<?xml version="1.0"?>
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<b>let </b><font color="Maroon">C</font> be   <a href="cat_4.html#NM1">Cartesian_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/>



<a NAME="E1:41"/><i><font color="Green">E34</font></i>: 
(  <a href="cat_1.html#K6">Hom</a> <font color="Maroon">a</font>,<span class="p1">(<span class="default"><a href="cat_4.html#K1" target="_self">[1]</a> <font color="Maroon">C</font></span>)</span> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a>  &amp;  <a href="cat_1.html#K6">Hom</a> <font color="Maroon">a</font>,<font color="Maroon">a</font> <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="cat_1.html#T56">CAT_1:56</a></i>;<br/>
<a NAME="E2:41"/><i><font color="Green">E35</font></i>: 
 <a href="cat_1.html#K6">Hom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="cat_4.html#K1" target="_self">[1]</a> <font color="Maroon">C</font></span>)</span> <a href="cat_4.html#K2" target="_self">[x]</a> <font color="Maroon">a</font></span>)</span>,<font color="Maroon">a</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a> 
 
<b>by </b><i/>;<br/>
<a NAME="E3:41"/><b>then </b>
( <span class="p1">(<span class="default"><a href="cat_1.html#K10">id</a> <font color="Maroon">a</font></span>)</span> <a href="cat_1.html#K9">*</a> <span class="p1">(<span class="default"><a href="cat_4.html#K8" target="_self">pr2</a> <span class="p2">(<span class="default"><a href="cat_4.html#K1" target="_self">[1]</a> <font color="Maroon">C</font></span>)</span>,<font color="Maroon">a</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="cat_4.html#K8" target="_self">pr2</a> <span class="p1">(<span class="default"><a href="cat_4.html#K1" target="_self">[1]</a> <font color="Maroon">C</font></span>)</span>,<font color="Maroon">a</font> &amp; <span class="p1">(<span class="default"><a href="cat_4.html#K6" target="_self">term</a> <font color="Maroon">a</font></span>)</span> <a href="cat_1.html#K9">*</a> <span class="p1">(<span class="default"><a href="cat_4.html#K8" target="_self">pr2</a> <span class="p2">(<span class="default"><a href="cat_4.html#K1" target="_self">[1]</a> <font color="Maroon">C</font></span>)</span>,<font color="Maroon">a</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="cat_4.html#K7" target="_self">pr1</a> <span class="p1">(<span class="default"><a href="cat_4.html#K1" target="_self">[1]</a> <font color="Maroon">C</font></span>)</span>,<font color="Maroon">a</font> &amp;  <a href="cat_1.html#K6">Hom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="cat_4.html#K1" target="_self">[1]</a> <font color="Maroon">C</font></span>)</span> <a href="cat_4.html#K2" target="_self">[x]</a> <font color="Maroon">a</font></span>)</span>,<span class="p1">(<span class="default"><a href="cat_4.html#K1" target="_self">[1]</a> <font color="Maroon">C</font></span>)</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="cat_1.html#T57">CAT_1:57</a></i>;<br/>
<a NAME="E4:41"/><b>then </b><i><font color="Green">E36</font></i>: 
<span class="p1"><a href="cat_4.html#K9" target="_self">&lt;:</a><span class="default"><span class="p2">(<span class="default"><a href="cat_4.html#K6" target="_self">term</a> <font color="Maroon">a</font></span>)</span>,<span class="p2">(<span class="default"><a href="cat_1.html#K10">id</a> <font color="Maroon">a</font></span>)</span></span><a href="cat_4.html#K9" target="_self">:&gt;</a></span> <a href="cat_1.html#K9">*</a> <span class="p1">(<span class="default"><a href="cat_4.html#K8" target="_self">pr2</a> <span class="p2">(<span class="default"><a href="cat_4.html#K1" target="_self">[1]</a> <font color="Maroon">C</font></span>)</span>,<font color="Maroon">a</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="cat_4.html#K9" target="_self">&lt;:</a><span class="default"><span class="p2">(<span class="default"><a href="cat_4.html#K7" target="_self">pr1</a> <span class="p3">(<span class="default"><a href="cat_4.html#K1" target="_self">[1]</a> <font color="Maroon">C</font></span>)</span>,<font color="Maroon">a</font></span>)</span>,<span class="p2">(<span class="default"><a href="cat_4.html#K8" target="_self">pr2</a> <span class="p3">(<span class="default"><a href="cat_4.html#K1" target="_self">[1]</a> <font color="Maroon">C</font></span>)</span>,<font color="Maroon">a</font></span>)</span></span><a href="cat_4.html#K9" target="_self">:&gt;</a></span>
 
<b>by </b><i>, , </i>;<br/>
<a NAME="E5:41"/>
<span class="p1">(<span class="default"><a href="cat_4.html#K8" target="_self">pr2</a> <span class="p2">(<span class="default"><a href="cat_4.html#K1" target="_self">[1]</a> <font color="Maroon">C</font></span>)</span>,<font color="Maroon">a</font></span>)</span> <a href="cat_1.html#K9">*</a> <span class="p1"><a href="cat_4.html#K9" target="_self">&lt;:</a><span class="default"><span class="p2">(<span class="default"><a href="cat_4.html#K6" target="_self">term</a> <font color="Maroon">a</font></span>)</span>,<span class="p2">(<span class="default"><a href="cat_1.html#K10">id</a> <font color="Maroon">a</font></span>)</span></span><a href="cat_4.html#K9" target="_self">:&gt;</a></span> <a href="hidden.html#R1">=</a>  <a href="cat_1.html#K10">id</a> <font color="Maroon">a</font>
 
<b>by </b><i>, </i>;<br/>
<b>hence </b><a NAME="E6:41"/>
 <a href="cat_1.html#K10">id</a> <font color="Maroon">a</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="cat_4.html#K10" target="_self">lambda</a> <font color="Maroon">a</font></span>)</span> <a href="cat_1.html#K9">*</a> <span class="p1">(<span class="default"><a href="cat_4.html#K11" target="_self">lambda'</a> <font color="Maroon">a</font></span>)</span>
 ;<br/>

<a NAME="E7:41"/>
<span class="p1"><a href="cat_4.html#K9" target="_self">&lt;:</a><span class="default"><span class="p2">(<span class="default"><a href="cat_4.html#K6" target="_self">term</a> <font color="Maroon">a</font></span>)</span>,<span class="p2">(<span class="default"><a href="cat_1.html#K10">id</a> <font color="Maroon">a</font></span>)</span></span><a href="cat_4.html#K9" target="_self">:&gt;</a></span> <a href="cat_1.html#K9">*</a> <span class="p1">(<span class="default"><a href="cat_4.html#K8" target="_self">pr2</a> <span class="p2">(<span class="default"><a href="cat_4.html#K1" target="_self">[1]</a> <font color="Maroon">C</font></span>)</span>,<font color="Maroon">a</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="cat_1.html#K10">id</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="cat_4.html#K1" target="_self">[1]</a> <font color="Maroon">C</font></span>)</span> <a href="cat_4.html#K2" target="_self">[x]</a> <font color="Maroon">a</font></span>)</span>
 
<b>by </b><i>, </i>;<br/>
<b>hence </b><a NAME="E8:41"/>
 <a href="cat_1.html#K10">id</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="cat_4.html#K1" target="_self">[1]</a> <font color="Maroon">C</font></span>)</span> <a href="cat_4.html#K2" target="_self">[x]</a> <font color="Maroon">a</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="cat_4.html#K11" target="_self">lambda'</a> <font color="Maroon">a</font></span>)</span> <a href="cat_1.html#K9">*</a> <span class="p1">(<span class="default"><a href="cat_4.html#K10" target="_self">lambda</a> <font color="Maroon">a</font></span>)</span>
 ;<br/>

<a NAME="E9:41"/><i><font color="Green">E37</font></i>: 
 <a href="cat_1.html#K6">Hom</a> <span class="p1">(<span class="default"><font color="Maroon">a</font> <a href="cat_4.html#K2" target="_self">[x]</a> <span class="p2">(<span class="default"><a href="cat_4.html#K1" target="_self">[1]</a> <font color="Maroon">C</font></span>)</span></span>)</span>,<font color="Maroon">a</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a> 
 
<b>by </b><i/>;<br/>
<a NAME="E10:41"/><b>then </b>
( <span class="p1">(<span class="default"><a href="cat_1.html#K10">id</a> <font color="Maroon">a</font></span>)</span> <a href="cat_1.html#K9">*</a> <span class="p1">(<span class="default"><a href="cat_4.html#K7" target="_self">pr1</a> <font color="Maroon">a</font>,<span class="p2">(<span class="default"><a href="cat_4.html#K1" target="_self">[1]</a> <font color="Maroon">C</font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a>  <a href="cat_4.html#K7" target="_self">pr1</a> <font color="Maroon">a</font>,<span class="p1">(<span class="default"><a href="cat_4.html#K1" target="_self">[1]</a> <font color="Maroon">C</font></span>)</span> &amp; <span class="p1">(<span class="default"><a href="cat_4.html#K6" target="_self">term</a> <font color="Maroon">a</font></span>)</span> <a href="cat_1.html#K9">*</a> <span class="p1">(<span class="default"><a href="cat_4.html#K7" target="_self">pr1</a> <font color="Maroon">a</font>,<span class="p2">(<span class="default"><a href="cat_4.html#K1" target="_self">[1]</a> <font color="Maroon">C</font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a>  <a href="cat_4.html#K8" target="_self">pr2</a> <font color="Maroon">a</font>,<span class="p1">(<span class="default"><a href="cat_4.html#K1" target="_self">[1]</a> <font color="Maroon">C</font></span>)</span> &amp;  <a href="cat_1.html#K6">Hom</a> <span class="p1">(<span class="default"><font color="Maroon">a</font> <a href="cat_4.html#K2" target="_self">[x]</a> <span class="p2">(<span class="default"><a href="cat_4.html#K1" target="_self">[1]</a> <font color="Maroon">C</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="cat_4.html#K1" target="_self">[1]</a> <font color="Maroon">C</font></span>)</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="cat_1.html#T57">CAT_1:57</a></i>;<br/>
<a NAME="E11:41"/><b>then </b><i><font color="Green">E38</font></i>: 
<span class="p1"><a href="cat_4.html#K9" target="_self">&lt;:</a><span class="default"><span class="p2">(<span class="default"><a href="cat_1.html#K10">id</a> <font color="Maroon">a</font></span>)</span>,<span class="p2">(<span class="default"><a href="cat_4.html#K6" target="_self">term</a> <font color="Maroon">a</font></span>)</span></span><a href="cat_4.html#K9" target="_self">:&gt;</a></span> <a href="cat_1.html#K9">*</a> <span class="p1">(<span class="default"><a href="cat_4.html#K7" target="_self">pr1</a> <font color="Maroon">a</font>,<span class="p2">(<span class="default"><a href="cat_4.html#K1" target="_self">[1]</a> <font color="Maroon">C</font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="cat_4.html#K9" target="_self">&lt;:</a><span class="default"><span class="p2">(<span class="default"><a href="cat_4.html#K7" target="_self">pr1</a> <font color="Maroon">a</font>,<span class="p3">(<span class="default"><a href="cat_4.html#K1" target="_self">[1]</a> <font color="Maroon">C</font></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="cat_4.html#K8" target="_self">pr2</a> <font color="Maroon">a</font>,<span class="p3">(<span class="default"><a href="cat_4.html#K1" target="_self">[1]</a> <font color="Maroon">C</font></span>)</span></span>)</span></span><a href="cat_4.html#K9" target="_self">:&gt;</a></span>
 
<b>by </b><i>, <a class="ref" href="cat_4.html#T1" target="_self">Th1</a>, </i>;<br/>
<a NAME="E12:41"/>
<span class="p1">(<span class="default"><a href="cat_4.html#K7" target="_self">pr1</a> <font color="Maroon">a</font>,<span class="p2">(<span class="default"><a href="cat_4.html#K1" target="_self">[1]</a> <font color="Maroon">C</font></span>)</span></span>)</span> <a href="cat_1.html#K9">*</a> <span class="p1"><a href="cat_4.html#K9" target="_self">&lt;:</a><span class="default"><span class="p2">(<span class="default"><a href="cat_1.html#K10">id</a> <font color="Maroon">a</font></span>)</span>,<span class="p2">(<span class="default"><a href="cat_4.html#K6" target="_self">term</a> <font color="Maroon">a</font></span>)</span></span><a href="cat_4.html#K9" target="_self">:&gt;</a></span> <a href="hidden.html#R1">=</a>  <a href="cat_1.html#K10">id</a> <font color="Maroon">a</font>
 
<b>by </b><i>, </i>;<br/>
<b>hence </b><a NAME="E13:41"/>
 <a href="cat_1.html#K10">id</a> <font color="Maroon">a</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="cat_4.html#K12" target="_self">rho</a> <font color="Maroon">a</font></span>)</span> <a href="cat_1.html#K9">*</a> <span class="p1">(<span class="default"><a href="cat_4.html#K13" target="_self">rho'</a> <font color="Maroon">a</font></span>)</span>
 ;<br/>

<a NAME="E14:41"/>
<span class="p1"><a href="cat_4.html#K9" target="_self">&lt;:</a><span class="default"><span class="p2">(<span class="default"><a href="cat_1.html#K10">id</a> <font color="Maroon">a</font></span>)</span>,<span class="p2">(<span class="default"><a href="cat_4.html#K6" target="_self">term</a> <font color="Maroon">a</font></span>)</span></span><a href="cat_4.html#K9" target="_self">:&gt;</a></span> <a href="cat_1.html#K9">*</a> <span class="p1">(<span class="default"><a href="cat_4.html#K7" target="_self">pr1</a> <font color="Maroon">a</font>,<span class="p2">(<span class="default"><a href="cat_4.html#K1" target="_self">[1]</a> <font color="Maroon">C</font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a>  <a href="cat_1.html#K10">id</a> <span class="p1">(<span class="default"><font color="Maroon">a</font> <a href="cat_4.html#K2" target="_self">[x]</a> <span class="p2">(<span class="default"><a href="cat_4.html#K1" target="_self">[1]</a> <font color="Maroon">C</font></span>)</span></span>)</span>
 
<b>by </b><i>, </i>;<br/>
<b>hence </b><a NAME="E15:41"/>
 <a href="cat_1.html#K10">id</a> <span class="p1">(<span class="default"><font color="Maroon">a</font> <a href="cat_4.html#K2" target="_self">[x]</a> <span class="p2">(<span class="default"><a href="cat_4.html#K1" target="_self">[1]</a> <font color="Maroon">C</font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="cat_4.html#K13" target="_self">rho'</a> <font color="Maroon">a</font></span>)</span> <a href="cat_1.html#K9">*</a> <span class="p1">(<span class="default"><a href="cat_4.html#K12" target="_self">rho</a> <font color="Maroon">a</font></span>)</span>
 ;<br/>


</div>
