<?xml version="1.0"?>
<div class="add">

<a NAME="E1:4_1_1"/><i><font color="Green">E36</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> <span class="p1">(<span class="default"><font color="Maroon">F</font> <a href="relat_1.html#K7">|</a> <font color="Maroon">X</font></span>)</span> holds <br/><font color="Olive">x</font> is  <a href="funcop_1.html#V1">Function-yielding</a> <a href="funct_1.html#NM1">Function</a>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="4_1_1_1"><b>proof </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="E1:4_1_1_1"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><font color="Maroon">F</font> <a href="relat_1.html#K7">|</a> <font color="Maroon">X</font></span>)</span>
 ;<br/>

<a NAME="E2:4_1_1_1"/><b>then </b>
<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>
 
<b>by </b><i><a class="ref" href="relat_1.html#T86">RELAT_1:86</a></i>;<br/>
<b>hence </b><a NAME="E3:4_1_1_1"/>
<font color="Maroon">x</font> is  <a href="funcop_1.html#V1">Function-yielding</a> <a href="funct_1.html#NM1">Function</a>
 <b>by </b><i/>;<br/>


</div><b>end;</b></div>
<a NAME="E2:4_1_1"/>
for <font color="Olive">f</font> being  <a href="funct_1.html#NM1">Function</a>  st <font color="Olive">f</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><font color="Maroon">F</font> <a href="relat_1.html#K7">|</a> <font color="Maroon">X</font></span>)</span> holds <br/><span class="p1">(<span class="default"><font color="Maroon">F</font> <a href="relat_1.html#K7">|</a> <font color="Maroon">X</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Olive">f</font> <a href="hidden.html#R1">=</a>  <a href="funct_5.html#K4">uncurry</a> <font color="Olive">f</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="4_1_1_2"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">f</font> be   <a href="funct_1.html#NM1">Function</a>;<br/>

<b>assume </b><a NAME="E1:4_1_1_2"/><i><font color="Green">E38</font></i>: 
<font color="Maroon">f</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><font color="Maroon">F</font> <a href="relat_1.html#K7">|</a> <font color="Maroon">X</font></span>)</span>
 ;<br/>

<a NAME="E2:4_1_1_2"/><b>then </b><i><font color="Green">E39</font></i>: 
<font color="Maroon">f</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">F</font>
 
<b>by </b><i><a class="ref" href="relat_1.html#T86">RELAT_1:86</a></i>;<br/>
<b>thus </b><span class="p1">(<span class="default"><font color="Maroon">F</font> <a href="relat_1.html#K7">|</a> <font color="Maroon">X</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">f</font> = 
<font color="Maroon">F</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">f</font>
<b>by </b><i>, <a class="ref" href="funct_1.html#T70">FUNCT_1:70</a></i>
<br/>.= 
 <a href="funct_5.html#K4">uncurry</a> <font color="Maroon">f</font>
<b>by </b><i>, </i>
;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E3:4_1_1"/>
<font color="Maroon">F</font> <a href="relat_1.html#K7">|</a> <font color="Maroon">X</font> is <a href="waybel27.html#V1" target="_self">uncurrying</a>
 <b>by </b><i>, </i>;<br/>


</div>
