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<b>let </b><font color="Maroon">a</font> be    <a href="subset_1.html#M2">Element</a> of  <a href="cat_5.html#K12" target="_self">Hom</a> <font color="Maroon">o</font>, <font color="Maroon">b</font> be    <a href="subset_1.html#M2">Element</a> of  <a href="cat_5.html#K12" target="_self">Hom</a> <font color="Maroon">o</font>, <font color="Maroon">c</font> be    <a href="subset_1.html#M2">Element</a> of  <a href="cat_5.html#K12" target="_self">Hom</a> <font color="Maroon">o</font>;<br/><b>let </b><font color="Maroon">f</font> be   <a href="cat_1.html#NM2">Morphism</a> of <font color="Maroon">C</font>, <font color="Maroon">g</font> be   <a href="cat_1.html#NM2">Morphism</a> of <font color="Maroon">C</font>;<br/>



<b>assume </b><a NAME="E1:53_1"/><i><font color="Green">E40</font></i>: 
(  <a href="cat_1.html#K2">dom</a> <font color="Maroon">b</font> <a href="hidden.html#R1">=</a>  <a href="cat_1.html#K3">cod</a> <font color="Maroon">f</font> &amp; <font color="Maroon">a</font> <a href="hidden.html#R1">=</a> <font color="Maroon">b</font> <a href="cat_1.html#K4">*</a> <font color="Maroon">f</font> &amp;  <a href="cat_1.html#K2">dom</a> <font color="Maroon">c</font> <a href="hidden.html#R1">=</a>  <a href="cat_1.html#K3">cod</a> <font color="Maroon">g</font> &amp; <font color="Maroon">b</font> <a href="hidden.html#R1">=</a> <font color="Maroon">c</font> <a href="cat_1.html#K4">*</a> <font color="Maroon">g</font> )
 ;<br/>

<a NAME="E2:53_1"/><b>then </b>
 <a href="cat_1.html#K2">dom</a> <font color="Maroon">g</font> <a href="hidden.html#R1">=</a>  <a href="cat_1.html#K3">cod</a> <font color="Maroon">f</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">g</font>,<font color="Maroon">f</font>) <a href="hidden.html#R2">in</a> the <a href="cat_1.html#U2">Morphisms</a> of <font color="Maroon">C</font> &amp; <font color="Maroon">S<sub>1</sub></font>[<font color="Maroon">a</font>,<font color="Maroon">c</font>,<font color="Maroon">H<sub>1</sub></font>(<font color="Maroon">g</font>,<font color="Maroon">f</font>)] )
 <b>by </b><i>, <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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