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<b>let </b><font color="Maroon">c<sub>5</sub></font>, <font color="Maroon">c<sub>6</sub></font>, <font color="Maroon">c<sub>7</sub></font> be    <a href="subset_1.html#M2">Element</a> of  <a href="cat_5.html#K12" target="_self">Hom</a> <font color="Maroon">c<sub>2</sub></font>;<br/><b>let </b><font color="Maroon">c<sub>8</sub></font>, <font color="Maroon">c<sub>9</sub></font> be   <a href="cat_1.html#NM2">Morphism</a> of <font color="Maroon">c<sub>1</sub></font>;<br/>



<b>assume </b><a NAME="E1:53_1"/><i><font color="Green">E33</font></i>: 
(  <a href="cat_1.html#K2">dom</a> <font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R1">=</a>  <a href="cat_1.html#K3">cod</a> <font color="Maroon">c<sub>8</sub></font> &amp; <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>6</sub></font> <a href="cat_1.html#K4">*</a> <font color="Maroon">c<sub>8</sub></font> &amp;  <a href="cat_1.html#K2">dom</a> <font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R1">=</a>  <a href="cat_1.html#K3">cod</a> <font color="Maroon">c<sub>9</sub></font> &amp; <font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>7</sub></font> <a href="cat_1.html#K4">*</a> <font color="Maroon">c<sub>9</sub></font> )
 ;<br/>

<a NAME="E2:53_1"/><b>then </b>
 <a href="cat_1.html#K2">dom</a> <font color="Maroon">c<sub>9</sub></font> <a href="hidden.html#R1">=</a>  <a href="cat_1.html#K3">cod</a> <font color="Maroon">c<sub>8</sub></font>
 
<b>by </b><i><a class="ref" href="cat_1.html#T42">CAT_1:42</a></i>;<br/>
<b>hence </b><a NAME="E3:53_1"/>
( <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>8</sub></font>) <a href="hidden.html#R2">in</a> the <a href="cat_1.html#U2">Morphisms</a> of <font color="Maroon">c<sub>1</sub></font> &amp; <font color="Maroon">S<sub>1</sub></font>[<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">H<sub>1</sub></font>(<font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>8</sub></font>)] )
 <b>by </b><i><a class="txt" href="cat_5.html#E1:53_1"><i><font color="Green">E33</font></i></a>, <a class="ref" href="cat_1.html#T42">CAT_1:42</a>, <a class="ref" href="cat_1.html#T43">CAT_1:43</a></i>;<br/>


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