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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">T</font> be   <a href="funct_2.html#NM1">Function</a> of the <a href="cat_1.html#U2">Morphisms</a> of <font color="Maroon">C</font>, <a href="ens_1.html#K2" target="_self">Maps</a> <span class="p1">(<span class="default"><a href="ens_1.html#K17" target="_self">Hom</a> <font color="Maroon">C</font></span>)</span>;<br/>





<b>assume </b><a NAME="E1:70"/>
 <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/>

<a NAME="E2:70"/><b>then </b>
(  <a href="ens_1.html#K17" target="_self">Hom</a> <font color="Maroon">C</font> is  non <a href="xboole_0.html#V1">empty</a> <a href="subset_1.html#NM2">Subset</a> of <font color="Maroon">V</font> &amp;  <a href="ens_1.html#K12" target="_self">Ens</a> <font color="Maroon">V</font> <a href="hidden.html#R1">=</a>  <a href="cat_1.html#G1">CatStr</a>(# <font color="Maroon">V</font>,<span class="p1">(<span class="default"><a href="ens_1.html#K2" target="_self">Maps</a> <font color="Maroon">V</font></span>)</span>,<span class="p1">(<span class="default"><a href="ens_1.html#K8" target="_self">fDom</a> <font color="Maroon">V</font></span>)</span>,<span class="p1">(<span class="default"><a href="ens_1.html#K9" target="_self">fCod</a> <font color="Maroon">V</font></span>)</span>,<span class="p1">(<span class="default"><a href="ens_1.html#K10" target="_self">fComp</a> <font color="Maroon">V</font></span>)</span>,<span class="p1">(<span class="default"><a href="ens_1.html#K11" target="_self">fId</a> <font color="Maroon">V</font></span>)</span> #) )
 
;<br/>
<a NAME="E3:70"/><b>then </b>
(  <a href="ens_1.html#K2" target="_self">Maps</a> <span class="p1">(<span class="default"><a href="ens_1.html#K17" target="_self">Hom</a> <font color="Maroon">C</font></span>)</span> <a href="tarski.html#R1">c=</a>  <a href="ens_1.html#K2" target="_self">Maps</a> <font color="Maroon">V</font> &amp; the <a href="cat_1.html#U2">Morphisms</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> <a href="hidden.html#R1">=</a>  <a href="ens_1.html#K2" target="_self">Maps</a> <font color="Maroon">V</font> &amp;  <a href="ens_1.html#K2" target="_self">Maps</a> <span class="p1">(<span class="default"><a href="ens_1.html#K17" target="_self">Hom</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/>;<br/>
<b>hence </b><a NAME="E4:70"/>
<font color="Maroon">T</font> is   <a href="funct_2.html#NM1">Function</a> of the <a href="cat_1.html#U2">Morphisms</a> of <font color="Maroon">C</font>,the <a href="cat_1.html#U2">Morphisms</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>
 <b>by </b><i><a class="ref" href="funct_2.html#T9">FUNCT_2:9</a></i>;<br/>


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