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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> be   <a href="cat_1.html#NM1">Object</a> of <font color="Maroon">c<sub>1</sub></font>;<br/>





<b>assume </b><a NAME="E1:78"/><i><font color="Green">E44</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> 
 ; <i><font color="Red">:: according to </font></i><a class="ref" href="cat_1.html#D17" target="_self">CAT_1:def 17</a><br/>

<b>given </b><font color="Maroon">c<sub>4</sub></font> being    <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><b> such that </b><a NAME="E2:78"/><i><font color="Green">E45</font></i>: 
<font color="Maroon">c<sub>4</sub></font> is <a href="cat_1.html#V5" target="_self">invertible</a>
 ;<br/>

<b>thus </b><a NAME="E3:78"/><i><font color="Green">E46</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>2</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#E1:78"><i><font color="Green">E44</font></i></a>, <a class="txt" href="cat_1.html#E2:78"><i><font color="Green">E45</font></i></a>, <a class="ref" href="cat_1.html#T70" target="_self">Th70</a></i>; <i><font color="Red">:: according to </font></i><a class="ref" href="cat_1.html#D17" target="_self">CAT_1:def 17</a><br/>

<b>consider </b><font color="Maroon">c<sub>5</sub></font> being    <a href="cat_1.html#M1" target="_self">Morphism</a> of <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>2</sub></font><b> such that </b><br/><a NAME="E5:78"/><i><font color="Green">E47</font></i>: 
( <font color="Maroon">c<sub>4</sub></font> <a href="cat_1.html#K9" target="_self">*</a> <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a>  <a href="cat_1.html#K10" target="_self">id</a> <font color="Maroon">c<sub>3</sub></font> &amp; <font color="Maroon">c<sub>5</sub></font> <a href="cat_1.html#K9" target="_self">*</a> <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a>  <a href="cat_1.html#K10" target="_self">id</a> <font color="Maroon">c<sub>2</sub></font> )
 <b>by </b><i><a class="txt" href="cat_1.html#E1:78"><i><font color="Green">E44</font></i></a>, <a class="txt" href="cat_1.html#E2:78"><i><font color="Green">E45</font></i></a>, <a class="ref" href="cat_1.html#T70" target="_self">Th70</a></i>;<br/>
<b>take </b>
<font color="Maroon">c<sub>5</sub></font>
;<br/>

<b>thus </b><a NAME="E6:78"/>
<font color="Maroon">c<sub>5</sub></font> is <a href="cat_1.html#V5" target="_self">invertible</a>
 <b>by </b><i><a class="txt" href="cat_1.html#E1:78"><i><font color="Green">E44</font></i></a>, <a class="txt" href="cat_1.html#E3:78"><i><font color="Green">E46</font></i></a>, <a class="txt" href="cat_1.html#E5:78"><i><font color="Green">E47</font></i></a>, <a class="ref" href="cat_1.html#T70" target="_self">Th70</a></i>;<br/>


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