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<b>let </b><font color="Maroon">C</font> be  <a href="cat_5.html#V3" target="_self">Categorial</a> <a href="cat_1.html#NM4">Category</a>;<br/><b>let </b><font color="Maroon">D</font> be  <a href="cat_5.html#V3" target="_self">Categorial</a> <a href="cat_5.html#V4" target="_self">full</a> <a href="cat_1.html#NM4">Category</a>;<br/>



<b>assume </b><a NAME="E1:44"/><i><font color="Green">E17</font></i>: 
the <a href="cat_1.html#U1">Objects</a> of <font color="Maroon">C</font> <a href="tarski.html#R1">c=</a> the <a href="cat_1.html#U1">Objects</a> of <font color="Maroon">D</font>
 ;<br/>

<a NAME="E2:44"/>
the <a href="cat_1.html#U2">Morphisms</a> of <font color="Maroon">C</font> <a href="tarski.html#R1">c=</a> the <a href="cat_1.html#U2">Morphisms</a> of <font color="Maroon">D</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="44_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">x</font> be    <a href="hidden.html#M1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3">TARSKI:def 3</a><br/>

<b>assume </b><a NAME="E1:44_1"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> the <a href="cat_1.html#U2">Morphisms</a> of <font color="Maroon">C</font>
 ;<br/>

<b>then reconsider </b><font color="Maroon">x</font> = <font color="Maroon">x</font> as   <a href="cat_1.html#NM2">Morphism</a> of <font color="Maroon">C</font> ;<br/>
<b>reconsider </b><font color="Maroon">y1</font> =  <a href="cat_1.html#K2">dom</a> <font color="Maroon">x</font>, <font color="Maroon">y2</font> =  <a href="cat_1.html#K3">cod</a> <font color="Maroon">x</font> as   <a href="cat_1.html#NM4">Category</a> <b>by </b><i><a class="txt" href="cat_5.html#E1:44"><i><font color="Green">E17</font></i></a></i>;<br/>
<b>consider </b><font color="Maroon">F</font> being    <a href="cat_1.html#M2">Functor</a> of <font color="Maroon">y1</font>,<font color="Maroon">y2</font><b> such that </b><br/><a NAME="E5:44_1"/><i><font color="Green">E40</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><span class="p2"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">y1</font>,<font color="Maroon">y2</font></span><a href="tarski.html#K4">]</a></span>,<font color="Maroon">F</font></span><a href="tarski.html#K4">]</a></span>
 <b>by </b><i/>;<br/>
<a NAME="E6:44_1"/>
( <font color="Maroon">y1</font> is   <a href="cat_1.html#NM1">Object</a> of <font color="Maroon">D</font> &amp; <font color="Maroon">y2</font> is   <a href="cat_1.html#NM1">Object</a> of <font color="Maroon">D</font> )
 
<b>by </b><i>, <a class="ref" href="tarski.html#D3">TARSKI:def 3</a></i>;<br/>
<a NAME="E7:44_1"/><b>then </b>
<span class="p1"><a href="tarski.html#K4">[</a><span class="default"><span class="p2"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">y1</font>,<font color="Maroon">y2</font></span><a href="tarski.html#K4">]</a></span>,<font color="Maroon">F</font></span><a href="tarski.html#K4">]</a></span> is   <a href="cat_1.html#NM2">Morphism</a> of <font color="Maroon">D</font>
 
<b>by </b><i/>;<br/>
<b>hence </b><a NAME="E8:44_1"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> the <a href="cat_1.html#U2">Morphisms</a> of <font color="Maroon">D</font>
 <b>by </b><i/>;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E3:44"/>
<font color="Maroon">C</font> is    <a href="cat_2.html#M3">Subcategory</a> of <font color="Maroon">D</font>
 <b>by </b><i/>;<br/>


</div>
