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<b>let </b><font color="Maroon">V</font> be  non <a href="xboole_0.html#V1">empty</a>  <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">C</font> be   <a href="cat_1.html#NM4">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/>







<b>assume </b><a NAME="E1:84"/><i><font color="Green">E16</font></i>: 
 <a href="ens_1.html#K17" target="_self">Hom</a> <font color="Maroon">C</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">V</font>
 ;<br/>

<b>let </b><font color="Maroon">d</font> be   <a href="cat_1.html#NM1">Object</a> of <span class="p1">(<span class="default"><a href="ens_1.html#K12" target="_self">Ens</a> <font color="Maroon">V</font></span>)</span>;<br/>

<b>assume </b><a NAME="E2:84"/><i><font color="Green">E17</font></i>: 
<font color="Maroon">d</font> <a href="hidden.html#R1">=</a>  <a href="cat_1.html#K6">Hom</a> <font color="Maroon">a</font>,<font color="Maroon">b</font>
 ;<br/>

<a NAME="E3:84"/>
 <a href="cat_1.html#K6">Hom</a> <font color="Maroon">a</font>,<font color="Maroon">b</font> <a href="hidden.html#R2">in</a>  <a href="ens_1.html#K17" target="_self">Hom</a> <font color="Maroon">C</font>
 
;<br/>
<b>then reconsider </b><font color="Maroon">A</font> =  <a href="cat_1.html#K6">Hom</a> <font color="Maroon">a</font>,<font color="Maroon">b</font> as    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">V</font> <b>by </b><i><a class="txt" href="ens_1.html#E33"><i><font color="Green">Lemma61</font></i></a></i>;<br/>
<a NAME="E5:84"/>
(  <a href="cat_1.html#K2">dom</a> <span class="p1">(<span class="default"><a href="cat_1.html#K10">id</a> <font color="Maroon">a</font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">a</font> &amp;  <a href="cat_1.html#K3">cod</a> <span class="p1">(<span class="default"><a href="cat_1.html#K10">id</a> <font color="Maroon">a</font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">a</font> &amp;  <a href="cat_1.html#K2">dom</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> <font color="Maroon">b</font> &amp;  <a href="cat_1.html#K3">cod</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> <font color="Maroon">b</font> &amp;  <a href="ens_1.html#K22" target="_self">hom</a> <span class="p1">(<span class="default"><a href="cat_1.html#K10">id</a> <font color="Maroon">a</font></span>)</span>,<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="partfun1.html#K6">id</a> <font color="Maroon">A</font> )
 
<b>by </b><i>, <a class="ref" href="cat_1.html#T44">CAT_1:44</a></i>;<br/>
<b>hence </b><span class="p1">(<span class="default"><a href="ens_1.html#K23" target="_self">hom??</a> <font color="Maroon">C</font></span>)</span> <a href="funct_2.html#K3">.</a> <span class="p1"><a href="cat_2.html#K13">[</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_1.html#K10">id</a> <font color="Maroon">b</font></span>)</span></span><a href="cat_2.html#K13">]</a></span> = 
 <a href="ens_1.html#K5" target="_self">id$</a> <span class="p1">(<span class="default"><a href="ens_1.html#K14" target="_self">@</a> <font color="Maroon">d</font></span>)</span>
<b>by </b><i>, </i>
<br/>.= 
 <a href="cat_1.html#K10">id</a> <font color="Maroon">d</font>
<b>by </b><i><a class="ref" href="ens_1.html#T7" target="_self">Th7</a></i>
;<br/><br/>


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