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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/><b>let </b><font color="Maroon">b</font> be   <a href="cat_1.html#NM1">Object</a> of <font color="Maroon">C</font>;<br/>





<a NAME="E1:56"/>
(  <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> <font color="Maroon">b</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>  &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> <font color="Maroon">b</font></span>)</span>,<font color="Maroon">b</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="E2:56"/><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>,<font color="Maroon">b</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="cat_4.html#K7" target="_self">pr1</a> <font color="Maroon">a</font>,<font color="Maroon">b</font> &amp; <span class="p1">(<span class="default"><a href="cat_1.html#K10">id</a> <font color="Maroon">b</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> <font color="Maroon">a</font>,<font color="Maroon">b</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="cat_4.html#K8" target="_self">pr2</a> <font color="Maroon">a</font>,<font color="Maroon">b</font> )
 
<b>by </b><i><a class="ref" href="cat_1.html#T57">CAT_1:57</a></i>;<br/>
<a NAME="E3:56"/><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_4.html#K18" target="_self">[x]</a> <span class="p1">(<span class="default"><a href="cat_1.html#K10">id</a> <font color="Maroon">b</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> <font color="Maroon">a</font>,<font color="Maroon">b</font></span>)</span>,<span class="p2">(<span class="default"><a href="cat_4.html#K8" target="_self">pr2</a> <font color="Maroon">a</font>,<font color="Maroon">b</font></span>)</span></span><a href="cat_4.html#K9" target="_self">:&gt;</a></span>
 
;<br/>
<b>hence </b><a NAME="E4:56"/>
<span class="p1">(<span class="default"><a href="cat_1.html#K10">id</a> <font color="Maroon">a</font></span>)</span> <a href="cat_4.html#K18" target="_self">[x]</a> <span class="p1">(<span class="default"><a href="cat_1.html#K10">id</a> <font color="Maroon">b</font></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> <font color="Maroon">b</font></span>)</span>
 <b>by </b><i/>;<br/>


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