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<b>let </b><font color="Maroon">C</font> be   <a href="altcat_1.html#NM4">category</a>;<br/><b>let </b><font color="Maroon">o</font> be   <a href="altcat_1.html#NM1">object</a> of <font color="Maroon">C</font>;<br/>



<a NAME="E1:9"/><i><font color="Green">E21</font></i>: 
<span class="p1"><a href="altcat_1.html#K1">&lt;^</a><span class="default"><font color="Maroon">o</font>,<font color="Maroon">o</font></span><a href="altcat_1.html#K1">^&gt;</a></span> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a> 
 
<b>by </b><i><a class="ref" href="altcat_1.html#T23">ALTCAT_1:23</a></i>;<br/>
<a NAME="E2:9"/>
(  <a href="altcat_1.html#K8">idm</a> <font color="Maroon">o</font> is <a href="altcat_3.html#V1" target="_self">retraction</a> &amp;  <a href="altcat_1.html#K8">idm</a> <font color="Maroon">o</font> is <a href="altcat_3.html#V2" target="_self">coretraction</a> )
 
<b>by </b><i/>;<br/>
<a NAME="E3:9"/><b>then </b><i><font color="Green">E22</font></i>: 
<span class="p1">(<span class="default"><a href="altcat_1.html#K8">idm</a> <font color="Maroon">o</font></span>)</span> <a href="altcat_3.html#K1" target="_self">"</a>  <a href="altcat_3.html#R1" target="_self">is_left_inverse_of</a>  <a href="altcat_1.html#K8">idm</a> <font color="Maroon">o</font>
 
<b>by </b><i>, </i>;<br/>
<b>thus </b><span class="p1">(<span class="default"><a href="altcat_1.html#K8">idm</a> <font color="Maroon">o</font></span>)</span> <a href="altcat_3.html#K1" target="_self">"</a>  = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="altcat_1.html#K8">idm</a> <font color="Maroon">o</font></span>)</span> <a href="altcat_3.html#K1" target="_self">"</a> </span>)</span> <a href="altcat_1.html#K5">*</a> <span class="p1">(<span class="default"><a href="altcat_1.html#K8">idm</a> <font color="Maroon">o</font></span>)</span>
<b>by </b><i>, <a class="ref" href="altcat_1.html#D19">ALTCAT_1:def 19</a></i>
<br/>.= 
 <a href="altcat_1.html#K8">idm</a> <font color="Maroon">o</font>
<b>by </b><i>, </i>
;<br/>


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