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<b>let </b><font color="Maroon" title="c1">C</font> be   <a href="cat_1.html#NM4" title="CAT_1:NM.4">Category</a>;<br/><b>let </b><font color="Maroon" title="c2">a</font>, <font color="Maroon" title="c3">b</font>, <font color="Maroon" title="c4">c</font> be   <a href="cat_1.html#NM1" title="CAT_1:NM.1">Object</a> of <font color="Maroon" title="c1">C</font>;<br/>







<b>assume </b><a NAME="E1:78"/><i><font color="Green" title="E38">A1</font></i>: 
 <a href="cat_1.html#K6" title="CAT_1:func.6">Hom</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 ; <i><font color="Red">:: according to </font></i><a class="ref" href="cat_1.html#D17" target="_self" title="CAT_1:def.17">CAT_1:def 17</a><br/>

<b>given </b><font color="Maroon" title="c5">f</font> being    <a href="cat_1.html#M1" title="CAT_1:mode.1">Morphism</a> of <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font><b> such that </b><a NAME="E3:78"/><i><font color="Green" title="E39">A2</font></i>: 
<font color="Maroon" title="c5">f</font> is <a href="cat_1.html#V5" title="CAT_1:attr.5">invertible</a>
 ;<br/>

<b>assume </b><a NAME="E4:78"/><i><font color="Green" title="E40">A3</font></i>: 
 <a href="cat_1.html#K6" title="CAT_1:func.6">Hom</a> <font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c4">c</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 ; <i><font color="Red">:: according to </font></i><a class="ref" href="cat_1.html#D17" target="_self" title="CAT_1:def.17">CAT_1:def 17</a><br/>

<b>given </b><font color="Maroon" title="c6">g</font> being    <a href="cat_1.html#M1" title="CAT_1:mode.1">Morphism</a> of <font color="Maroon" title="c3">b</font>,<font color="Maroon" title="c4">c</font><b> such that </b><a NAME="E6:78"/><i><font color="Green" title="E41">A4</font></i>: 
<font color="Maroon" title="c6">g</font> is <a href="cat_1.html#V5" title="CAT_1:attr.5">invertible</a>
 ;<br/>

<b>thus </b><a NAME="E7:78"/>
 <a href="cat_1.html#K6" title="CAT_1:func.6">Hom</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c4">c</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 <b>by </b><i><a class="txt" href="cat_1.html#E1:78"><i><font color="Green" title="E38">A1</font></i></a>, <a class="txt" href="cat_1.html#E4:78"><i><font color="Green" title="E40">A3</font></i></a>, <a class="ref" href="cat_1.html#T51" target="_self" title="CAT_1:th.51">Th51</a></i>; <i><font color="Red">:: according to </font></i><a class="ref" href="cat_1.html#D17" target="_self" title="CAT_1:def.17">CAT_1:def 17</a><br/>

<b>take </b>
<font color="Maroon" title="c6">g</font> <a href="cat_1.html#K9" title="CAT_1:func.9">*</a> <font color="Maroon" title="c5">f</font>
;<br/>

<b>thus </b><a NAME="E8:78"/>
<font color="Maroon" title="c6">g</font> <a href="cat_1.html#K9" title="CAT_1:func.9">*</a> <font color="Maroon" title="c5">f</font> is <a href="cat_1.html#V5" title="CAT_1:attr.5">invertible</a>
 <b>by </b><i><a class="txt" href="cat_1.html#E1:78"><i><font color="Green" title="E38">A1</font></i></a>, <a class="txt" href="cat_1.html#E3:78"><i><font color="Green" title="E39">A2</font></i></a>, <a class="txt" href="cat_1.html#E4:78"><i><font color="Green" title="E40">A3</font></i></a>, <a class="txt" href="cat_1.html#E6:78"><i><font color="Green" title="E41">A4</font></i></a>, <a class="ref" href="cat_1.html#T75" target="_self" title="CAT_1:th.75">Th75</a></i>;<br/>


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