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<b>let </b><font color="Maroon">C</font> be   <a href="cat_1.html#NM4">Category</a>;<br/><b>let </b><font color="Maroon">a</font> be   <a href="cat_1.html#NM1">Object</a> of <font color="Maroon">C</font>;<br/><b>let </b><font color="Maroon">b</font> be   <a href="cat_1.html#NM1">Object</a> of <font color="Maroon">C</font>;<br/><b>let </b><font color="Maroon">f</font> be    <a href="cat_1.html#M1" target="_self">Morphism</a> of <font color="Maroon">a</font>,<font color="Maroon">b</font>;<br/>







<b>assume </b><a NAME="E1:64"/><i><font color="Green">E20</font></i>: 
 <a href="cat_1.html#K6" target="_self">Hom</a> <font color="Maroon">a</font>,<font color="Maroon">b</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a> 
 ;<br/>

<b>assume </b><a NAME="E2:64"/>
<font color="Maroon">f</font> is <a href="cat_1.html#V5" target="_self">invertible</a>
 ;<br/>

<a NAME="E3:64"/><b>then </b>
(  <a href="cat_1.html#K6" target="_self">Hom</a> <font color="Maroon">b</font>,<font color="Maroon">a</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a>  &amp; <span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="cat_1.html#K11" target="_self">"</a> </span>)</span> <a href="cat_1.html#K9" target="_self">*</a> <font color="Maroon">f</font> <a href="hidden.html#R1">=</a>  <a href="cat_1.html#K10" target="_self">id</a> <font color="Maroon">a</font> &amp; <font color="Maroon">f</font> <a href="cat_1.html#K9" target="_self">*</a> <span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="cat_1.html#K11" target="_self">"</a> </span>)</span> <a href="hidden.html#R1">=</a>  <a href="cat_1.html#K10" target="_self">id</a> <font color="Maroon">b</font> )
 
<b>by </b><i>, <a class="ref" href="cat_1.html#T22" target="_self">Th22</a>, <a class="ref" href="cat_1.html#T18" target="_self">Th18</a></i>;<br/>
<b>hence </b><a NAME="E4:64"/>
<font color="Maroon">f</font> <a href="cat_1.html#K11" target="_self">"</a>  is <a href="cat_1.html#V5" target="_self">invertible</a>
 <b>by </b><i>, <a class="ref" href="cat_1.html#T18" target="_self">Th18</a></i>;<br/>


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