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<b>let </b><font color="Maroon">A</font> be   <a href="altcat_1.html#NM4">category</a>, <font color="Maroon">B</font> be   <a href="altcat_1.html#NM4">category</a>;<br/>

<b>assume </b><a NAME="E1:28"/><i><font color="Green">E35</font></i>: 
<font color="Maroon">A</font>,<font color="Maroon">B</font> <a href="yellow18.html#R2" target="_self">are_opposite</a> 
 ;<br/>

<b>let </b><font color="Maroon">a</font> be   <a href="altcat_1.html#NM1">object</a> of <font color="Maroon">A</font>;<br/><b>let </b><font color="Maroon">b</font> be   <a href="altcat_1.html#NM1">object</a> of <font color="Maroon">B</font>;<br/>



<b>assume </b><a NAME="E2:28"/><i><font color="Green">E36</font></i>: 
<font color="Maroon">a</font> <a href="hidden.html#R1">=</a> <font color="Maroon">b</font>
 ;<br/>

<b>reconsider </b><font color="Maroon">i</font> =  <a href="altcat_1.html#K8">idm</a> <font color="Maroon">b</font> as   <a href="altcat_1.html#NM2">Morphism</a> of <font color="Maroon">a</font>,<font color="Maroon">a</font> <b>by </b><i>, , </i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="28_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">c</font> be   <a href="altcat_1.html#NM1">object</a> of <font color="Maroon">A</font>;<br/><b>assume </b><a NAME="E1:28_1"/><i><font color="Green">E39</font></i>: 
<span class="p1"><a href="altcat_1.html#K1">&lt;^</a><span class="default"><font color="Maroon">a</font>,<font color="Maroon">c</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">c</font>;<br/><b>reconsider </b><font color="Maroon">d</font> = <font color="Maroon">c</font> as   <a href="altcat_1.html#NM1">object</a> of <font color="Maroon">B</font> <b>by </b><i>, </i>;<br/><a NAME="E3:28_1"/><i><font color="Green">E42</font></i>: 
<span class="p1"><a href="altcat_1.html#K1">&lt;^</a><span class="default"><font color="Maroon">a</font>,<font color="Maroon">c</font></span><a href="altcat_1.html#K1">^&gt;</a></span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="altcat_1.html#K1">&lt;^</a><span class="default"><font color="Maroon">d</font>,<font color="Maroon">b</font></span><a href="altcat_1.html#K1">^&gt;</a></span>
 <b>by </b><i>, , </i>;<br/><b>reconsider </b><font color="Maroon">g</font> = <font color="Maroon">f</font> as   <a href="altcat_1.html#NM2">Morphism</a> of <font color="Maroon">d</font>,<font color="Maroon">b</font> <b>by </b><i>, , </i>;<br/><b>thus </b><font color="Maroon">f</font> <a href="altcat_1.html#K5">*</a> <font color="Maroon">i</font> = 
<span class="p1">(<span class="default"><a href="altcat_1.html#K8">idm</a> <font color="Maroon">b</font></span>)</span> <a href="altcat_1.html#K5">*</a> <font color="Maroon">g</font>
<b>by </b><i>, , , </i>
<br/>.= 
<font color="Maroon">f</font>
<b>by </b><i>, , <a class="ref" href="altcat_1.html#T24">ALTCAT_1:24</a></i>
;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E5:28"/>
 <a href="altcat_1.html#K8">idm</a> <font color="Maroon">a</font> <a href="hidden.html#R1">=</a>  <a href="altcat_1.html#K8">idm</a> <font color="Maroon">b</font>
 <b>by </b><i><a class="ref" href="altcat_1.html#D19">ALTCAT_1:def 19</a></i>;<br/>


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