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<b>let </b><font color="Maroon">C</font> be  <a href="yellow18.html#V4" target="_self">concrete</a> <a href="altcat_1.html#NM4">category</a>;<br/><b>let </b><font color="Maroon">a</font> be   <a href="altcat_1.html#NM1">object</a> of <font color="Maroon">C</font>, <font color="Maroon">b</font> be   <a href="altcat_1.html#NM1">object</a> of <font color="Maroon">C</font>;<br/>



<b>assume </b><a NAME="E1:83"/><i><font color="Green">E35</font></i>: 
( <span class="p1"><a href="altcat_1.html#K1">&lt;^</a><span class="default"><font color="Maroon">a</font>,<font color="Maroon">b</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>  &amp; <span class="p1"><a href="altcat_1.html#K1">&lt;^</a><span class="default"><font color="Maroon">b</font>,<font color="Maroon">a</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>  )
 ;<br/>

<b>let </b><font color="Maroon">f</font> be   <a href="altcat_1.html#NM2">Morphism</a> of <font color="Maroon">a</font>,<font color="Maroon">b</font>;<br/>

<b>assume </b><a NAME="E2:83"/>
<font color="Maroon">f</font> is <a href="altcat_3.html#V3">iso</a>
 ;<br/>

<a NAME="E3:83"/><b>then </b>
( <font color="Maroon">f</font> is <a href="altcat_3.html#V1">retraction</a> &amp; <font color="Maroon">f</font> is <a href="altcat_3.html#V2">coretraction</a> )
 
<b>by </b><i><a class="ref" href="altcat_3.html#T5">ALTCAT_3:5</a></i>;<br/>
<b>hence </b><a NAME="E4:83"/>
( <font color="Maroon">f</font> is <a href="funct_1.html#V2">one-to-one</a> &amp;  <a href="relat_1.html#K2">rng</a> <font color="Maroon">f</font> <a href="hidden.html#R1">=</a>  <a href="yellow18.html#K3" target="_self">the_carrier_of</a> <font color="Maroon">b</font> )
 <b>by </b><i>, , </i>;<br/>


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