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<b>let </b><font color="Maroon">f1</font> be  <a href="relat_1.html#V2">non-empty</a> <a href="funct_1.html#NM1">Function</a>, <font color="Maroon">f2</font> be  <a href="relat_1.html#V2">non-empty</a> <a href="funct_1.html#NM1">Function</a>;<br/>

<b>assume </b><b>that </b><br/><a NAME="E1:16_1_2"/><i><font color="Green">E30</font></i>: 
 <a href="relat_1.html#K1">dom</a> <font color="Maroon">f1</font> <a href="hidden.html#R1">=</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">F</font>
 <b>and </b><br/><a NAME="E2:16_1_2"/><i><font color="Green">E45</font></i>: 
for <font color="Olive">x</font> being   <a href="hidden.html#M1">set</a>   st <font color="Olive">x</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">F</font> holds <br/>for <font color="Olive">C</font> being  <a href="cat_1.html#NM4">Category</a>  st <font color="Olive">C</font> <a href="hidden.html#R1">=</a> <font color="Maroon">F</font> <a href="funct_1.html#K1">.</a> <font color="Olive">x</font> holds <br/><font color="Maroon">f1</font> <a href="funct_1.html#K1">.</a> <font color="Olive">x</font> <a href="hidden.html#R1">=</a> the <a href="cat_1.html#U1">Objects</a> of <font color="Olive">C</font>
 <b>and </b><br/><a NAME="E3:16_1_2"/><i><font color="Green">E46</font></i>: 
 <a href="relat_1.html#K1">dom</a> <font color="Maroon">f2</font> <a href="hidden.html#R1">=</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">F</font>
 <b>and </b><br/><a NAME="E4:16_1_2"/><i><font color="Green">E47</font></i>: 
for <font color="Olive">x</font> being   <a href="hidden.html#M1">set</a>   st <font color="Olive">x</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">F</font> holds <br/>for <font color="Olive">C</font> being  <a href="cat_1.html#NM4">Category</a>  st <font color="Olive">C</font> <a href="hidden.html#R1">=</a> <font color="Maroon">F</font> <a href="funct_1.html#K1">.</a> <font color="Olive">x</font> holds <br/><font color="Maroon">f2</font> <a href="funct_1.html#K1">.</a> <font color="Olive">x</font> <a href="hidden.html#R1">=</a> the <a href="cat_1.html#U1">Objects</a> of <font color="Olive">C</font>
 ;<br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="16_1_2_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">x</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>assume </b><a NAME="E1:16_1_2_1"/><i><font color="Green">E48</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">F</font>
 ;<br/><b>then reconsider </b><font color="Maroon">C</font> = <font color="Maroon">F</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font> as   <a href="cat_1.html#NM4">Category</a> <b>by </b><i/>;<br/><b>thus </b><font color="Maroon">f1</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font> = 
the <a href="cat_1.html#U1">Objects</a> of <font color="Maroon">C</font>
<b>by </b><i>, </i>
<br/>.= 
<font color="Maroon">f2</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font>
<b>by </b><i>, </i>
;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E6:16_1_2"/>
<font color="Maroon">f1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f2</font>
 <b>by </b><i>, , <a class="ref" href="funct_1.html#T9">FUNCT_1:9</a></i>;<br/>


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