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







<b>assume </b><a NAME="E1:79"/><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>5</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="E2:79"/><i><font color="Green">E45</font></i>: 
<font color="Maroon">c<sub>5</sub></font> is <a href="cat_1.html#V5" target="_self">invertible</a>
 ;<br/>

<b>assume </b><a NAME="E3:79"/><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>4</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>6</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>4</sub></font><b> such that </b><a NAME="E4:79"/><i><font color="Green">E47</font></i>: 
<font color="Maroon">c<sub>6</sub></font> is <a href="cat_1.html#V5" target="_self">invertible</a>
 ;<br/>

<b>thus </b><a NAME="E5:79"/>
 <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#E1:79"><i><font color="Green">E44</font></i></a>, <a class="txt" href="cat_1.html#E3:79"><i><font color="Green">E46</font></i></a>, <a class="ref" href="cat_1.html#T51" target="_self">Th51</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>take </b>
<font color="Maroon">c<sub>6</sub></font> <a href="cat_1.html#K9" target="_self">*</a> <font color="Maroon">c<sub>5</sub></font>
;<br/>

<b>thus </b><a NAME="E6:79"/>
<font color="Maroon">c<sub>6</sub></font> <a href="cat_1.html#K9" target="_self">*</a> <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#E1:79"><i><font color="Green">E44</font></i></a>, <a class="txt" href="cat_1.html#E2:79"><i><font color="Green">E45</font></i></a>, <a class="txt" href="cat_1.html#E3:79"><i><font color="Green">E46</font></i></a>, <a class="txt" href="cat_1.html#E4:79"><i><font color="Green">E47</font></i></a>, <a class="ref" href="cat_1.html#T75" target="_self">Th75</a></i>;<br/>


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