/>
<b>hence </b><span class="p1">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="cat_1.html#K9" target="_self">*</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="cat_1.html#K9" target="_self">*</a> <font color="Maroon">c<sub>6</sub></font> = 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="cat_1.html#K9" target="_self">*</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="cat_1.html#K4" target="_self">*</a> <font color="Maroon">c<sub>9</sub></font>
<b>by </b><i><a class="txt" href="cat_1.html#E1:42"><i><font color="Green">E28</font></i></a>, <a class="ref" href="cat_1.html#D13" target="_self">Def13</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>11</sub></font> <a href="cat_1.html#K4" target="_self">*</a> <font color="Maroon">c<sub>10</sub></font></span>)</span> <a href="cat_1.html#K4" target="_self">*</a> <font color="Maroon">c<sub>9</sub></font>
<b>by </b><i><a class="txt" href="cat_1.html#E2:42"><i><font color="Green">E29</font></i></a>, <a class="txt" href="cat_1.html#E3:42"><i><font color="Green">E30</font></i></a>, <a class="ref" href="cat_1.html#D13" target="_self">Def13</a></i>
<br/>.= 
<font color="Maroon">c<sub>11</sub></font> <a href="cat_1.html#K4" target="_self">*</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="cat_1.html#K4" target="_self">*</a> <font color="Maroon">c<sub>9</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="cat_1.html#E8:42"><i><font color="Green">E31</font></i></a>, <a class="ref" href="cat_1.html#T43" target="_self">Th43</a></i>
<br/>.= 
<font color="Maroon">c<sub>11</sub></font> <a href="cat_1.html#K4" target="_self">*</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="cat_1.html#K9" target="_self">*</a> <font color="Maroon">c<sub>6</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="cat_1.html#E1:42"><i><font color="Green">E28</font></i></a>, <a class="txt" href="cat_1.html#E2:42"><i><font color="Green">E29</font></i></a>, <a class="ref" href="cat_1.html#D13" target="_self">Def13</a></i>
<br/>.= 
<font color="Maroon">c<sub>8</sub></font> <a href="cat_1.html#K9" target="_self">*</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="cat_1.html#K9" target="_self">*</a> <font color="Maroon">c<sub>6</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="cat_1.html#E3:42"><i><font color="Green">E30</font></i></a>, <a class="txt" href="cat_1.html#E9:42"><i><font color="Green">E32</font></i></a>, <a class="ref" href="cat_1.html#D13" target="_self">Def13</a></i>
;<br/><br/>


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